projective texture atlas for 3d photography jonas sossai júnior luiz velho impa
TRANSCRIPT
Motivation Texture maps describe surface properties
Important for Visualization and Modelling
Surface parameterization(Mapping a 2D domain to a 3D surface) Difficult to compute / Introduces distortion
Solution: use an atlas structure(set of charts individually parameterized)
Problem Description Our work:
Build texture atlas for 3D photography
Strategy: Projective atlas Variational optimization
Applications: 3D photography Attribute editing
3D photography (Scopigno et al. 2002)
Surface representation (Sander et al. 2003)
Variational approximation (Desbrun et al. 2004)
Related Work
Contributions
Projective texture atlas:
3D Photography Application
Optimal Patch Construction
Texture Compression and Smoothing
Texture for 3D Photography The problem:
Construct a good texture map from photographs
Requirements: Minimize texture distortion Space-optimized texture Reduce color discontinuity
Variational projective texture atlas: Surface partitioning (distortion and frequency-based) Parametrization, discretization and packing
PDE-based color diffusion Texture smoothing
Techniques: Partitioning:
Variational minimization of texture distortion and space
Parameterization: Projective mapping
Packing: Simple algorithm
Overview Partitioning Parameterization Packing
Variational Surface Partitioning Given a surface S, a desired number of regions n,
and an error metric E An optimal atlas A with a partition R over S,
is a set of regions Ri, associated with charts Ci, that minimizes the total error:
E(R, A) = ∑ E(Ri, Ci)
Error Metrics Texture Distortion Frequency Dissimilarity
Lloyd’s Algorithm Clustering by Fixed Point Iteration
Repeat until done: Assign points to regions
according to centers Update centers
Scheduling Chart adding Chart growing Chart merging
Minimizing Texture Distortion Texture Distortion
Visibility
Ci – Chart
ci – Camera associate to chart Ci
ni – camera direction
n(x) – surface normal
Texture has different levels of detail
Algorithm: Compute frequency content
using wavelet analysis Make charts based on
frequency similarity Scale images according
to frequency
Maximizing Frequency Coherency
Color Compatibilization Problem:
Color discontinuity between images (different exposure)
Solution:Frontier faces share an edge(color from two images)
PDE-based Diffusion Algorithm:
For each frontier edge compute the color difference between corresponding texels
Multigrid diffusion of differences over charts
Parameterization and Discretization Parameterization of each chart is the projective mapping of
its associated camera
The discretization is obtained by projecting the chart boundary onto its associated image
Output Texture Map
Simple Algorithm: For each chart clip the bounding box Sort these clipped regions by height Place sequentially into rows
OBS: Could use better packing, but frequency analysis makes the size of the texture atlas small enough
Packing
Real photograph Scopigno et al. 2002 Our results
6 charts, 256 x 512 5 charts, 220 x 396
Comparison I
Real photograph Scopigno et al. 2002 Our results
73 charts, 512 x 1024 39 charts, 750 x 755
Comparison II