Inconsistency of Pitman-Yor process mixtures for the number of components

In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these models may be well-suited for Bayesian density estimation, many investigators are using them for inferences about the number of components, by considering the posterior on the number of components represented in the observed data. We show that this posterior is not consistent --- that is, on data from a finite mixture, it does not concentrate at the true number of components. This result applies to a large class of nonparametric mixtures, including DPMs and PYMs, over a wide variety of families of component distributions, including essentially all discrete families, as well as continuous exponential families satisfying mild regularity conditions (such as multivariate Gaussians).Comment: This is a general treatment of the problem discussed in our related article, "A simple example of Dirichlet process mixture inconsistency for the number of components", Miller and Harrison (2013) arXiv:1301.270

Photometric Depth Super-Resolution

This study explores the use of photometric techniques (shape-from-shading and uncalibrated photometric stereo) for upsampling the low-resolution depth map from an RGB-D sensor to the higher resolution of the companion RGB image. A single-shot variational approach is first put forward, which is effective as long as the target's reflectance is piecewise-constant. It is then shown that this dependency upon a specific reflectance model can be relaxed by focusing on a specific class of objects (e.g., faces), and delegate reflectance estimation to a deep neural network. A multi-shot strategy based on randomly varying lighting conditions is eventually discussed. It requires no training or prior on the reflectance, yet this comes at the price of a dedicated acquisition setup. Both quantitative and qualitative evaluations illustrate the effectiveness of the proposed methods on synthetic and real-world scenarios.Comment: IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI), 2019. First three authors contribute equall

Improving "bag-of-keypoints" image categorisation: Generative Models and PDF-Kernels

In this paper we propose two distinct enhancements to the basic ''bag-of-keypoints" image categorisation scheme proposed in [4]. In this approach images are represented as a variable sized set of local image features (keypoints). Thus, we require machine learning tools which can operate on sets of vectors. In [4] this is achieved by representing the set as a histogram over bins found by k-means. We show how this approach can be improved and generalised using Gaussian Mixture Models (GMMs). Alternatively, the set of keypoints can be represented directly as a probability density function, over which a kernel can be de ned. This approach is shown to give state of the art categorisation performance