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Transcript of Asma Kanwal Lecturer Department of Computer Science, GC University, Lahore Dr. Wajahat Mahmood Qazi...
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Image Acquisition
Asma KanwalLecturer Department of Computer Science, GC University, Lahore
Dr. Wajahat Mahmood QaziAssistant ProfessorDepartment of Computer Science, GC University, Lahore
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Human Visual Perception
• Why study visual perception?• Image processing algorithms are
designed based on how our visual system works.
• In image compression, we need to know what information is not perceptually important and can be ignored.
• In image enhancement, we need to know what types of operations that are likely to improve an image visually.
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The Human Visual System
• The human visual system consists of two primary components – the eye and the brain, which are connected by the optic nerve.• Eye – receiving sensor (camera,
scanner).• Brain – information processing unit
(computer system).• Optic nerve – connection cable (physical
wire).
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The Human Visual System
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Cross Section of the Human Eye
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Visual Perception: Human Eye (cont.)
1. The lens contains 60-70% water, 6% of fat.
2. The iris diaphragm controls amount of light that enters the eye.
3. Light receptors in the retina- About 6-7 millions cones for bright light vision called photopic • - Density of cones is about 150,000
elements/mm2.• - Cones involve in color vision.• - Cones are concentrated in fovea about
1.5x1.5 mm2.• - About 75-150 millions rods for dim light vision called
scotopic• - Rods are sensitive to low level of light and are
not involved• color vision.
Blind spot is the region of emergence of the optic nerve from the eye.
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Image Formation in the Human Eye
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Image Formation in the Human Eye
• Focal length of the eye: 17 to 14 mm• Let h be the height in mm of that
object in the retinal image, then 15/100 = h / 17 , h =
2.55mm• The retinal image is reflected
primarily in the area of the fovea.
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What is light?
• The visible portion of the electromagnetic (EM) spectrum.
• It occurs between wavelengths of approximately 400 and 700 nanometers.
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Light and the Electromagnetic Spectrum
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Light and the Electromagnetic SpectrumLight and the Electromagnetic Spectrum
• Three basic quantities described the quality of a chromatic light source:• Radiance: the total amount energy that
flow from the light source (can be measured)
• Luminance: the amount of energy an observer perceives from a light source (can be measured)
• Brightness: a subjective descriptor of light perception; perceived quantity of light emitted (cannot be measured)
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Light and the Electromagnetic SpectrumLight and the Electromagnetic Spectrum
• Relationship between frequency ( ) and wavelength ( )
, where c is the speed of light• Energy of a photon , where h is Planck’s constant
c
hE
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Terminologies
Wave Length:The distance between peaks (high points) iscalled wavelength.
Frequency:Frequency describes the number of waves that pass a fixed place in a given amount of time.
Amplitude:Amplitude is the height of a wave.
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Terminologies
Reflection:
Refraction:Refraction of waves involves a change in the direction of waves as they pass from one medium to another.
Diffraction: Diffraction involves a change in direction of waves as they pass through an opening or around a barrier in their path.
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Image formation
• There are two parts to the image formation process:
• The geometry of image formation, which determines where in the image plane the projection of a point in the scene will be located.
• The physics of light, which determines the brightness of a point in the image plane as a function of illumination and surface properties.
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A Simple model of image formation
• The scene is illuminated by a single source.• The scene reflects radiation towards the
camera.• The camera senses it via chemicals on film.
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Pinhole camera
• This is the simplest device to form an image of a 3D scene on a 2D surface.
• Straight rays of light pass through a “pinhole” and form an inverted image of the object on the image plane.
fXx
Z
fYy
Z
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Video on Pinhole Camera
http://www.howcast.com/videos/387145-How-to-Transform-a-Room-into-a-Camera-Obscura
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Camera optics
• In practice, the aperture must be larger to admit more light.
• Lenses are placed to in the aperture to focus the bundle of rays from each scene point onto the corresponding point in the image plane
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Camera Image Side Up
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Image formation (cont’d)
• Optical parameters of the lens• lens type• focal length• field of view
• Photometric parameters• type, intensity, and direction of illumination• reflectance properties of the viewed surfaces
• Geometric parameters• type of projections• position and orientation of camera in space• perspective distortions introduced by the imaging
process
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Pixel Transformation
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Spatial Domain Methods
f(x,y)
g(x,y)
g(x,y)
f(x,y)
Point Processing
Area/Mask Processing
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Color Transformation
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Color Models
• The purpose of a color model (also called Color Space or Color System) is to facilitate the specification of colors in some standard way
• A color model is a specification of a coordinate system and a subspace within that system where each color is represented by a single point
• Color Models
RGB (Red, Green, Blue)CMY (Cyan, Magenta, Yellow)HSI (Hue, Saturation, Intensity)
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RGB Model
• Each color is represented in its primary color components Red, Green and Blue
• This model is based on Cartesian Coordinate System
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CMY Color Model
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CMY Color Model
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HSI Color Model
• Hue (dominant colour seen) • Wavelength of the pure colour observed in the signal.• Distinguishes red, yellow, green, etc.• More the 400 hues can be seen by the human eye.
• Saturation (degree of dilution)• Inverse of the quantity of “white” present in the
signal. A pure colour has 100% saturation, the white and grey have 0% saturation.
• Distinguishes red from pink, marine blue from royal blue, etc.
• About 20 saturation levels are visible per hue.
• Intensity• Distinguishes the gray levels.
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Color Transformations
Color transformation can be represented by the expression ::
g(x,y)=T[f(x,y)]
f(x,y): input imageg(x,y): processed (output) imageT[*]: an operator on f defined over neighborhood of (x,y).
The pixel values here are triplets or quartets (i.e group of 3 or 4 values)
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Color Transformations
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Geometric Transformation
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Image alignment
Why don’t these image line up exactly?
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What is the geometric relationship between these two images?
?
Answer: Similarity transformation (translation, rotation, uniform scale)
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What is the geometric relationship between these two images?
?
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What is the geometric relationship between these two images?
Very important for creating mosaics!
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Geometric Processes
• Transformation applied on the coordinates of the pixels (i.e., relocate pixels).
• A geometric transformation has the general form
(x,y) = T{(v,w)} where (v,w) are the original pixel coordinates
and (x,y) are the transformed pixel coordinates.
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Image Warping
• image filtering: change range of image
g(x) = h(f(x))
• image warping: change domain of
imageg(x) = f(h(x))
f
x
hg
x
f
x
hg
x
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Image Warping
• image filtering: change range of image
g(x) = h(f(x))
• image warping: change domain of
imageg(x) = f(h(x))
h
h
f
f g
g
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Parametric (global) warping• Examples of parametric warps:
translation
rotation aspect
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Parametric (global) warping
• Transformation T is a coordinate-changing machine:p’ = T(p)
• What does it mean that T is global?• Is the same for any point p• can be described by just a few numbers (parameters)
• Let’s consider linear xforms (can be represented by a 2D matrix):
T
p = (x,y) p’ = (x’,y’)
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All 2D Linear Transformations
• Linear transformations are combinations of …• Scale,• Rotation,• Shear, and• Mirror
• Properties of linear transformations:• Origin maps to origin• Lines map to lines• Parallel lines remain parallel• Ratios are preserved• Closed under composition
y
x
dc
ba
y
x
'
'
yx
lkji
hgfe
dcba
yx
''
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Homogeneous coordinates
Trick: add one more coordinate:
homogeneous image coordinates
Converting from homogeneous coordinates
x
y
w
(x, y, w)
w = 1 (x/w, y/w, 1)
homogeneous plane
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2D Translation
• Moves a point to a new location by adding translation amounts to the coordinates of the point.
or
or
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2D Translation (cont’d)
• To translate an object, translate every point of the object by the same amount.
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2D Scaling
• Changes the size of the object by multiplying the coordinates of the points by scaling factors.
oror
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2D Scaling (cont’d)
• Uniform vs non-uniform scaling
• Effect of scale factors:
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2D Rotation
• Rotates points by an angle θ about origin
(θ >0: counterclockwise rotation)
• From ABP triangle:
• From ACP’ triangle:A
BC
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2D Rotation (cont’d)
• From the above equations we have: or
or
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Homogeneous coordinates
• Add one more coordinate: (x,y) (xh, yh, w)
• Recover (x,y) by homogenizing (xh, yh, w):
• So, xh=xw, yh=yw,
(x, y) (xw, yw, w)
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Homogeneous coordinates (cont’d)
• (x, y) has multiple representations in homogeneous coordinates:• w=1 (x,y) (x,y,1)• w=2 (x,y) (2x,2y,2)
• All these points lie on a line in the space of homogeneous coordinates !!
projectivespace
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2D Translation using homogeneous coordinates
w=1
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2D Translation using homogeneous coordinates (cont’d)
• Successive translations:
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2D Scaling using homogeneous coordinates
w=1
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2D Scaling using homogeneous coordinates (cont’d)
• Successive scalings:
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2D Rotation using homogeneous coordinates
w=1
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2D Rotation using homogeneous coordinates (cont’d)
• Successive rotations:
or
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Composition of transformations
• The transformation matrices of a series of transformations can be concatenated into a single transformation matrix.* Translate P1 to origin
* Perform scaling and rotation* Translate to P2Example:
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Composition of transformations (cont’d)
• Important: preserve the order of transformations!
translation + rotation rotation + translation
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2D shear transformation
• Shearing along x-axis:
• Shearing along y-axis
changes objectshape!
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Affine transformations
any transformation with last row [ 0 0 1 ] we call an affine transformation
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Basic affine transformations
1100
0cossin
0sincos
1
'
'
y
x
y
x
1100
10
01
1
'
'
y
x
t
t
y
x
y
x
1100
01
01
1
'
'
y
x
sh
sh
y
x
y
x
Translate
2D in-plane rotation Shear
1100
00
00
1
'
'
y
x
s
s
y
x
y
x
Scale
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Affine Transformations
• Under certain assumptions, affine transformations can be used to approximate the effects of perspective projection!
G. Bebis, M. Georgiopoulos, N. da Vitoria Lobo, and M. Shah, " Recognition by learning affine transformations", Pattern Recognition, Vol. 32, No. 10, pp. 1783-1799, 1999.
affine transformed object
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Affine Transformations
• Affine transformations are combinations of …• Linear transformations, and• Translations
• Properties of affine transformations:• Origin does not necessarily map to origin• Lines map to lines• Parallel lines remain parallel• Ratios are preserved• Closed under composition
wyx
fedcba
wyx
100''
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Projective Transformations aka Homographies aka Planar Perspective Maps
Called a homography (or planar perspective map)
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Projective Transformations
• Projective transformations …• Affine transformations, and• Projective warps
• Properties of projective transformations:• Origin does not necessarily map to origin• Lines map to lines• Parallel lines do not necessarily remain parallel• Ratios are not preserved• Closed under composition
wyx
ihgfedcba
wyx
'''
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2D image transformations
These transformations are a nested set of groups• Closed under composition and inverse is a member
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3D Transformations
• Right-handed / left-handed systems
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3D Transformations (cont’d)
• Positive rotation angles for right-handed systems:
(counter-clockwise rotations)
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Homogeneous coordinates
• Add one more coordinate: (x,y,z) (xh, yh, zh,w)• Recover (x,y,z) by homogenizing (xh, yh, zh,w):
• In general, xh=xw, yh=yw, zh=zw
• (x, y,z) (xw, yw, zw, w)
• Each point (x, y, z) corresponds to a line in the 4D-space of homogeneous coordinates.
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3D Translation
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3D Scaling
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3D Rotation
• Rotation about the z-axis:
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3D Rotation (cont’d)
• Rotation about the x-axis:
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3D Rotation (cont’d)
• Rotation about the y-axis