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

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 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

(5 charts, distortion=5875.18) 220 x 396

(39 charts, distortion=4680.54) 750 x 755

Results I

39 charts 750 x 755

70 charts 320 x 433

Results II

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

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)