This document summarizes a paper on mesh colorization. The proposed method uses (1) vertex similarity based on spin images to propagate color from labeled to unlabeled vertices, and (2) a feature line field to help constrain color propagation along features. The method formulates colorization as an energy minimization problem. It was presented at the Eurographics conference in Italy and introduces a novel algorithm for automatically colorizing meshes.

1. Mesh Colorization
Author: George Leifman and Ayellet Tal
EUROGRAPHICS 2012, May in Italy
Speaker: Chung-Yuan Lee
Yuan-Ze University

2. Outline
 Introduction
 Proposed method
◦ Basic algorithm
 Vertex similarity
 Color propagation
◦ Feature line field
 Result
 Reference

3. Introduction
A novel algorithm for colorization of
meshes.

4. Basic algorithm
 Vertex similarity
◦ Step1. Vertex descriptor
◦ Use spin image to describe vertex
spreading.

5. 2D histograms

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

7. Basic algorithm
 Step2. Similarity measure
Model the difference between two
histograms
where

9.  σ is a constant standard deviation for
the Gaussian filter ϕ
 The notation denotes half size
down-sampling

10. 

11. Basic algorithm

1

12. Basic algorithm
 Color propagation
For 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.

14. The result might include color bleeding near the
boundaries !

15. Feature line field
 Definition
 For neighboring points that belong to the
same region, the directions of the
associated vectors should have similar
orientations.
 And vice versa!

16. Feature line field
 Computation
 This method describe the computation
for the case of valleys.

17. Surrounding face
Feature line field direction lies on the
line perpendicular to the edge adjacent
to it
Solve the Laplace’s equation
The average of all the field vectors
computed for each face independently

18. Similarity measure adjustment

19. ԑis set to half of the shortest edge of the
mesh
Case1:
Case2:

20. Result

22. Reference
[1]
 “Spin Images”
◦ Georgios Papadimitriou
 [2]
 Ridge-Valley Lines on Meshes via
Implicit Surface Fitting
◦ Yutaka Ohtake , Alexander Belyaev
◦ Hans-Peter Seidel 2