Stochastic methods in computational stereo

Computational stereo estimates 3D structure by analyzing visual changes between two or more passive images of a scene that are captured from different viewpoints. It is a key enabler for ubiquitous autonomous systems, large-scale surveying, virtual reality, and improved techniques for compression, tracking, and object recognition. The fact that computational stereo is an under-constrained inverse problem causes many challenges. Its computational and memory requirements are high. Typical heuristics and assumptions, used to constrain solutions or reduce computation, prevent treatment of key realities such as reflection, translucency, ambient lighting changes, or moving objects in the scene. As a result, a general solution is lacking.

Stochastic models are common in computational stereo, but stochastic algorithms are severely under-represented. In this dissertation I present two stochastic algorithms and demonstrate their advantages over deterministic approaches.

I first present the Quality-Efficient Stochastic Sampling (QUESS) approach. QUESS reduces the number of match quality function evaluations needed to estimate dense stereo correspondences. This facilitates the use of complex quality metrics or metrics that take unique values at non-integer disparities. QUESS is shown to outperform two competing approaches, and to have more attractive memory and scaling properties than approaches based on exhaustive sampling.

I then present a second novel approach based on the Hough transform and extend it with distributed ray tracing (DRT). DRT is a stochastic anti-aliasing technique common to computer rendering but which has not been used in computational stereo. I demonstrate that the DRT-enhanced approach outperforms the unenhanced approach, a competing variation that uses re-accumulation in the Hough domain, and another baseline approach. DRT’s advantages are particularly strong for reduced image resolution and/or reduced accumulator matrix resolution. In support of this second approach, I develop two novel variations of the Hough transform that use DRT, and demonstrate that they outperform competing variations on a traditional line segment detection problem.

I generalize these two examples to draw broader conclusions, suggest future work, and call for a deeper exploration by the community. Both practical and academic gaps in the state of the art can be reduced by a renewed exploration of stochastic computational stereo techniques.