Projective Texture Atlas for 3D Photography Jonas Sossai Júnior Luiz Velho IMPA

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 R i, associated with charts C i, that minimizes the total error : E(R, A) = ∑ E(R i, C i )  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 C i – Chart c i – Camera associate to chart C i n i – 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

(5 charts, distortion= ) 220 x 396 (39 charts, distortion= ) 750 x 755 Results I

39 charts 750 x charts 320 x 433 Results II

Real photograph Scopigno et al Our results 6 charts, 256 x charts, 220 x 396 Comparison I

Real photograph Scopigno et al Our results 73 charts, 512 x charts, 750 x 755 Comparison II

Conclusions and Future Work  Projective texture atlas: Powerful structure for 3D photography Foundation for attribute editing  Improvements: Better packing algorithm Other surface attributes (normal and displacement)