3D Shape Similarity Using Vectors of Locally Aggregated Tensors

IEEE International Conference on Image Processing 2013International audienceIn this paper, we present an efficient 3D object retrieval method invariant to scale, orientation and pose. Our approach is based on the dense extraction of discriminative local descriptors extracted from 2D views. We aggregate the descriptors into a single vector signature using tensor products. The similarity between 3D models can then be efficiently computed with a simple dot product. Experiments on the SHREC12 commonly-used benchmark demonstrate that our approach obtains superior performance in searching for generic shapes

Enhancing Deep Learning Models through Tensorization: A Comprehensive Survey and Framework

The burgeoning growth of public domain data and the increasing complexity of deep learning model architectures have underscored the need for more efficient data representation and analysis techniques. This paper is motivated by the work of (Helal, 2023) and aims to present a comprehensive overview of tensorization. This transformative approach bridges the gap between the inherently multidimensional nature of data and the simplified 2-dimensional matrices commonly used in linear algebra-based machine learning algorithms. This paper explores the steps involved in tensorization, multidimensional data sources, various multiway analysis methods employed, and the benefits of these approaches. A small example of Blind Source Separation (BSS) is presented comparing 2-dimensional algorithms and a multiway algorithm in Python. Results indicate that multiway analysis is more expressive. Contrary to the intuition of the dimensionality curse, utilising multidimensional datasets in their native form and applying multiway analysis methods grounded in multilinear algebra reveal a profound capacity to capture intricate interrelationships among various dimensions while, surprisingly, reducing the number of model parameters and accelerating processing. A survey of the multi-away analysis methods and integration with various Deep Neural Networks models is presented using case studies in different application domains.Comment: 34 pages, 8 figures, 4 table

Image Completion with Heterogeneously Filtered Spectral Hints

Image completion with large-scale free-form missing regions is one of the most challenging tasks for the computer vision community. While researchers pursue better solutions, drawbacks such as pattern unawareness, blurry textures, and structure distortion remain noticeable, and thus leave space for improvement. To overcome these challenges, we propose a new StyleGAN-based image completion network, Spectral Hint GAN (SH-GAN), inside which a carefully designed spectral processing module, Spectral Hint Unit, is introduced. We also propose two novel 2D spectral processing strategies, Heterogeneous Filtering and Gaussian Split that well-fit modern deep learning models and may further be extended to other tasks. From our inclusive experiments, we demonstrate that our model can reach FID scores of 3.4134 and 7.0277 on the benchmark datasets FFHQ and Places2, and therefore outperforms prior works and reaches a new state-of-the-art. We also prove the effectiveness of our design via ablation studies, from which one may notice that the aforementioned challenges, i.e. pattern unawareness, blurry textures, and structure distortion, can be noticeably resolved. Our code will be open-sourced at: https://github.com/SHI-Labs/SH-GAN.Comment: wacv2

The Role of Riemannian Manifolds in Computer Vision: From Coding to Deep Metric Learning

A diverse number of tasks in computer vision and machine learning enjoy from representations of data that are compact yet discriminative, informative and robust to critical measurements. Two notable representations are offered by Region Covariance Descriptors (RCovD) and linear subspaces which are naturally analyzed through the manifold of Symmetric Positive Definite (SPD) matrices and the Grassmann manifold, respectively, two widely used types of Riemannian manifolds in computer vision. As our first objective, we examine image and video-based recognition applications where the local descriptors have the aforementioned Riemannian structures, namely the SPD or linear subspace structure. Initially, we provide a solution to compute Riemannian version of the conventional Vector of Locally aggregated Descriptors (VLAD), using geodesic distance of the underlying manifold as the nearness measure. Next, by having a closer look at the resulting codes, we formulate a new concept which we name Local Difference Vectors (LDV). LDVs enable us to elegantly expand our Riemannian coding techniques to any arbitrary metric as well as provide intrinsic solutions to Riemannian sparse coding and its variants when local structured descriptors are considered. We then turn our attention to two special types of covariance descriptors namely infinite-dimensional RCovDs and rank-deficient covariance matrices for which the underlying Riemannian structure, i.e. the manifold of SPD matrices is out of reach to great extent. %Generally speaking, infinite-dimensional RCovDs offer better discriminatory power over their low-dimensional counterparts. To overcome this difficulty, we propose to approximate the infinite-dimensional RCovDs by making use of two feature mappings, namely random Fourier features and the Nystrom method. As for the rank-deficient covariance matrices, unlike most existing approaches that employ inference tools by predefined regularizers, we derive positive definite kernels that can be decomposed into the kernels on the cone of SPD matrices and kernels on the Grassmann manifolds and show their effectiveness for image set classification task. Furthermore, inspired by attractive properties of Riemannian optimization techniques, we extend the recently introduced Keep It Simple and Straightforward MEtric learning (KISSME) method to the scenarios where input data is non-linearly distributed. To this end, we make use of the infinite dimensional covariance matrices and propose techniques towards projecting on the positive cone in a Reproducing Kernel Hilbert Space (RKHS). We also address the sensitivity issue of the KISSME to the input dimensionality. The KISSME algorithm is greatly dependent on Principal Component Analysis (PCA) as a preprocessing step which can lead to difficulties, especially when the dimensionality is not meticulously set. To address this issue, based on the KISSME algorithm, we develop a Riemannian framework to jointly learn a mapping performing dimensionality reduction and a metric in the induced space. Lastly, in line with the recent trend in metric learning, we devise end-to-end learning of a generic deep network for metric learning using our derivation