Dense Scale Invariant Descriptors for Images and Surfaces

Local descriptors are ubiquitous in image and shape analysis, as they allow the compact and robust description of the local content of a signal (image or 3D shape). A common problem that emerges in the computation of local descriptors is the variability of the signal scale. The standard approach to cope with this is scale selection, which consists in estimating a characteristic scale around the few image or shape points where scale estimation can be performed reliably. However, it is often desired to have a scale-invariant descriptor that can be constructed densely, namely at every point of the image or 3D shape. In this work, we construct scale-invariant signal descriptors by introducing a method that does not rely on scale selection; this allows us to apply our method at any point. Our method relies on a combination of logarithmic sampling with multi-scale signal processing that turns scaling in the original signal domain into a translation in a new domain. Scale invariance can then be guaranteed by computing the Fourier transform magnitude (FTM), which is unaffected by signal translations. We use our technique to construct scale- and rotation- invariant descriptors for images and scale- and isometry-invariant descriptors for 3D surfaces, and demonstrate that our descriptors outperform state-of-the-art descriptors on standard benchmarks.Les descripteurs locaux sont omniprésents dans l'analyse d'image et de la forme, car ils permettent la description compacte et robuste du contenu local d'un signal (image ou une forme 3D). Un problème commun qui se dégage dans le calcul de descripteurs locaux est la variabilité de l'échelle du signal. L'approche standard pour faire face à cette probleme est la sélection d'échelle, qui consiste à estimer une échelle caractéristique autour des ces points d'image ou de la forme où l'estimation échelle peuvent être réalisées de manière fiable. Cependant, il est souvent souhaité d'avoir un descripteur invariant d'échelle qui peut être construit densément, soit à chaque point de l'image ou la forme 3D. Dans ce travail, nous construisons des descripteurs de signaux invariante d'échelle par l'introduction d'une méthode qui ne repose pas sur la sélection d'échelle; ce qui nous permet d'appliquer notre méthode à un point quelconque. Notre méthode repose sur une combinaison de l'échantillonnage logarithmique avec le traitement du signal multi-échelle qui transforme le changement d'échelle dans le domaine du signal original dans une translation dans un nouveau domaine. L'invariance d'échelle peut être garanti par le calcul de la magnitude de la transformée de Fourier (Fourier Transform Modulus -FTM), qui n'est pas affecté par les translations du signal. Nous utilisons notre technique pour construire descripteurs invariantes de l'échelle et la rotation pour les images et les descripteurs invariantes de l'échelle et l'isométrie pour les surfaces 3D, et de démontrer que nos descripteurs peuvent surperformer l'état de l'art des descripteurs sur les benchmarks standards

Steklov Spectral Geometry for Extrinsic Shape Analysis

We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many previous extrinsic methods lack theoretical justification. Instead, we consider the Steklov eigenvalue problem, computing the spectrum of the Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable property of this operator is that it completely encodes volumetric geometry. We use the boundary element method (BEM) to discretize the operator, accelerated by hierarchical numerical schemes and preconditioning; this pipeline allows us to solve eigenvalue and linear problems on large-scale meshes despite the density of the Dirichlet-to-Neumann discretization. We further demonstrate that our operators naturally fit into existing frameworks for geometry processing, making a shift from intrinsic to extrinsic geometry as simple as substituting the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.Comment: Additional experiments adde

Geometric and Photometric Data Fusion in Non-Rigid Shape Analysis

In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global shape descriptors. Our construction is based on the definition of a diffusion process on the shape manifold embedded into a high-dimensional space where the embedding coordinates represent the photometric information. Experimental results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fai

A cylindrical shape descriptor for registration of unstructured point clouds from real-time 3D sensors

To deal with data sets from real-time 3D sensors of RGB-D or TOF cameras, this paper presents a method for registration of unstructured point clouds. We firstly derive intrinsic shape context descriptors for 3D data organization. To replace the Fast-Marching method, a vertex-oriented triangle propagation method is applied to calculate the ’angle’ and ’radius’ in descriptor charting, so that the matching accuracy at the twisting and folding area is significantly improved. Then, a 3D cylindrical shape descriptor is proposed for registration of unstructured point clouds. The chosen points are projected into the cylindrical coordinate system to construct the descriptors. The projection parameters are respectively determined by the distances from the chosen points to the reference normal vector, and the distances from the chosen points to the reference tangent plane and the projection angle. Furthermore, Fourier transform is adopted to deal with orientation ambiguity in descriptor matching. Practical experiments demonstrate a satisfactory result in point cloud registration and notable improvement on standard benchmarks