Igor Guskov

Multiresolution signal processing for meshes

We generalize basic signal processing tools such as downsampling, upsampling, and filters to irregular connectivity triangle meshes. This is accomplished through the design of a non-uniform relaxation procedure whose weights depend on the geometry and we show its superiority over existing schemes whose weights depend only on connectivity. This is combined with known mesh simplification methods to build subdivision and pyramid algorithms. We demonstrate the power of these algorithms through a number of application examples including smoothing, enhancement, editing, and texture mapping.

Multi-scale features for approximate alignment of point-based surfaces

We introduce a novel method for approximate alignment of point-based surfaces. Our approach is based on detecting a set of salient feature points using a scale-space representation. For each feature point we compute a signature vector that is approximately invariant under rigid transformations. We use the extracted signed feature set in order to obtain approximate alignment of two surfaces. We apply our method for the automatic alignment of multiple scans using both scan-to-scan and scan-to-model matching capabilities.

Wavelets on irregular point sets

In this article we review techniques for building and analysing wavelets on irregular point sets in one and two dimensions. We discuss current results both on the practical and theoretical side. In particular, we focus on subdivision schemes and commutation rules. Several examples are included.

Wavelet compression of parametrically coherent mesh sequences

We introduce an efficient compression method for animated sequences of irregular meshes of the same connectivity. Our approach is to transform the original input meshes with an anisotropic wavelet transform running on top of a progressive mesh hierarchy, and progressively encode the resulting wavelet details. For temporally coherent mesh sequences we get additional improvement by encoding the differences of the wavelet coefficients. The resulting compression scheme is scalable, efficient, and significantly improves upon the current state of the art for the animated mesh compression.

Compression of Normal Meshes

Open image in new window Fig. 1. Partial reconstructions from a progressive encoding of the molecule model. File sizes are given in bytes, errors in multiples of 10−4 and PSNR in dB (model courtesy of The Scripps Research Institute).

3D object recognition from range images using pyramid matching

Recognition of 3D objects from different viewpoints is a difficult problem. In this paper, we propose a new method to recognize 3D range images by matching local surface descriptors. The input 3D surfaces are first converted into a set of local shape descriptors computed on surface patches defined by detected salient features. We compute the similarities between input 3D images by matching their descriptors with a pyramid kernel function. The similarity matrix of the images is used to train for classification using SVM, and new images can be recognized by comparing with the training set. The approach is evaluated on both synthetic and real 3D data with complex shapes.

Hybrid meshes: multiresolution using regular and irregular refinement

A hybrid mesh is a multiresolution surface representation that combines advantages from regular and irregular meshes. Irregular operations allow a hybrid mesh to change topology throughout the hierarchy and approximate detailed features at multiple scales. A preponderance of regular refinements allows for efficient data-structures and processing algorithms. We provide a user driven procedure for creating a hybrid mesh from scanned geometry and present a progressive hybrid mesh compression algorithm.

Manifold-based approach to semi-regular remeshing

This paper describes a method for semi-regular remeshing of arbitrary shapes. The proposed approach is based on building a parameterization map which is smooth with respect to a differential structure built on the base domain. A global parametric energy functional is introduced and optimized in order to establish a globally smooth parameterization. The proposed approach avoids using meta-mesh construction during the parameterization and resampling stages which allows for an easier implementation. A simple extension of the method is proposed to improve the approximation properties of the resulting remesh.

Efficient tracking of regular patterns on non-rigid geometry

We introduce a real-time robust tracking procedure for a regular pattern marked on a flexible moving surface such as cloth. Our system is capable of maintaining the tracked grid structure for long periods of time without quality deterioration, and requires minimal user interaction. It has been tested on videos of an actor dressed in a specially marked T-shirt and behaves favorably with the presence of self-occlusions, self-shadowing and folding of the cloth. The focus of this paper is on single camera video sequence processing, even though 3D shape reconstruction with multiple cameras is the motivating goal.

An anisotropic mesh parameterization scheme

We introduce a simple anisotropic modification of Floater’s shape-preserving parameterization scheme. The original scheme is formulated as a discrete energy minimization and the modification is performed by introducing an additional stretching term. Results and example applications to anisotropic regular surface meshing are presented.