Post on 02-Aug-2020
Weighting-Adjacent-Region Segmentation and Application
to Image Vectorisation
Master’s Thesis of
Xu Xiang Dong
January 2007
University of Nottingham Malaysia Campus
Faculty of Engineering & Computer Science
Supervisor: Dr. Michael Hartley
Dr. Qussay Salih
Abstract
The use of vector drawing has long been practiced in the field of
Computer-Aided Design. Hence, research on Image Vectorisation has been an
active topic for both engineering drawing and coloured image. However, the
needs for identifying regions of interest while vectorising the image are also
undeniably important. This process of subdividing an image into its
constituent parts and extracting these parts of objects is widely known as
Image Segmentation.
Image Segmentation is one of the problems of image processing for which
there is still no general-purpose solution approaching human-level
competence. In order to obtain a meaningful segmentation, the higher level
descriptions of the objects and often also of the relations among them must
be taken into account. Generally, research on the typical segmentation tasks
involves edge detection, region segmentation, and detection of curvilinear
structures.
This research concentrates on discovering and applying a mathematical
analysis with algorithms applied and implemented in finding a better image
vectorisation approach. An improved Weighting-Adjacent-Region
Segmentation technique is devised and integrated into BATIK application
applicable particularly to Image Vectorisation. In addition, experimental
results demonstrate that this technique performs better and shows improved
results than the existing techniques.
Table of Contents
1. Introduction 1
2. Background Studies 4
2.1 Image Vectorisation 4
2.2 Image Segmentation 5
2.2.1 Reviews on Image Segmentation 6
2.2.1.1 Histogram Thresholding 6
2.2.1.2 Edge-based Segmentation 7
2.2.1.3 Region-based Segmentation 8
• Region Growing 8
• Split and Merge Algorithm 9
• Data Clustering 10
2.2.2 Reviews on Evaluation Techniques of
Image Segmentation 17
2.2.3 Reviews on Border Tracing Technique 19
3. Methodology 21
3.1 Overview of BATIK 22
3.2 Colour Space Conversion 24
3.3 Discontinuity-Preserving Smoothing 25
3.3.1 Bilateral Filtering 26
3.3.2 Mean-Shift Filtering 31
3.4 WAR (Weighting Adjacent Regions) Segmentation 34
3.4.1 Building Region Adjacent Graph (RAG) 34
3.4.2 Weighting Adjacent Regions (WARs) 38
3.4.3 Merging Adjacent Regions 40
3.5 Region Pruning 45
3.6 Region Border Tracing 47
4. Experimentation and Evaluation 51
4.1 Results Evaluation 52
4.1.1 Comparison between WAR and Mean-Shift
based Segmentation 53
4.1.2 Comparison among WAR, CorelTrace, and
BitmapTrace 55
5. Conclusion 57
6. Bibliography 59
7. Appendices 64
List of Tables
Table 1. Comparison among WAR, CorelTrace, and BitmapTrace
56
List of Figures
Figure 1. The Flow of BATIK application 23
Figure 2. An illustration of building the initial RAG map 37
Figure 3. Two different Regions-Merging approaches 41
Figure 4. Proposed Regions-Merging approach 42
Figure 5. Tracing steps based on conventional look-up table 48
Figure 6. The proposed look-up table 49
Figure 7. Tracing result by using proposed look-up table 49
Figure 8. Ethnic-Lady (a) Original (b, b’) Mean-Shift Segmented
(c, c’) WAR Segmented 53
Figure 9. Ethnic-Lady (c, c’) WAR Segmented (d, d’) Corel-
Trace Segmented (e, e’) BitmapTrace Segmented 55
Figure 10. Landscape images (a) Original (b, c) WAR segmented
65
Figure 11. House images (a) Original (b, c) WAR segmented 65
Figure 12. Fruit images (a) Original (b, c) WAR segmented 66
Figure 13. Flower images (a) Original (b, c) WAR segmented 67
Figure 14. Flamingo images (a) Original (b, c) WAR segmented 68
List of Algorithms
Algorithm 1. Bilateral Filtering 31
Algorithm 2. Labelling pixels in image 36
Algorithm 3. Building first level RAG map 38
Algorithm 4. Weighting Adjacent Regions 40
Algorithm 5. Merging Adjacent Regions 44
Algorithm 6. Region Pruning 46
Algorithm 7. Extended Boundary Tracing 50
1. Introduction
Vector drawing is the main course of Computer-Aided Design (CAD) for
both engineering design and graphics design. Unlike raster image or bitmap,
or digital image where graphics are represented by a collection of pixels,
vector image uses geometrical objects such as lines, curves, and polygons
with editable attributes such as colour, fill, and outline to represent image.
It is worth noting that choosing vector images over raster images has
indeed brought certain benefits. Vector images can be easily stored,
manipulated or analysed. It even closely mimics the human brain in
interpreting visual world. Unfortunately, computers are only able to perceive
raster image rather than vector image, therefore the conversion between
raster image and vector image is very significant. This conversion is believed
to bridge the understanding gap from computer’s perspective to human’s
perspective.
Image Vectorisation, which is a process of converting raster image to
vector image, has been a research topic for both engineering drawing (most
of the drawing covers binary or grey scale image) and colour image. This can
be seen from the amount of research work to devise algorithms and software
packages in solving the problem of Vectorisation, such as Dori and Liu [1],
Nieuwenhuizen et al. [2], Jimenez and Navalon [3], Tombre and Tabbone [4],
Ju and Hong [5], and Valiente et al. [6]. The works from [1, 2, 3, 4] are
applicable to engineering drawing that mostly concentrate on binary or grey
scale image. On the other hand, [5, 6] focus on artificial kind of colour image
such as cartoon and textile pattern.
1
This research work devises an Image Vectorisation technique (which also
involves Image Segmentation) that can be applied not only to artificial image
but also real image to be used in computer graphic design. Moreover, the
vectorisation result needs to be as reliable as possible in terms of both shapes
and colour of objects. Hence, it is understood that the needs for identifying
regions of interest while vectorising the image are also undeniably important,
and this is widely known as Image Segmentation.
Therefore, a research work is proposed to develop an improved
Weighting-Adjacent-Region Segmentation technique applicable to Image
Vectorisation, particularly on two-dimensional colour images such as a
photograph of a natural scene or an artificial image to be used in computer
graphics design. To show the reliability of the proposed technique, an
experimental BATIK application is developed and results demonstrate that the
technique performs better with improved results over the existing
segmentation techniques.
The presentation of this thesis is organised as follows. Chapter 2 covers
literature reviews and background studies on the Image Vectorisation and
Image Segmentation. Chapter 3 presents an in-depth discussion on the
overview flow of the colour Image Vectorisation application and the processes
inside Weighting-Adjacent-Regions (WAR) segmentation. Chapter 4
elaborates the newly devised distinct set of evaluation criteria and the
experimentation conducted to compare the results generated by EDISON
(Mean-shift based Segmentation) [10, 11, 17], CorelTrace (©Corel Draw),
and BitmapTrace (©Macromedia). Chapter 5 concludes the findings and
outlines future direction. Finally, chapter 6 shows the list of references used
2
1. Introduction
in this research study and chapter 7 includes other samples of images
experimented with WAR segmentation approach.
3
1. Introduction
2. Background Studies
In the following sections, comprehensive discussions on the theoretical
studies, empirical work and the state of art in the domains of Image
Vectorisation and Image Segmentation are presented. Discussions on the
techniques, and processes involved in these domains are both elaborated in
detail.
2.1 Image Vectorisation
In order to accommodate the various requirements in image vectorisation,
there are numerous different studies that come out with approaches to do
raster to vector conversion. Liu and Dori [7] have identified that the basic
method or Crude Vectorisation has to be as accurate as possible. Hence, the
method needs to preserve the original shapes of the graphic objects in the
raster image. Moreover, they have classified Crude Vectorisation method into
six categories: Hough Transform based, Thinning based, Contour based, Run-
graph based, Mesh-pattern based, and Sparse-pixel based. Other work such
as Tombre et. al. [8] have also devised the steps involved in the Crude
Vectorisation are: to find the lines in the original raster image; to
approximate the lines found into a set of vectors; to not only perform some
post-processing but also find better positions for the junction points; to merge
some vectors and remove some others, etc.; and to find the circular arcs.
However, the methods and steps outlined are particularly aimed at
engineering drawing. Therefore, they might not be suitable for very complex
colour image, such as natural scene image.
4
The vectorisation technique proposed in this research mainly focuses on
two-dimensional colour image such as a photograph of natural scene or
artificial image to be used in computer graphics design. The suggested
examples of computer graphic design may range from batik pattern design,
cartoon design, and etc. Therefore the vectorisation result needs to be as
reliable as possible in terms of both shapes and colour of objects. It is
believed that colour image segmentation can be one of the optimal choices as
a core technique to do raster-to-vector conversion. This is due to fact that all
critical objects and their colours in raster image can be easily preserved
during the process. Moreover, image segmentation is a relatively mature
image processing technique since there have been numbers of different image
segmentation techniques proposed for different application areas, for example
in object recognition and object motion tracking areas [36, 37, 38].
The outcome of this research work shows promising result such that the
author strongly believes that any good image segmentation method can be
easily adopted in this vectorisation application with little or no modifications
needed.
2.2 Image Segmentation
The field of image segmentation has been an active research topic for
years. This can be seen from the availability of numerous different image
segmentation techniques presently. The following sections will analyse and
review the segmentation techniques that are aimed at complex colour image.
Studies on other segmentation methods are also conducted and outlined to
help categorising the different segmentation techniques. In addition to that,
study on evaluation of segmentation technique will also be briefly discussed.
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2.2 Image Segmentation
And finally the review on a technique known as Boundary Tracing that is used
to extract regions in an image to vector representation from segmentation
results is succinctly outlined.
2.2.1 Reviews on Image Segmentation
Image segmentation, which partitions a raster image into multiple
regions, is one of the most important steps in image analysis and processing.
According to Sonka et. al. [12], segmentation methods can be divided into
three groups based on dominant features they employ: histogram
thresholding, edge-based, and region-based.
2.2.1.1 Histogram Thresholding
The basic thresholding is a very simple segmentation process that
compares each pixel in an image to a brightness constant or threshold. It sets
the pixel to object pixel if it is greater than the threshold or to background
pixel otherwise. On the other hand, an image histogram is used to analyse
the image and help finding the threshold. Sezgin and Sankur [14] have
categorised the thresholding methods into six groups according to the
information they are exploiting, which namely are:
1. Histogram shape-based methods that get thresholding by analysing the
shape properties, such as the peaks, valleys, convex hulls of the
histogram.
2. Clustering-based methods that generally group grey-level data into two
parts as background and foreground, or alternatively model the data as a
mixture of two Gaussians.
3. Entropy-based methods, which divide the histogram of the image into the
entropy of the distribution of both background and foreground objects.
6
2. Background Studies
4. Object attribute-based methods, which use a measure of similarity, such
as edge coincidence, fuzzy shape, etc, between the grey-level and the
binarised image.
5. Spatial information-based methods, which utilise both grey value
distribution and correlation between pixels in a neighbourhood.
6. Local adaptive methods, which calculate a threshold at every pixel that
depends on some local statistics like range or variance.
Thresholding is computationally inexpensive and fast, and can be easily
done in real time using specialised hardware [12]. However, it is observed
that by using only thresholding technique may not create satisfactory result in
this research application because thresholding usually outputs a binary image
and binary image is not commonly accepted in graphic design patterns.
Furthermore, Sox et. al. [32] believe that threshold-based approaches often
lack of sensitivity and specificity needed for accurate classification.
2.2.1.2 Edge-based Segmentation
Edge-based segmentation is one of the earliest segmentations relying on
edges found in a digital image [12]. Prager [17] has proposed a set of
algorithms or procedures, used to perform segmentation on natural scenes
through boundary analysis. According to Prager [17], firstly, a pre-processing
method is needed to remove any noise data in the image, or to smooth the
image. Secondly, the edge representation is generated by applying an edge
detector to the image. Edges are the abrupt changes in the intensity function
found in an image. The edge detectors locate edges in the image relying on
edge detecting operators. There have been numbers of operators proposed in
earlier years and to name a few are: Sobel operator, Laplace operator, and
7
2.2 Image Segmentation
Prewitt operator. Thirdly, the edges produced in second stage are joined into
line segments and their features are computed. The features include length,
contrast, frequency, mean, variance and location of each line segment. Lastly,
a post-processing named Edge Relaxation is used to construct continuous
region border based on edge confidences.
It is worth noting that edge-based segmentation is capable of detecting
the borders of significant objects in an image, and generally the shapes of the
objects are usually preserved. Nevertheless, the two most common and
remains unsolved problem of edge-based segmentation are the edge’s
presence in locations where there is no border, and no edge’s presence where
a real border exists caused by either image noise or unsuitable information in
an image. Being able to retrieve accurate colour in the found regions is
another problem to be considered in the proposed vectorisation application.
2.2.1.3 Region-based Segmentation
Unlike edge-based segmentation, which uses object borders to retrieve
regions, region-based segmentation directly constructs regions over image
[12].
• Region Growing
One of the common region-based segmentations is Region Growing,
which basically take one or more pixels called seeds, and grow the regions
around them based on a uniformity predicate. A uniformity predicate is a
logical statement that is true only if pixels in the regions are sufficiently
similar in terms of a certain homogeneity criteria such as grey-level, colour,
texture, shape or some other property. According to Efford [31], one main
limitation of Region Growing is that it is not a particularly stable operation.
8
2. Background Studies
For instance, the results obtained by 4-connected region growing may differ
from 8-connected region growing. In addition to that, the results obtained can
be very dependent on the choice of uniformity predicate. Furthermore, the
selection of the seeds can be problematic because the user will not know that
the seeds defined are sufficient to create a region for every pixel.
• Split and Merge Algorithm
Another common segmentation algorithm is split-and-merge algorithm. A
top-down approach is adopted in the algorithm, in which the whole image is
considered initially to be a single region. The region will be divided into many
sub-regions based on a certain criteria, and remerged to meet the uniformity
predicate. The split-and-merge algorithm is better than the region growing
because it is an unsupervised operation and it ensures a complete
segmentation [12, 31].
Cho and Meer [19] propose an image segmentation technique by using
Consensus Information applied to a Region-Adjacent-Graph (RAG) pyramid-
based segmentation. The RAG of an input image is given by the 8-connected
graph of the underlying mesh, which takes every pixel in the image as a
homogeneous region. Every vertex (initially pixels) in the graph is allocated a
random number drawn from the (0, 1) uniform distribution. To generate the
next level of the hierarchy, only a subset of the vertices is retained. Only
retained vertices are called survivors, and the rests are non-survivors. This
satisfies the condition that no two survivors can be neighbours and every
non-survivor must have at least one survivor. A vertex becomes a survivor if
its outcome is a local maximum. The algorithm merges non-survivors to their
most similar (in terms of grey-level property) survivor neighbours to generate
9
2.2 Image Segmentation
an initial RAG. A probabilistic component called co-occurrence probability is
introduced, calculating from the neighbouring pixels in the same region.
Associating the co-occurrence probability with the initial RAG, a new graph
called weighted region adjacent graph is constructed. Thus, a reliable
segmentation can be performed through analysis of the co-occurrence
probability fields in the weighted RAG. When the value of a probability is high,
there is a consensus among different initial regions that two adjacent
supports can be merged. It has been observed that building RAG map is an
effective method used especially in region-based image segmentation.
However, the initial RAG pyramid produced by randomly choosing the
survivors and the non-survivors process is only a trial as different samples of
the initial survivors may cause different segmentation results.
• Data Clustering
There are works that propose to consider image segmentation problem as
one of data clustering, which to name a few are works from [10, 11, 16, 17,
40]. The following section presents techniques applied in image segmentation
based on data clustering approach.
i. Mean shift-based Segmentation
Mean shift, an iterative procedure that shifts a fixed size window
towards the average of the data points within, was first introduced by
Fukunaga and Hostetler [18], and re-proposed by Cheng [9] as a mode
seeking and clustering algorithm. It was further proposed as a
nonparametric estimator of density gradient in the joint, spatial-range
(value) domain of grey scale and colour image for discontinuity preserving
filtering and image segmentation by Comaniciu and Meer [10, 11, 17].
10
2. Background Studies
According to [10, 17], the local mean, which is the average of the data
points within small window in a domain, is always shifted toward the
direction of the maximum increase in the density and is guaranteed to
converge (stop) at a nearby point where the estimate has zero-gradient.
From the previously derived theoretical observations, a simple iterative
algorithm that is mathematically proven by [10, 17] is proposed for mode
detection and discontinuity (edge) preserving smoothing. The algorithm
runs the mean shift procedure to find the local maxima of the sequences
of points, prune these points by retaining only the local maxima, or
replace these points by the local maxima for mode detection or
discontinuity-preserving-smoothing respectively.
Devised by Comaniciu and Meer [10], the major advantage of mean
shift filtering over other edge preserving smoothing algorithm is that
mean shift is run till convergence and it maintains the structure of the
data; whereas other algorithms do not have a stopping criterion. For
instance, image processed by other adaptive smoothing algorithm like
Tomasi and Manduchi [21], Saint-Marc et. al. [26], and Perona and Malik
[28], collapses to a flat surface after a sufficient number of iterations.
Extended directly from the discontinuity-preserving-smoothing, a
simple image segmentation by building a region adjacent graph (RAG) is
also proposed by Comaniciu and Meer [17]. The segmentation results are
controlled by two bandwidth, which namely are spatial and range
parameters, and one optional parameter that refers to minimum region
size. The perceptually uniform L*u*v* colour space (to be discussed in
Section 3.2) is used to represent the colour information for both spatial-
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2.2 Image Segmentation
range filtering and segmentation. By applying the mean shift filtering, the
segmentation process uses the spatial and range parameters to smooth
an image. Then it further decomposes the filtered image to clusters.
Subsequent to this, a RAG is built directly from the clusters. Eventually all
adjacent regions, which are closer than a threshold, are merged to create
an over-segmentation image. An optional phase to further merge all small
regions, which are typically smaller than the minimum region size to the
closest joint regions, are usually helpful in the aim of removing non-
critical regions. However, it is found that a static threshold is used in both
phase of filtered image decomposition and phase of adjacent regions
composition. The static threshold is used to measure the acceptable colour
difference between pixels or regions. The measure signifies that two
adjacent pixels will be separated into two different regions if the difference
of the two pixels is more than the threshold in the decomposition phase;
and two adjacent regions will be merged if the difference between them is
less than the threshold in the composition phase. Consequently, this
raises the problem that the segmentation result is influenced heavily by
the composition and decomposition sequence. More elaborated discussion
on this problem and proposed solution to it will be discussed in the next
few chapters.
Luo and Khoshgoftaar [20] further improve the work of Comaniciu and
Meer [17] for colour and texture image segmentation by combining mean-
shift clustering and minimum description length (MDL) principle. In their
opinion, the segmentation algorithm proposed by [17] is capable of
producing complete and accurate over-segmentation. Over-segmentation
means the feature palette is rich enough such that the image is
12
2. Background Studies
decomposed into many small regions from which any sought information
can be assembled under knowledge control [11]. It is enhanced by
applying MDL-guided region merging to adaptively prune insignificant
boundaries in textured areas of an image while at the same time
preserving salient boundaries. The major idea behind their method is that
minimising description length, which is the sum of the coding length of the
data given the model and the coding length of the model itself, to be
equivalent to maximising a posterior probability. Hence, it could be
effectively applied to image segmentation. The region merging process is
continued until no pairs of adjacent regions can be found whose merging
will lead to a decrease in the total coding length. From the author’s
observation, the method produces an under-segmentation result since
only the most significant regions are retained. However not all the region
boundaries are accurately found and retrieving region colour could be
another problem.
Wang and Suter [23] propose another colour image segmentation
technique based on mean shift clustering. They claim that the method
takes consideration of both global information and local homogeneity and
reduces the complexity of the method proposed by Comaniciu and Meer
[17] by replacing the L*u*v* colour space to the hue and intensity
subspace only in Hue-Saturation-Value (HSV). Their major idea is that, it
computes local homogeneity value of a source image and retains the pixel
only with high homogeneity values before applying mean shift algorithm
to the image. After clustering procedure, it removes all of the so-called
repeated peaks, the peaks found by the mean shift clustering which are
very close to each other, and small peaks, the peaks has smaller value
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2.2 Image Segmentation
compared to their neighbours. Finally it assigns pixels to its nearest
clusters by calculating the cyclic property of the hue component. It has
been studied that, while validating the peaks, the process of choosing and
removing one from two peaks is not a stable operation, for instance,
choosing sample peaks from the direction of left-to-right may produce
different sets of validated peaks than the ones chosen from right-to-left
direction.
ii. JSEG technique
Deng and Manjunath [27] propose a new criterion for Good
segmentation by using class-map. Their unsupervised segmentation
method, namely JSEG, quantises colours in an image to several
representative classes that can be used to differentiate regions in the
image. Then each region will be labelled and the corresponding region
label will replace all pixels in region to create a class-map of the image. In
addition to this, a novel measure for segmentation, namely J-Value, based
on statistics of the colour classes was defined. Calculating the J-value and
applying it to a local area of the class-map can indicate whether the area
is within the region or near region boundaries. The higher the local J-value
is, the more likely that the corresponding pixel is near a region boundary.
Finally in the spatial segmentation phase, those pixels with lower J-value
are considered as region centres and used as seed pixels. A seed growing
process is then preformed from those seed pixels to create over-
segmentation image. Eventually a region merging process, which is based
on the similarity of the regions in colour histogram is performed to merge
all adjacent regions where their colour difference is less than a maximum
threshold. According to Deng and Manjunath [27], the major limitation of
14
2. Background Studies
JSEG is caused by the varying shades due to the illumination. For
instance, the colour of a sunset sky can vary from red to orange to dark in
a very smooth transition. Literally, it has been observed in this research
study that the causes of its limitation is due to the region with smooth
transition are usually separated into different regions based on the
illumination. This is because of the colour quantisation method applied in
the first phase of their method. Unfortunately, there is no way to recover
the separated regions back to the one region through the following
phases.
iii. Adaptive Fuzzy C-Means (FCM) based Segmentation
Liew et. al. [16] point out that a conventional fuzzy c-means clustering
algorithm is solely based on the distribution of pixel attributes in the
feature space. Furthermore, the conventional FCM does not consider the
spatial distribution of pixels in an image, which may cause classification of
ambiguities due to overlap in intensity value between clusters or noise
corruption. Therefore, they propose a new adaptive fuzzy clustering
algorithm for both synthetic and real colour image segmentation. This
algorithm is believed to be able to take into consideration the high
correlation between neighbouring pixels, and be adaptive in smoothing
intensity variation within homogenous regions. The implementation of
their algorithm is different from the conventional FCM because it
adaptively measures the dissimilarity between a pixel and a cluster
prototype under the influence of its local neighbourhood in homogenous
regions. In this case, the adaptive measure implies the centre pixel is
smoothed by its neighbouring pixels during the computation only if the
window is in a homogeneous region. Liew et. al. [16] also find out that by
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2.2 Image Segmentation
applying only their clustering algorithm may wrongly segment a
homogenous region into multiple regions due to variation in its intensity
profile. Therefore a re-labelling procedure is incorporated in order to
retain the regions that have boundaries correspond to significant
transitions, and merge adjacent regions that do not have boundaries with
significant transitions. As a consequence, homogenous region within an
object can be segmented into one contiguous region. The re-labelling
procedure proposed generally solves the over-segmentation problem
caused by variation of intensity in a homogenous region for some cases.
Unfortunately, it has been discovered in this research study that the
shapes of objects are distorted and their boundaries are zigzagged.
iv. Adaptive Colour Image Segmentation (ACIS)
Deshmukh and Shinde [34] propose an Adaptive Colour Image
Segmentation system that uses an adaptive thresholding process to find
the number of segments in an image followed by use of neural network to
detect the number of objects automatically from the image. ACIS uses
HSV (hue, saturation, intensity) space for colour image representation.
The saturation and intensity planes are utilised for colour image
segmentation. By assuming that for a given colour object, these are the
two parameters that may vary and hue value remains the same. Hence
the histograms of given image for saturation and intensity planes are
computed independently in adaptive thresholding process to find number
of clusters without a priori knowledge on the number of objects in the
image. Once threshold and target values are calculated, the neural
network with multi-sigmoid function labels and colours the objects with
their mean colour. From their experimental results, the credibility of their
16
2. Background Studies
approach is robust to noisy images. Unfortunately, this research work has
studied that the images are also distorted such that the clarity of the
objects’ shapes is lessened.
2.2.2 Reviews on Evaluation Techniques of Image Segmentation
Due to the various availabilities of image segmentation techniques, a good
image segmentation evaluation method is needed to conduct comparison on
different image segmentation techniques.
Martin et. al. [29] believe that although different human segmentations of
the same image are not identical, but they are highly consistent. Therefore
“ground truth” segmentations produced by humans are reliable to be used to
evaluate machine-produced segmentations by comparing the two.
Segmentation error measures used to evaluate segmentation algorithms in an
objective manner are developed to provide an empirical comparison between
two segmentations of an image. Basically, a segmentation error measure
takes two segmentations (usually the second is the refinement of the first) as
input, and calculates the difference of pixel sets in region by using a standard
formula defined where zero signifies no error. This local error measure
supports only one direction; for instance, the difference is zero when the
second is the refinement of the first, but not vice versa. Two different error
values are combined into an error measure for the entire image: Global
Consistency Error (GCE) forces all local refinements to be in the same
direction; Local Consistency Error (LCE) allows refinement in different parts of
the image to be in different directions. The only condition when comparing
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2.2 Image Segmentation
two segmentations for both two measures is that the two segmentations must
contain approximately equal number of segments.
Jiang et. al. [40] categorise various methods for performance evaluation
according to the following taxonomy: theoretical evaluation and experimental
evaluation. In addition to that, experimental evaluation involves feature-
based evaluation and task-based evaluation. The feature-based evaluation
can be further categorised into non-GT(Ground-Truth)-based evaluation and
GT-based evaluation. Jiang et. al. [40] adopt the GT-based evaluation
paradigm to measure the difference between the machine segmentation
result and the ground truth (expected ideal segmentation produced by
humans). They propose to consider the image segmentation problem as one
of data clusterings and, as a consequence, to use measures for comparing
clusterings developed in statistics and machine learning. Seven different
measures for comparing clusterings are introduced and classified into three
categories based on the nature of distance measures: distance of clustering
by counting pairs, distance of clustering by set matching, and information-
theoretic distance of clusterings. Jiang et. al. [40] realise that the
performance measures may be themselves biased in certain situations.
Therefore taking a collection of measures and defining an overall performance
measures, for instance, a linear combination, may achieve a better behaviour.
Zhang et. al. [30] believe that manually generating a reference image, or
ground truth, is a difficult, subjective, and time-consuming job. And for most
images, especially natural images, it is hard to guarantee that one manually
generated segmentation image is better than another. They propose a co-
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2. Background Studies
evaluation framework, which combines different effectiveness measures by
using a machine learning approach to coalesce the results from the constitute
measures. The main advantage of such method is that it improves the
evaluation accuracy when using a combiner that employs a machine learning
approach. However, it has been studied in this research work that this
method is dependent on the base evaluators, which are the existing
measures. As described in Zhang et. al. [30], the existing evaluation
measures examine different fundamental criteria of the objects, and rely
heavily on the image characteristics they are measuring. Therefore, none of
these evaluation measures work well for all cases. Furthermore, it has been
observed that selecting “effectiveness” measures as base evaluators is
relatively subjective and it involves lots of manual work, which falls short
under modern computer application category.
2.2.3 Reviews on Border Tracing Technique
Border tracing algorithm is a process used to trace the border of a region
deals with arranging all nodes of the border that is sequentially chained. This
algorithm is used to produce non-overlapping boundaries between regions
generally after segmentation process. Basically, there are three types of
borders: inner border, outer border, and extended border. An inner border is
a subset of the region and in contrast, the outer border is never a subset of
the region [12]. Both inner and outer borders cause difficulties in region
description because two adjacent regions could never have a common border.
On the other hand, extended border overcomes the problem by defining a
single common border between two adjacent regions.
19
2.2 Image Segmentation
The extended boundary-tracing algorithm, which is proposed by Liow [13]
based on a look-up table, is found more sophisticated compared to
conventional methods. It uses a look-up table defining all twelve possible
situations that may happen during extended border tracing and it moves the
trace dependings on the previous detected direction of boundary until a
closed extended border is produced. In addition to extended boundary
tracing, the look-up approach provides a description of each boundary
segment in chain code form together with information about vertices.
Moreover, the complexity can be reduced because each border between two
adjacent regions could be traced once. The only problem discovered was that
the original look-up table could separate a region to different regions if for
example in a case where the region is a one pixel wide diagonal line. This is
because the look-up table applied supports four-connectivity only and the
trace simply ignores the diagonal direction pixel if there is no horizontal or
vertical pixel links to that pixel. However, the problem could be easily
overcome by applying more adaptive look-up table. A thorough discussion
and application on this research proposal of newly improved and adaptive
look-up table is elaborated in the next chapter.
Finally, based on the theoretical studies and literature reviews conducted,
it is realised that none of the proposed segmentation technique satisfy this
research work’s requirements in producing high quality images in terms of
complex and rich colour image to be used in computer graphic design. Hence,
the research concentrates on finding a new image segmentation technique
that contributes in vectoring the image into high quality and yet reliable result
in terms of both shapes and colour of objects.
20
2. Background Studies
3. Methodology
The background of the field of Image Vectorisation particularly on Image
Segmentation has been discussed in previous chapter. It is understood that
the availability of numerous approaches to do raster-to-vector image
conversion are resulted from various different requirements in Image
Vectorisation. Regrettably, none of the approaches are suitable for very
complex colour image such as natural scene image.
In this research work, colour Image Vectorisation is considered as one of
the problems in Image Segmentation. Thus, an improved and higher quality
of Image Segmentation approach, which called WAR (Weighting Adjacent
Regions) Segmentation applicable for both colour and grey scale images are
produced. Unlike common segmentation techniques that generally rely on
particular pre-processing technique such as smoothing and clustering
techniques, WAR on the other hand can be used with or without any pre-
processing techniques.
This chapter includes an in-depth discussion on the flow of the Image
Vectorisation application named BATIK. In addition to that, a further
elaboration on the processes inside WAR segmentation is also described.
21
3.1 Overview of BATIK
Figure 1 shows the overview of processes in BATIK application. Initially,
in step 1, a source image is converted from originally represented in a
nonlinear colour space or RGB model (referring to red, green, and blue), to a
linear colour space. Step 2 is an optional pre-processing stage where the
source image is filtered typically by removing noise and insignificant parts in
the image, and enhancing significant image features for further processing.
Step 3 concentrates on WAR segmentation where regions of interest are
segmented. Step 4 is an optional post-processing stage where reliable objects
are identified and extracted in the source image. And finally step 5 converts
significant objects to vector representation. A more detailed explanation on
each respective step will be covered in the following subsections.
22
3. Methodology
Figure 1. The Flow of Image Vectorisation in BATIK Application
23
3.1 Overview of BATIK
3.2 Colour Space Conversion
The novel concept of proposed segmentation approach is similar to a
typical kind of region-based segmentation technique. It measures the colour
difference among all adjacent regions as follows:
Let r be a region, R be the set of regions adjacent to r , be the
default threshold of colour difference, and
∆
( )M be a merge function,
( )⎪⎩
⎪⎨⎧ ∈∆≤−
=otherwiseFALSE
RandxxrifTRUExrM )( U (1)
The predicate specifies two adjacent regions can be merged only if the two
regions are similar in terms of colour property.
A colour space is a method, which is used to specify, create and visualise
colour [25]. In this research, a perceptually linear colour space, meaning a
change of the same amount in a colour value should produce a change of
about the same visual importance, is used to easily measure colour
difference. The most common colour space RGB, being used in visually every
computer system, is non-linear with visual perception. Consequently before
doing any further processes, it is necessary to do the conversion from RGB to
one of the linear colour spaces, for example CIE L*a*b*, CIE L*u*v*, etc.
CIE L*a*b*, a colour space introduced by the CIE in 1976, in which L* is
the luminance component, a* and b* are red/blue and yellow/blue
chrominance. CIE L*u*v* is also defined by the CIE in 1976. Likewise, L*
defines the luminance, u* and v* define chrominance. CIE L*a*b* is chosen
to linearise the perceptibility of colour differences in this research work
24
3. Methodology
because it performs better visual quality than CIE L*u*v* for image
compression according to Han [24]. The simplest CIE colour difference
formula, which is known as CIE 1976 used to calculate the difference between
two measured colours is given as follows:
222 )21()21()21( bbaaLLE −+−+−=∆ (2)
where L1, a1, b1 and L2, a2, b2 are three components of two colours. For
extremely small colour differences, the two modification versions of CIE 1976
are CIE 1994 and CIE 2000. Another extremely small colour difference
formula is CMC, which is similar to the CIE versions but it includes weighting
functions for different areas. CIE 1994, CIE 2000 and CMC may give better
correlation with perceived differences. Although CIE 2000 is a recently
developed formula and through the in-depth experimentation studies
conducted in this research work, it is found that CIE 2000 produces better
result, but it’s computationally expensive and impractical in terms of
processing time.
3.3 Discontinuity-Preserving Smoothing
Traditional domain-filtering algorithms such as Mean Filter and Gaussian
Filter are generally used to smooth image through replacement of every pixel
in the image by averaging the pixel’s neighbours in a kernel. It blurs the
image and removes not only noise but also salient information. It is believed
that discontinuity (edge)-preserving smoothing used to remove noise and
insignificant information whereas salient information in an image is retained,
is better than the conventional smoothing algorithms particularly in this
vectorisation application.
25
3.3 Discontinuity-Preserving Smoothing
A number of discontinuity-preserving smoothing algorithms based on
different techniques have been proposed and a brief discussion on them can
be found in [17]. Based on background studies on discontinuity-preserving
smoothing algorithms, this research work proposes to either use Mean-Shift
Filtering or Bilateral Filtering as the smoothing technique in the vectorisation
application. It is discovered that both Mean Shift Filter [17] and Bilateral Filter
[21] apply similar kernel density estimation technique working in the joint
spatial-range domain. More discussions on Bilateral Filtering and Mean-Shift
Filtering can be found in the following sections.
3.3.1 Bilateral Filtering
Bilateral Filtering, originally proposed by Tomasi and Manduchi [21], is a
discontinuity (edge)-preserving smoothing technique, which is based on
simultaneous processing of both the spatial and range domains. The
traditional domain filtering such as Gaussian Filter, weights only pixel values
of the neighbourhood samples based on computing spatial distance between
the centre and the neighbours. A given traditional domain filtering formula is
shown below:
( ) (∑ ∑−= −=
− ++=w
wx
h
hyss yxGyjxifjig ,,),(1 ) (3)
where indicates the weighted value at location ),(1 jigs− ( )ji, .
),( yjxif ++ measures the geometric closeness between the
neighbourhood centre ( )ji, and all nearby points within the small
26
3. Methodology
neighbourhood that has size of ( ) ( )( )1212 +×+ hw . f is the intensity and
is the Gaussian distribution [12] in 2-dimensional (2D) space, is given by sG
2
22
2),( s
yx
s eyxG σ
+−
= (4)
where sσ is a standard deviation in the spatial domain distribution. The
geometric spread sσ in the domain is chosen based on the size of desired
neighbourhood. A large sσ needs more distant image locations and blurs
more. If the filter is shift-invariant, is radially symmetric and constant for
whole domain independent of the image as specified by Sonka, Hlavac, and
Boyle [12].
sG
Nevertheless, bilateral filtering computes pixel values in the centre of a
window based on both geometric closeness (spatial domain) and photometric
similarity (range domain) of the centre and its neighbourhood samples. The
range function is given by
( ) ( ) ( )( )
( ) ( )( )∑ ∑
∑ ∑
−= −=
−= −=
+−
+−++
=w
wx
h
hyr
w
wx
h
hyr
r
yjxifjifG
yjxfjifGyjxif
jig
,,
,,,
),(
+
+i
(5)
where ( ) ( )( )yjxifjifGr ++− ,, measures the photometric similarity
between the neighbourhood centre ( )ji, and the nearby points. Let
( ) ( )( )yjxifjif ++− ,, be R , the Gaussian function rG is given by
27
3.3 Discontinuity-Preserving Smoothing
( )2
2
2 r
R
r eRG σ−
= (6)
where rσ is a standard deviation in the range distribution. Similarly, the
photometric spread rσ in the image range is set to achieve the desired
amount of combination of pixel values. Loosely speaking, the difference
between pixels in terms of intensity values less than rσ is mixed together
and the difference greater than rσ is not mixed together [21]. Unlike in the
spatial domain, the geometric closeness distribution is constant for the
whole domain whereas the photometric similarity distribution
sG
rG is variant
depending on the difference of input pixels.
The combined domain and range filtering thereby enforcing both
geometric and photometric locality is given by
( ) ( ) ( )( )
( ) ( ) ( )( )∑ ∑
∑ ∑
−= −=
−= −=
++−++
++−++++
=w
wx
h
hyrs
w
wx
h
hyrs
yjxifjifGyjxiG
yjxifjifGyjxiGyjxif
jig
,,,
,,,),(
),(
(7)
Every pixel value in a window is hence replaced by the average of similar and
nearby pixel values. In smooth regions, pixel values in a small neighbourhood
are usually similar to each other. In other words, if a pixel is very different to
others in a small neighbourhood, then that pixel either belongs to other
region or is assumed as a noise. As a consequence, the bilateral filtering
28
3. Methodology
averages away the small, weakly correlated differences between pixel values
caused by noise, whereas salient information are preserved.
One point worth noting on the implementation of bilateral filtering is that
input image could be multi-band (e.g. a colour is represented by red, green
and blue bands). Tomasi and Manduchi [21] find out that the edge-preserving
smoothing can be applied to the red, green, and blue components of the
image separately. However, the intensity profiles across the edge in the three
colour bands are typically different. As a consequence, the smoothed image
not only appears blurred but also exhibits odd-looking, coloured auras around
objects. The uniform CIE L*a*b* colour space can therefore be applied to
measure Euclidean distance in the photometric similarity function rG .
Moreover, bilateral filtering can be preformed using two standard 1D
convolution; once in the horizontal direction and once in the vertical direction,
rather than a 2D convolution. This is simply because the complexity in
calculating the Gaussian kernel can be reduced from its square to its size
[12]. Thus the spatial function (3) is modified into
( ) (∑ )−=
− +=w
wxss xGxifig )(1 (8)
where the Gaussian distribution , which in 1D space is given by sG
2
2
2)( s
x
s exG σ−
= . (9)
The photometric similarity function modified from (5) is given by
29
3.3 Discontinuity-Preserving Smoothing
( ) ( ) ( )( )
( ) ( )( )∑
∑
−=
−=
+−
+−+
=w
wxr
w
wxr
r
xififG
xififGxif
ig )( . (10)
The Gaussian distribution in range domain remains unchanged. Finally the
combined domain and range filtering is given by:
( ) ( ) ( ) (( )
( ) ( ) ( )( )
)
∑
∑
−=
−=
+−
+−+
=w
wxrs
w
wxrs
xififGxG
xififGxGxif
ig )( . (11)
The convolution algorithm devised in this research work (as illustrated in
Algorithm 1.) using bilateral filtering in 1D space is given as follows:
Let { }nindexI K1= and { }nindexO K1= be the d-dimensional original and
filtered image points respectively in the spatial domain; h and be the
width and the height of the image respectively, so that n . Let w be
the radius of the kernel;
v
vh ×=
sσ and rσ be the standard deviation of the spatial
and the range domains respectively.
30
3. Methodology
Conceptually, step 4 is necessary to re-initialise the original image I by
taking data from the filtered image space O , and using original image’s width
as height and original image’s height as width. Eventually, step 5 takes all of
the re-initialised values to the step 3 and computes the final filtered image.
Algorithm 1. Bilateral Filtering
1. Calculate spatial Gaussian kernel k using (8). s
2. Assign hX = and Y v=
3. For each Yj K1=
a. Assign joi =
b. Assign Xjio ×=
c. For each Xi K1=
i. For each wwx K−=
ii. Calculate ( )iiog + using expression (11)
iii. Assign ( )iiogOoi +=
iv. Assign Yoioi +=
4. Assign , OI = vX = and Y h=
5. Repeat step 3.
3.3.2 Mean Shift Filtering
Let I be an n-dimensional Euclidean space and be a flat kernel
with a continuous random sample
nXK K1=
nXX K1 embedded in I , use kernel K to
replace the Gaussian function rG and x to replace the intensity ( )if in
expression (10) yields:
( )( )
( )∑
∑
=
=
−
−
=n
ii
n
iii
xxK
xxKx
xm
1
1 (12)
31
3.3 Discontinuity-Preserving Smoothing
where Xx ∈ . ( )xm is called sample mean. The difference ( ) xxm − is
called mean shift. The repeated movement of data points to the sample
means is called mean shift algorithm in Fukunaga and Hostetler [18].
Mean Shift is initially proposed by Cheng [9] used as a mode seeking and
clustering algorithm. Comaniciu and Meer [10, 17] further propose it to be
used as a nonparametric estimator of density gradient in the joint spatial-
range (value) domain of grey scale and colour image for discontinuity-
preserving filtering. One fact worth noting observed by Comaniciu and Meer
[10] is that Bilateral Filtering and Mean Shift Filtering are based on the same
principle, which is the simultaneous processing of both the spatial and range
domains. However, the domain filter in Bilateral Filtering is shift-invariant,
whereas the Mean Shift window is dynamic, moving the direction of the
maximum increase in the density gradient.
Let f be uni-variate density, the kernel density estimator in Wand and
Jones [35] is given by
( ) ∑=
∧⎟⎠
⎞⎜⎝
⎛ −=
n
i
ihXx
Knh
xf1
1 (13)
where kernel K has the similar assumption as in (12) and h is bandwidth.
By introducing multivariate kernel, Comaniciu and Meer [17] modify the
density estimator (13) as
( ) ∑=
∧
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −=
n
i
iddk
Khh
xxk
nh
cxf
1
2,
, (14)
32
3. Methodology
where is the normalisation constant making kernel K integrate to one
and assumed strictly positive in d-dimensional space. They also apply the
above similar multivariate kernel estimator principle and successfully rewrite
the sample mean expression (12) into Mean Shift as
dkc ,
x
hxx
g
hxx
gx
xmn
ii
n
ii
i
Gh −
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −
=
∑
∑
=
=
1
2
1
2
, )( (15)
where kernel is for weights, and G x is the centre of the kernel.
The local mean is shifted toward the region where the majority of the
points reside and stops when it gets fairly close to a local maximum, which is
the unique stationary point that has zero gradient calculated from the
estimator (14) within a small neighbourhood. The convergence of Mean Shift
procedure is guaranteed as proven in [17].
Another issue worth noting that was introduced by Sochen, Kimmel and
Malladi [33] is that an image is typically represented in the (X, I) space, in
which 2D surface embedded in the 3D (x, y, g) space for grey level images,
and 2D surface embedded in the 5D (x, y, R, G, B) space for colour images.
The similar representation is used in such that using (x, y, L*) for grey level
images and (x, y, L*, a* b*) for colour images. As explained in [17], the joint
domain employs both spatial domain, the space of the kernel, and range
domain, colour property. Euclidean metric is assumed for both respective
domains. Thus, multivariate kernel is defined as the product of two radially
33
3.3 Discontinuity-Preserving Smoothing
symmetric kernels and the Euclidean metric allows a single bandwidth
parameter for each domain in [17] is given by
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⎟
⎟⎠
⎞⎜⎜⎝
⎛⋅=
r
r
s
s
rhsh hx
khx
kCxK )(,
where sx is the spatial part, rx is the range part of a feature vector, ( )xk is
the common profile used in both two domains, and sh rh are the employed
kernel bandwidths, and c is the corresponding normalisation constant. A
comprehensive explanation on the implementation of Mean Shift filtering
algorithm is best described in [17].
To sum up, the Bilateral filtering and Mean Shift filtering are somehow
similar in terms of principles adopted. In Bilateral filtering, the kernel
estimation of each pixel is computed only once. On the contrary, Mean Shift
filtering will not generally perform the computation only one time but it will
keep on computing until the convergence is achieved.
3.4 WAR (Weighting Adjacent Region) Segmentation
The novel research work in this thesis is to develop an improved and
higher quality of segmentation approach. WAR, a newly designed
segmentation approach in this study, is derived from the Split-and-Merge
technique and based on Weighting Adjacent Regions on the produced Region
Adjacent Graph (RAG). WAR segmentation incorporates a set of iterative
processes, which are Building the RAG, followed by Weighting Adjacent
Regions, and finally merging closest regions. The processes automatically end
when no further merging process can be performed. To show the applicability
and practicality of WAR segmentation, it will be implemented in the BATIK
34
3. Methodology
application. The following shows elaborated sections that comprehensively
discuss the processes involve in WAR segmentation.
3.4.1 Building Region Adjacent Graph (RAG)
The Region Adjacent Graph (RAG) is a traditional image data structure, in
which regions and their adjacencies are depicted in a region map. It can be
applied in region-merging approach such that neighbouring regions assumed
to have the same interpretation are merged into one region [12]. By
introducing colour differences corresponding to Euclidean distance in
perceptually linear colour space, for instance CIE L*a*b*, the RAG map can
be easily built using the colour properties for homogeneity criterion. Initially,
the RAG map can be built by taking every pixel in the input image as a
homogenous region, followed by merging all the adjacent regions (pixels)
whose colour properties are exactly the same.
Based on this RAG map approach, a customised RAG map that conforms
to the requirements in WAR segmentation is defined and built. This
customised RAG map has an added labelling function to build initial
identification for every pixel and their adjacent regions in the neighbourhood.
A comprehensive explanation on the customised RAG map can be seen as
follows.
Let { } and niI K1= { }niL K1= be the original and labelled image with length
equals to n and 0=iL ; { }81K=jh be the neighbourhood location of i ; l be
an integer initially equals to zero; S be an empty stack.
35
3.4 WAR (Weighting Adjacent Region) Segmentation
Algorithm 2. Labelling pixels in image
For each i nK1=
i1. If , assign L0==iL l++= , push to S . i
2. While is not empty S
a. Pop value from S and assign it to the label t .
b. For each 8...1=j
i. If Ijhtt I +== and 0≠+ jhtL , assign ijht LL =+
ii. Push t jh+ to S .
As illustrated in algorithm 2, all pixels and their adjacent pixels in the
neighbourhood will eventually have their own labels or identities. Once all the
pixels are labelled or identified accordingly, a procedure to merge pixels with
same labels are performed. This whole procedure will finally generate a RAG
map, which contains all the inter-related regions. Thus, the follow-up
Weighting Adjacent Region process will directly manipulate this RAG map. An
example of building RAG map is best depicted in Figure 2.
36
3. Methodology
3.4 WAR (Weighting Adjacent Region) Segmentation
Figure 2. An illustration of building the initial RAG map. (a) Every pixel in
the image is taken as a region connected in 8 directions with its neighbours.
(b) All connected regions that have the same property and grouped
together are individually assigned by a unique label (number). (c) Regions
with the same label are merged and connections among them are revised.
One point worth noting in the implementation of building RAG map is that
each region defined can be consider as one object, which contains four
properties: label, colour property, amount of pixels contained in the region,
and a list of references to the adjacent regions. These four properties are
comprehensive to describe a region and the relations with its adjacent
37
regions. A region might be removed from RAG map if for example, the region
is successfully merged with other regions, which consequently causes a
different label to be used to identify the merged region. Alternatively, a
region with modified properties may remain in the RAG map only if the label
is unchanged in the above example. In another words, RAG map must be
revised when merging process is achieved. The algorithm to build RAG map is
given as follows.
Let { and }niI K1= { }niL K1= be the original and labelled image obtained
from Algorithm 2, { }mjR K1= be the set of region objects where m is the
maximum label found from Algorithm 2 and assign , nullRj = { }81K=jh be
the neighbourhood location of i
Algorithm 3. Building first level RAG map
For each i nK1=
For each 81K=j
1. If jhii LL +=!
a. If nullRiL == , set properties of R .
iL
b. If nullRjhiL ==
+, set properties of R .
ji hL +
+
c. Add to the neighbourhood of R . ji hLR + iL
d. Add to the neighbourhood of R . iLR
ji hL
As previously discussed, each defined region object contains four
properties, which are label, colour property, region size and neighbourhood
list. Therefore in step (a) and step (b), region properties including label,
colour property and region size can be set if the region is newly defined.
These three properties can easily be obtained from Algorithm 2. In step (c)
38
3. Methodology
and step (d), it basically adds a region to the neighbourhood list of its
adjacent region respectively.
3.4.2 Weighting Adjacent Regions (WARs)
WARs is a technique which weights or averages all pixels based on
photometric similarity (range domain) of the centre region and its
neighbourhood samples (spatial domain). Similar to the concept of Bilateral
filtering, both range and spatial domains are taken into consideration when
weighting the regions in neighbourhood samples. The only difference is that
Bilateral filtering weights pixels in the centre pixel’s neighbourhood samples
and replaces the centre pixel by using the weighted value whereas WARs
weights all pixels in both the centre region and its neighbourhood samples.
Obviously in a pixel map, the connections between a centre pixel and its
neighbourhood are fixed. However in a region map, the neighbourhood of
each region needs to be identified individually from the previously built RAG
map.
Algorithm 4 illustrates the steps involved in Weighting Adjacent Regions.
Let { be the set of region objects where n is the total number of
regions found from Algorithm 3; , , and be the
label, size, colour property and neighbourhood of R ;
}
}
niR K1=
IiR , SiR , CiR , { mNRiRK1, =
i ∆ be the threshold; C
and S be two variables used to sum up colour property and size respectively
and initially are null.
39
3.4 WAR (Weighting Adjacent Region) Segmentation
Algorithm 4. Weighting Adjacent Regions
For each i nK1=
1. Assign , SiRS ,= CiSi RRC ,, ×= ;
2. For each R { }mNRi K1, =
a. If ( ) ∆≤− CRCi INRR ,, ,
i. Assign C SRCR ININRRC ,, ,,
×+= ;
ii. Assign SR INRSS ,,
+= .
3. Set SCR Ci ÷=, .
The threshold bounds the desired range between the centre region and its
neighbourhood samples. Therefore, only similar regions in terms of colour
property are mixed together to minimise the differences among those
regions.
∆
Analogous to Bilateral filtering, WARs also averages away the small
weakly correlated differences between region values caused by noise, and at
the same time salient information is preserved. Furthermore, it retains
connections among regions and hence, enables the next merging process to
work with these connections.
3.4.3 Merging Adjacent Regions
Theoretically in a split-and-merge approach, the image’s region will first
be split or divided into many sub-regions based on a certain criteria, and
remerged to meet the uniformity predicate. A static threshold is defined in
this proposed merging approach. The threshold is used to measure the
acceptable colour difference between pixels or regions. The measure signifies
40
3. Methodology
two adjacent regions will be merged if the difference between them is less
than the threshold in the composition phase. However, this raises the
problem that the segmentation result is influenced heavily by the composition
sequence.
3.4 WAR (Weighting Adjacent Region) Segmentation
Figure 3. Two different Regions-Merging approaches. A constant threshold
0.2 is assumed in this illustration. (A) is the original map of 4-connective
regions. (B’) and (C’) are the map produced from sequentially merging
approach. (B”) and (C”) are the map produced from closest-regions-
merging approach.
As shown in Figure 3, an assumed constant threshold is 0.2. In (B’) and
(C’), the sequence of regions are mapped from top-down and left-right.
Region 1 is initially merged with region 2, and followed by merging with
region 4. Conceptually, region 3 could possibly be merged with region 4 due
to the fact that they are also legitimately closer regions. However, since
region 4 has already merged with region 1 and the final intensity of region 1
has also changed, therefore eventually region 3 remains unmerged. In (B”),
the merging algorithm follows closest-regions-merge-first approach. The
41
approach merges all joint regions with the closest intensities until no joint
regions are closer than a predefined threshold value. Therefore, region 2 is
merged with region 4 at first place. Since the intensity of the merged region 2
has been updated, this has consequently resulted the differences among
remaining regions are higher than the set threshold. As a result, the merging
algorithm ends with three regions unmerged.
Unlike the two different methods depicted in Figure 3, this research work
devises a new merging strategy that is able to maximise the merging process.
It is believed and proven that this newly developed strategy will eventually
merge all the inter-related regions. Figure 4 shows an illustration of the
proposed merging strategy.
3. Methodology
Figure 4. Proposed Regions-Merging approach. A constant threshold 0.2 is
assumed in this illustration. (A) is the original map of 4-connective regions.
(B”’), (C”’), (D”’) and (E”’) are the map produced from sequentially merging
approach.
42
The newly devised merging approach begins by first discovering the
possible sets of regions to be merged in the neighbourhood. In (B”’), region 1
is taken as the start-up referenced region. When referenced region identifies
that region 2 is the possible region to merge with, then region 2 is labelled as
sets of region 1 with no intensity value updated. Hence, the referenced region
utilises the intensity of region 2 and the search continues in the
neighbourhood of region 2. Likewise in (C”’) and (D”’), the processes of
initialising the referenced region, discovering its possible merging sets in the
neighbourhood, and utilising its corresponding intensity are performed.
Eventually in (E”’), all the sets of regions found will be merged together and
based on that, a new intensity value is computed.
To conclude, regions with similar density are merged together into each
respective region, and each region’s connectivity to its adjacent neighbour are
depicted in the RAG map. For more detailed explanation on the merging
procedure, its algorithm is presented as follows.
Let { be a set of regions obtained from Algorithm 4; , ,
and be the label, size, colour property and neighbourhood
of ;
}
}
niR K1= IiR , SiR ,
CiR , { mNRiRK1, =
iR σ be a pre-selected threshold.
43
3.4 WAR (Weighting Adjacent Region) Segmentation
Algorithm 5. Merging Adjacent Regions
For each i nK1=
K1, =
1. If , Push to a stack , nullRi ≠ IiR , S
2. While is not empty, do S
a. Pop value from S and assign it to a label L ,
b. For each R { }mNRL
I. If σ≤− CRCL INRR ,, ,
A. If S not contains R and IN,
,
, ,
IiIN RR ,, ≠
i. Push to INR , S
II. Merge to R with revised R , LR i Ni
3. Compute R and R . Ci Si
The Step 1 evaluates the availability of the selected region since the
respective region has possibly merged to other region. The Step 2 iteratively
finds all adjacent regions that could be merged with the selected region.
Essentially, step 2 (II) revises the connections among the potential merging
sets. The revising operation is used to keep the relations among the regions
even though certain region(s) has been “removed” from the region map as
explained in Figure 2 (c). Finally Step 3 updates colour property and size of
the region.
3.5 Region Pruning
A ingenuous post-processing is used as an optional step to remove all
small regions that are usually not significant in further processing and can be
considered as segmentation noise [12]. These small regions cannot be
merged with any adjacent regions according to the homogeneity criteria
44
3. Methodology
applied in the previous steps. The crude resolution can simply merge a small
region, which is smaller than a pre-selected size, to its adjacent region that is
most similar to the smaller region according to the homogeneity criteria used.
However, for image vectorisation, some small regions are significant yet
cannot be removed. For example in Figure 8 (a), the regions of the eyes and
the lips on the Ethnic-Lady’s face are smaller yet significant. Removing those
regions definitely causes the Ethnic-Lady has an odd-looking. Therefore the
pruning process needs to preserve these small yet significant regions in the
image.
As discovered, generally small yet significant regions are very different to
their adjacent regions according to the homogeneity criteria used. Hence, an
additional evaluation process can be incorporated with the crude pruning
process while suppressing small regions. It evaluates the difference between
every smaller region with its most similar adjacent region. Whenever the
difference is less than a pre-selected range, the follow-up merging process
will be executed. Otherwise, the smaller region will be retained. An extensive
conception on the region pruning is illustrated in Algorithm 6.
Let { be a set of regions obtained from Algorithm 5; , ,
and be the label, size, colour property and neighbourhood
of ; be a pre-selected minimal size;
}
}
niR K1= IiR , SiR ,
CiR , { mNRiRK1, =
iR Μ σ be a pre-selected range
property.
45
3.5 Region Pruning
For each i
1. While
nK1=
MR Si <,
a. Find m
the homog
LR
b. Assign the
c. If σ>d b
d. Merge iR
Step 1 does not on
availability of the sele
other region. Customar
the formula used in ste
process performed if th
pre-selected range. La
region) to the other.
Practically up to
segmented into region
With the given region m
capturing all regions’ b
Tracing process.
3.6 Region Border Tr
As a result from th
been properly labelled)
the image, one has to
vectors (namely region
3. Methodology
Algorithm 6. Region Pruning
and R nulli ≠ , do
ost similar to R from R , according to
eneity criteria.
i { mNRi }K1, =
difference CLCi RRd ,, −= ,
reak,
and . R
Lly search the smaller regions but also evaluates the
cted region since the region has possibly merged to
ily, step (a) involves numbers of calculations similar to
p (b). In addition to that, step (c) indicates no merging
e difference between two regions is greater than the
stly, step (d) merges one region (usually the smaller
this stage, a raster image has been successfully
s of interest and delineated as a form of region map.
ap, the follow-up work will concentrate on tracing and
order nodes, which is widely known as Region Border
acing
e previous stage, a finalised region map (regions have
of the raster image is produced. In order to vectorise
consider the needs of capturing all of the regions’
border nodes). This is achieved by implementing the
46
border-tracing algorithm. In general, there are three types of borders: inner
border, outer border, and extended border. Only extended border defines a
single common border between adjacent regions, and it may be specified
using standard pixel co-ordinates [12].
The extended boundary-tracing algorithm based on look-up table as
proposed in [13] is sophisticated and efficient. Despite this, a different yet
more efficient look-up table is proposed in this research study. It is believed
that the original look-up table is not adaptable in current study as it could
inappropriately separate a region to different regions. To better illustrate the
finding, Figure 5 is taken as an illustration example based on the original
look-up table. The region shown is a one pixel wide diagonal line. When a
starting pixel is found, the first move along the traced boundary from the
starting pixel is always moving down (Figure 5a). The next move successfully
goes to right based on the original look-up table (Figure 5b). After that, the
next move along the traced boundary ignores the next diagonally linked pixel
and inappropriately goes up (Figure 5c), and finally closes the traced
boundary as it meets the starting pixel (Figure 5d). Hence, the rest of pixels
in the region could be separated from the traced boundary and be considered
as other regions.
47
3.6 Region Border Tracing
The new
boundary-t
guarantees
the same e
3. Methodology
(a) (b)
(c) (d)
Figure 5: Tracing steps by using look-up table based extended border
tracing algorithm proposed in [13].
look-up table devised (as shown in Figure 6) in the extended
racing algorithm can successfully overcome the above problem and
that any regions can be closed. The anticipated tracing result from
xample (as shown in Figure 5) is best illustrated in Figure 7.
48
Figure 6: The look-up table defining all 12 possible situations that can
appear during extended border tracing. Note that the newly devised (a),
(c), (e), (f), (h), (i), (k), and (l) are different from the tables proposed in
[13].
Figure 7. Tracing result by using proposed look-up table.
49
3.6 Region Border Tracing
The extended boundary-tracing algorithm that directly applies to the
region map, which produced from the WAR segmentation, is outlined in
Algorithm 7.
Let { be a region map of an image with index from 0 to n and
each contains the label number . Initialize
}niI K0=
iI j { }mjR K0= be a set of regions
with is the estimated total number of regions and each . m 0=jR
Algorithm 7. Extended Boundary Tracing
For each i nK0=
1. If R 0==iI
a. Assign foreground label iIL = ,
b. Assign 1−=iIR ,
c. Set the starting pixel iP = , direction 6=d (down),
corresponding to the situation (i) in Figure 6,
d. Trace the extended boundary using the look-up table in Figure
6 until a closed extended border results.
Essentially, step (a), (b), and (c) locate every starting pixel of all regions
to begin with a new boundary trace. Algorithm 7 assists the trace of each
region boundary until a closed extended border is resulted.
Each boundary’s nodes in chain-code-form with information about vertices
are produced after region border tracing procedure. Using these region border
nodes together with colour information of each region preserved during the
segmentation stage may easily reconstruct the vector image.
50
3. Methodology
4. Experimentation and Evaluation
Since colour image vectorisation is considered as one of the problems in
image segmentation in this research work, the experimentation result will
concentrate on producing concise and reliable segmented objects of interest
from original colour image to be used in computer graphic design area. From
background studies and analysis, the most recent analysis on experimentation
and evaluation on segmentation is done by Jiang et. al. [40]. They adopt the
Ground Truth(GT)-based evaluation paradigm to measure the difference
between the machine segmentation result and the ground truth (expected
ideal segmentation produced by humans). However, manually generating a
reference image, or ground truth, is a difficult, subjective, and time-
consuming job [30]. Furthermore for most images, especially natural images,
it is hard to guarantee that one manually generated segmentation image is
better than another.
In the experimentation with the developed BATIK application,
performance measures are computed directly by means of desirable objects
of the segmentation results. The performance measures are identified by the
number of objects or regions defined and edges detected. The following
shows a set of distinct evaluation criterias that are adopted while comparing
segmentation results produced in this research study with others:
a. Result Resemblance
The machine-generated image should resemble the original image in
terms of preserving object’s shapes and colours.
b. Edge Preservation
51
Most of the critical edges found in the original image should be preserved
in the machine-generated image.
c. High accuracy of interesting regions defined
The generated image should not include insignificant regions caused by
the present of edge in location where there is no border.
4.1 Results Evaluation
Experimentation with the developed BATIK application that incorporates
WAR segmentation technique is carried out. A sample image of Ethnic-Lady is
used to be processed by the BATIK application and it shows promisingly
improved yet accurate segmented results. To show the reliability and
practicality of WAR segmentation, these results are compared with the results
generated by EDISON (applying Mean-shift based Segmentation) [10, 11,
17], CorelTrace (©Corel Draw), and BitmapTrace (©Macromedia). EDISON is
the mostly chosen colour image segmentation technique that is used in
comparison with other newly developed segmentation techniques. The others
are two of the most popular commercial graphic applications. Comparisons of
these results are done based on the defined distinct evaluation criterias. A
thorough description on the comparison results can be found as follow.
4. Experimentation and Evaluation
(a)
52
4
F
s
B
h
4.1 Result Evaluation
(b) (b’)
(c) (c’) Figure 8. Ethnic-Lady. (a) Original. (b) Mean-shift Segmented with spatial
and range resolution = (7, 6.5) (b’) Mean-shift Segmented Region
Boundaries (c) WAR Segmented with range resolution = (10) (c’) WAR
Segmented Region Boundaries. For post processing, both (b) and (c) use
minimum Region = 20.
.1.1 Comparison between WAR and Mean-Shift based Segmentation
igure 8 shows the segmentation results generated by Mean-shift based
egmentation (through EDISON) and WAR segmentation techniques (through
ATIK application). From the observation based on the results generated,
ere are the findings:
53
• Total segmented regions produced
WAR segmentation technique generates 596 regions whereas Mean-Shift
based segmentation produces 735 regions.
• Result Resemblance
WAR segmentation result highly resembles the original image in which
details such as the shapes of the lips and eyebrow are retained, and
regions with transition of colour due to illumination are uniformed and
segmented into only few distinct regions. On the other hand, Mean-Shift
based segmentation result resembles the original image with less
precision where no illustration of lips and eyebrow, non-uniform
illumination is segmented into many regions.
• Edge Preservation
WAR segmentation generated result shows critical edges of the image are
not only preserved, but also smoothed. In addition to that, insignificant
edges are disregarded. On the contrary, Mean-Shift based segmentation
generated result includes both significant and insignificant edges and they
are not smoothed (zigzagged). Moreover, some of the non-edges found in
the image are also taken as edges.
• Accuracy of Interesting Regions
As depicted in Figure 8 (c’), result generated from WAR segmentation
technique shows high level of accuracy in which the boundaries of
interesting regions are clearly depicted. However, Figure 8 (b’) shows a
moderate accuracy as the boundaries of interesting regions are combined
with insignificant regions, which consequently causes the boundaries to be
complexly depicted.
54
4. Experimentation and Evaluation
4.1.2 Comparison among WAR, CorelTrace, and BitmapTrace
Figure 9 shows the segmentation results and Table 1 summarises the
comparisons of the findings generated from CorelTrace (©Corel Draw),
BitmapTrace (©Macromedia), and WAR segmentation techniques (through
BATIK application).
(a) (b) (c)
(a’) (b’) (c’)
Figure 9. Ethnic-Lady. (a) WAR Segmented with range resolution = (10),
(a’) WAR Segmented Region Boundaries, (b) CorelTrace Segmented with
complexity = (6), (b’) CorelTrace Segmented Region Boundaries, (c)
BitmapTrace Segmented with colour threshold = (20), and (c’)
BitmapTrace Segmented Region Boundaries. All of them apply minimum
Region = (20) for post processing
55
4.1 Result Evaluation
Criteria Segmentation
Method
Results
WAR 596
CorelTrace 214
Total regions
BitmapTrace 1400
WAR Highly resembles the original image.
Regions with transition of colour due to
illumination is uniformed and segmented
into a few distinct regions; the shapes of
the lips and eyebrow are retained.
CorelTrace Low resemblance. Fewer details found in
the image, e.g. the shapes of the lips and
eyes are not shown; different regions are
incorrectly merged; regions with transition
of colour due to illumination are over-
segmented.
Result
Resemblance
BitmapTrace Moderate resemblance even though the
whole image is over-segmented. Some
details such as the shape of the lips and
eyes are incorrectly identified.
WAR Most of significant edges are preserved and
smoothed whereas insignificant edges are
ignored.
CorelTrace Not all significant edges are preserved.
Some edges used to identify regions are
missed due to erroneously merging
different regions.
Edge
Preserved
BitmapTrace Too many details of both significant and
insignificant edges and these edges are not
smoothed (zigzagged particularly on the
face, neck, and hair regions).
56
4. Experimentation and Evaluation
WAR High accuracy where boundaries of
interested regions are clearly depicted.
CorelTrace Compatible accuracy in defining the
interested regions. Some interested regions
are combined with insignificant regions.
Accuracy
of Interested
Regions
BitmapTrace Very low accuracy in defining the interested
regions. Most of significant regions are
cropped into scattered countless pieces.
To
betwee
CorelTr
techniq
WAR se
is stron
comput
domain
4.1 Result Evaluation
Table 1. Comparison among WAR, CorelTrace, and BitmapTrace
summarise findings in this research work, the comparison results
n WAR and 3 different segmentation techniques (Mean-shift based,
ace, and BitmapTrace) have demonstrated that WAR segmentation
ue produces reliable yet accurate results and this also means that
gmentation technique can serve for improving Image Segmentation. It
gly believed that WAR segmentation technique is an important
ational module and can extend its use for other application in other
.
57
5. Conclusion
In this thesis, an improved and higher quality of segmentation technique
based on Weighting-Adjacent-Regions strategy has been developed and
incorporates with Boundary Tracing Algorithm to perform Raster-to-Vector
conversion. The customised image vectorisation approach is integrated into
BATIK application. Then, a comparison is conducted on WAR segmentation
with several other segmentation techniques. From the experimental results
and based on the defined evaluation criteria, WAR segmentation results
significantly retain more meaningful and interesting regions where
insignificant regions are disregarded. The results also show high resemblance
to the original image and most of the critical edges are preserved properly.
The applicability of WAR segmentation works best, but is not limited, to
the domain of computer graphic design. It can also be applied to any domain
that requires region and feature extraction. Both Schek [40] and Jing et. al.
[41] propose an image similarity search system that explicitly compares the
similarity between the regions of the query image and the regions of the
indexed images. Hence, it is thought that by incorporating the improved WAR
segmentation technique to their application will result more powerful systems
with regards to retrieval quality.
Future work will concentrate on a further improved and optimised
algorithm to speed up the processing time in WAR segmentation. In the
current implementation, the Weighting-Adjacent-Regions and the Regions-
Merging procedure involve huge numbers of calculations on evaluation of
58
adjacent regions. A suggestion to minimise the complexity of computation is
to avoid the redundant evaluation on the same adjacent regions set.
59
5. Conclusion
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6. Bibliography
7. Appendix
To show the potential application of WAR segmentation, this chapter
presents other segmentation examples in which the original images are
segmented through WAR segmentation approach and have the regions
boundaries superposed are shown in Figure 10, 11, 12, 13, and 14.
6. Bibliography
(a) (b) (c) Figure 10. Landscape images (a) Original (b) WAR Segmented (c) Region
Boundaries
(a) (b)
65
7. Appendix
(c)
Figure 11. House images (a) Original (b) WAR Segmented (c) Region
Boundaries
(a) (b)
(c)
Figure 12. Fruit images (a) Original (b) WAR Segmented (c) Region Boundaries
66
(a) (b)
(c)
Figure 13. Flower images (a) Original (b) WAR Segmented (c) Region
Boundaries
67
7. Appendix
7. Appendix
(a)
(b) (c)
Figure 14. Flamingo images (a) Original (b) WAR Segmented (c) Region
Boundaries
68