Learning joint intensity-depth sparse representations

TL;DR

This paper introduces a novel joint basis pursuit algorithm for learning overcomplete dictionaries that capture the relationship between intensity and depth in 3D scenes, improving depth inpainting performance.

Contribution

It proposes a new JBP algorithm for joint sparse feature extraction across modalities and integrates it into a dictionary learning framework, with theoretical and experimental validation.

Findings

JBP outperforms Group Lasso in sparse recovery accuracy.

The learned dictionaries capture meaningful joint features like edges and textures.

The method achieves state-of-the-art depth inpainting results on 3D data.

Abstract

This paper presents a method for learning overcomplete dictionaries composed of two modalities that describe a 3D scene: image intensity and scene depth. We propose a novel Joint Basis Pursuit (JBP) algorithm that finds related sparse features in two modalities using conic programming and integrate it into a two-step dictionary learning algorithm. JBP differs from related convex algorithms because it finds joint sparsity models with different atoms and different coefficient values for intensity and depth. This is crucial for recovering generative models where the same sparse underlying causes (3D features) give rise to different signals (intensity and depth). We give a theoretical bound for the sparse coefficient recovery error obtained by JBP, and show experimentally that JBP is far superior to the state of the art Group Lasso algorithm. When applied to the Middlebury depth-intensity database, our learning algorithm converges to a set of related features, such as pairs of depth and intensity edges or image textures and depth slants. Finally, we show that the learned dictionary and JBP achieve the state of the art depth inpainting performance on time-of-flight 3D data.