A Comprehensive Look at Coding Techniques on Riemannian Manifolds

By Masoud Faraki, Mehrtash Harandi, Fatih Murat Porikli. 2018

15 citations recorded by the source corpus.

Core to many learning pipelines is visual recognition such as image and video classification. In such applications, having a compact yet rich and informative representation plays a pivotal role. An underlying assumption in traditional coding schemes [e.g., sparse coding (SC)] is that the data geometrically comply with the Euclidean space. In other words, the data are presented to the algorithm in vector form and Euclidean axioms are fulfilled. This is of course restrictive in machine learning, computer vision, and signal processing, as shown by a large number of recent studies. This paper takes a further step and provides a comprehensive mathematical framework to perform coding in curved and non-Euclidean spaces, i.e., Riemannian manifolds. To this end, we start by the simplest form of coding, namely, bag of words. Then, inspired by the success of vector of locally aggregated descriptors in addressing computer vision problems, we will introduce its Riemannian extensions. Finally, we study Riemannian form of SC, locality-constrained linear coding, and collaborative coding. Through rigorous tests, we demonstrate the superior performance of our Riemannian coding schemes against the state-of-the-art methods on several visual classification tasks, including head pose classification, video-based face recognition, and dynamic scene recognition.

Subfields: Computer Vision and Pattern Recognition

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Citations in the corpus

On Generalizing Beyond Domains in Cross-Domain Continual Learning (2022, background): “This will ensure Σ remains PSD and yields valid similarity scores [7, 8].”
Cross-Domain Similarity Learning for Face Recognition in Unseen Domains (2021, background): “In Riemannian geometry, the Euclidean space R is a Riemannian manifold equipped with the inner product defined as 〈x,y〉 = xΣ y,x,y ∈ R [11, 14].”