Mesh Colorization

Author: George Leifman and Ayellet TalEUROGRAPHICS 2012, May in Italy

Speaker: Chung-Yuan LeeYuan-Ze University

OutlineIntroductionProposed method

◦Basic algorithm Vertex similarity Color propagation

◦Feature line fieldResultReference

Introduction

A novel algorithm for colorization of meshes.

Basic algorithmVertex similarity◦Step1. Vertex descriptor◦Use spin image to describe vertex

spreading.

𝑆𝑝𝑖𝑛 𝑖𝑚𝑎𝑔𝑒[1]2D histograms

Use a relatively small support region, by setting α＝ β＝８

Basic algorithmStep2. Similarity measure

Model the difference between two histograms

where

σ is a constant standard deviation for the Gaussian filter ϕ

The notation denotes half size down-sampling

k(α) is the norm, making the diffusion distance a true metric.

This method use L = 3 and σ = 0.5

Basic algorithmStep3. Edge assignment

means similarity between the vertices I and j

MaxD is the maximal distance between all pairs of neighboring vertices of the mesh

The "amount of color" that can flow between and

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Basic algorithmColor propagationFor each color channel C in the YUV color space,the method minimize the following cost function.

This equation constraint that two neighboring vertices should have similar colors if their geometry is similar.

The result might include color bleeding near the boundaries !

Feature line fieldDefinitionFor neighboring points that belong

to the same region, the directions of the associated vectors should have similar orientations.

And vice versa!

Feature line fieldComputationThis method describe the

computation for the case of valleys.

Ridge −Valley  Lines  on  Meshes   via   Implicit   Surface  Fitting  [2 ]

Surrounding face

Feature line field direction lies on the line perpendicular to the edge adjacent to it

The average of all the field vectors computed for each face independently

Solve the Laplace’s equation

sum of cotangents of the angles opposite the edge (v, ) in the triangles sharing this edge

Similarity measure adjustment

Case1:

Case2:

ԑ is set to half of the shortest edge of the mesh

𝑣 𝑖 𝑣 𝑗

Result

Reference[1] “Spin Images”

◦Georgios Papadimitriou [2]Ridge-Valley Lines on Meshes

via Implicit Surface Fitting◦Yutaka Ohtake , Alexander Belyaev ◦Hans-Peter Seidel 2