Bayesian Helmholtz Stereopsis with Integrability Prior

Binocular Helmholtz Stereopsis

Helmholtz stereopsis has been introduced recently as a surface reconstruction technique that does not assume a model of surface reflectance. In the reported formulation, correspondence was established using a rank constraint, necessitating at least three viewpoints and three pairs of images. Here, it is revealed that the fundamental Helmholtz stereopsis constraint defines a nonlinear partial di...

Toward a Stratification of Helmholtz Stereopsis

Helmholtz stereopsis has been previously introduced as a surface reconstruction technique that does not assume a model of surface reflectance. This technique relies on the use of multiple cameras and light sources, and it has been shown to be effective when the camera and source positions are known. Here, we take a stratified look at uncalibrated Helmholtz stereopsis. We derive a new photometri...

Bayesian Fuzzy Hypothesis Testing with Imprecise Prior Distribution

This paper considers the testing of fuzzy hypotheses on the basis of a Bayesian approach. For this, using a notion of prior distribution with interval or fuzzy-valued parameters, we extend a concept of posterior probability of a fuzzy hypothesis. Some of its properties are also put into investigation. The feasibility and effectiveness of the proposed methods are also cla...

A Maximum Likelihood Surface Normal Estimation Algorithm for Helmholtz Stereopsis

Helmholtz stereopsis is a relatively recent reconstruction technique which is able to reconstruct scenes with arbitrary and unknown surface reflectance properties. Conventional implementations of the method estimate surface normal direction at each surface point via an eigenanalysis, thereby optimising an algebraic distance. We develop a more physically meaningful radiometric distance whose min...

Normalized Power Prior Bayesian Analysis Normalized Power Prior Bayesian Analysis