Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

Geometric modeling of non-rigid 3D shapes : theory and application to object recognition.

One of the major goals of computer vision is the development of flexible and efficient methods for shape representation. This is true, especially for non-rigid 3D shapes where a great variety of shapes are produced as a result of deformations of a non-rigid object. Modeling these non-rigid shapes is a very challenging problem. Being able to analyze the properties of such shapes and describe their behavior is the key issue in research. Also, considering photometric features can play an important role in many shape analysis applications, such as shape matching and correspondence because it contains rich information about the visual appearance of real objects. This new information (contained in photometric features) and its important applications add another, new dimension to the problem\u27s difficulty. Two main approaches have been adopted in the literature for shape modeling for the matching and retrieval problem, local and global approaches. Local matching is performed between sparse points or regions of the shape, while the global shape approaches similarity is measured among entire models. These methods have an underlying assumption that shapes are rigidly transformed. And Most descriptors proposed so far are confined to shape, that is, they analyze only geometric and/or topological properties of 3D models. A shape descriptor or model should be isometry invariant, scale invariant, be able to capture the fine details of the shape, computationally efficient, and have many other good properties. A shape descriptor or model is needed. This shape descriptor should be: able to deal with the non-rigid shape deformation, able to handle the scale variation problem with less sensitivity to noise, able to match shapes related to the same class even if these shapes have missing parts, and able to encode both the photometric, and geometric information in one descriptor. This dissertation will address the problem of 3D non-rigid shape representation and textured 3D non-rigid shapes based on local features. Two approaches will be proposed for non-rigid shape matching and retrieval based on Heat Kernel (HK), and Scale-Invariant Heat Kernel (SI-HK) and one approach for modeling textured 3D non-rigid shapes based on scale-invariant Weighted Heat Kernel Signature (WHKS). For the first approach, the Laplace-Beltrami eigenfunctions is used to detect a small number of critical points on the shape surface. Then a shape descriptor is formed based on the heat kernels at the detected critical points for different scales. Sparse representation is used to reduce the dimensionality of the calculated descriptor. The proposed descriptor is used for classification via the Collaborative Representation-based Classification with a Regularized Least Square (CRC-RLS) algorithm. The experimental results have shown that the proposed descriptor can achieve state-of-the-art results on two benchmark data sets. For the second approach, an improved method to introduce scale-invariance has been also proposed to avoid noise-sensitive operations in the original transformation method. Then a new 3D shape descriptor is formed based on the histograms of the scale-invariant HK for a number of critical points on the shape at different time scales. A Collaborative Classification (CC) scheme is then employed for object classification. The experimental results have shown that the proposed descriptor can achieve high performance on the two benchmark data sets. An important observation from the experiments is that the proposed approach is more able to handle data under several distortion scenarios (noise, shot-noise, scale, and under missing parts) than the well-known approaches. For modeling textured 3D non-rigid shapes, this dissertation introduces, for the first time, a mathematical framework for the diffusion geometry on textured shapes. This dissertation presents an approach for shape matching and retrieval based on a weighted heat kernel signature. It shows how to include photometric information as a weight over the shape manifold, and it also propose a novel formulation for heat diffusion over weighted manifolds. Then this dissertation presents a new discretization method for the weighted heat kernel induced by the linear FEM weights. Finally, the weighted heat kernel signature is used as a shape descriptor. The proposed descriptor encodes both the photometric, and geometric information based on the solution of one equation. Finally, this dissertation proposes an approach for 3D face recognition based on the front contours of heat propagation over the face surface. The front contours are extracted automatically as heat is propagating starting from a detected set of landmarks. The propagation contours are used to successfully discriminate the various faces. The proposed approach is evaluated on the largest publicly available database of 3D facial images and successfully compared to the state-of-the-art approaches in the literature. This work can be extended to the problem of dense correspondence between non-rigid shapes. The proposed approaches with the properties of the Laplace-Beltrami eigenfunction can be utilized for 3D mesh segmentation. Another possible application of the proposed approach is the view point selection for 3D objects by selecting the most informative views that collectively provide the most descriptive presentation of the surface

2-D shapes description by using features based on the differential turning angle scalogram

International audienceA 2-D shape description using the turning angle is presented 1 . This descriptor is based on a scalogram obtained from a progressive filtering of a planar closed contour. At a given scale, the differential turning angle function is calculated from which, three essential points are derived: the minimum differential-turning angle (α-points), the maximum differential-turning angle (β-points) and the zero-crossing of the turning angle (γ-points). For a continuum of the scale values in the filtering process, a map (called d-TASS map) is generated. As shown experimentally in a previous study, this map is invariant under rotation, translation and scale change. Moreover, it is shearing and noise resistant. The contribution of the present study is firstly, to prove theoretically that d-TASS is rotation and scale change invariant and secondly to propose a new descriptor extracted from the blocks within the scalogram. When applied to shape retrieval from commonly used image databases like MPEG-7 Core Experiments Shape-1 dataset, Multiview Curve Dataset and marines animals of SQUID dataset, experimental results yield very encouraging efficiency and effectiveness of the new analysis approach and the proposed descriptor

Next Generation of Product Search and Discovery

Online shopping has become an important part of people’s daily life with the rapid development of e-commerce. In some domains such as books, electronics, and CD/DVDs, online shopping has surpassed or even replaced the traditional shopping method. Compared with traditional retailing, e-commerce is information intensive. One of the key factors to succeed in e-business is how to facilitate the consumers’ approaches to discover a product. Conventionally a product search engine based on a keyword search or category browser is provided to help users find the product information they need. The general goal of a product search system is to enable users to quickly locate information of interest and to minimize users’ efforts in search and navigation. In this process human factors play a significant role. Finding product information could be a tricky task and may require an intelligent use of search engines, and a non-trivial navigation of multilayer categories. Searching for useful product information can be frustrating for many users, especially those inexperienced users. This dissertation focuses on developing a new visual product search system that effectively extracts the properties of unstructured products, and presents the possible items of attraction to users so that the users can quickly locate the ones they would be most likely interested in. We designed and developed a feature extraction algorithm that retains product color and local pattern features, and the experimental evaluation on the benchmark dataset demonstrated that it is robust against common geometric and photometric visual distortions. Besides, instead of ignoring product text information, we investigated and developed a ranking model learned via a unified probabilistic hypergraph that is capable of capturing correlations among product visual content and textual content. Moreover, we proposed and designed a fuzzy hierarchical co-clustering algorithm for the collaborative filtering product recommendation. Via this method, users can be automatically grouped into different interest communities based on their behaviors. Then, a customized recommendation can be performed according to these implicitly detected relations. In summary, the developed search system performs much better in a visual unstructured product search when compared with state-of-art approaches. With the comprehensive ranking scheme and the collaborative filtering recommendation module, the user’s overhead in locating the information of value is reduced, and the user’s experience of seeking for useful product information is optimized