A parallel implementation of 3D Zernike moment analysis

Zernike polynomials are a well known set of functions that find many applications in image or pattern characterization because they allow to construct shape descriptors that are invariant against translations, rotations or scale changes. The concepts behind them can be extended to higher dimension spaces, making them also fit to describe volumetric data. They have been less used than their properties might suggest due to their high computational cost. We present a parallel implementation of 3D Zernike moments analysis, written in C with CUDA extensions, which makes it practical to employ Zernike descriptors in interactive applications, yielding a performance of several frames per second in voxel datasets about 2003 in size. In our contribution, we describe the challenges of implementing 3D Zernike analysis in a general-purpose GPU. These include how to deal with numerical inaccuracies, due to the high precision demands of the algorithm, or how to deal with the high volume of input data so that it does not become a bottleneck for the system.

Fast human pose estimation using 3D Zernike descriptors

Markerless video-based human pose estimation algorithms face a high-dimensional problem that is frequently broken down into several lower-dimensional ones by estimating the pose of each limb separately. However, in order to do so they need to reliably locate the torso, for which they typically rely on time coherence and tracking algorithms. Their losing track usually results in catastrophic failure of the process, requiring human intervention and thus precluding their usage in real-time applications. We propose a very fast rough pose estimation scheme based on global shape descriptors built on 3D Zernike moments. Using an articulated model that we configure in many poses, a large database of descriptor/pose pairs can be computed off-line. Thus, the only steps that must be done on-line are the extraction of the descriptors for each input volume and a search against the database to get the most likely poses. While the result of such process is not a fine pose estimation, it can be useful to help more sophisticated algorithms to regain track or make more educated guesses when creating new particles in particle-filter-based tracking schemes. We have achieved a performance of about ten fps on a single computer using a database of about one million entries.

Image analysis by moment invariants using a set of step-like basis functions

Moment invariants have been thoroughly studied and repeatedly proposed as one of the most powerful tools for 2D shape identification. In this paper a set of such descriptors is proposed, being the basis functions discontinuous in a finite number of points. The goal of using discontinuous functions is to avoid the Gibbs phenomenon, and therefore to yield a better approximation capability for discontinuous signals, as images. Moreover, the proposed set of moments allows the definition of rotation invariants, being this the other main design concern. Translation and scale invariance are achieved by means of standard image normalization. Tests are conducted to evaluate the behavior of these descriptors in noisy environments, where images are corrupted with Gaussian noise up to different SNR values. Results are compared to those obtained using Zernike moments, showing that the proposed descriptor has the same performance in image retrieval tasks in noisy environments, but demanding much less computational power for every stage in the query chain.