Fourier Descriptors Based on the Structure of the Human Primary Visual Cortex with Applications to Object Recognition

Abstract

In this paper we propose a supervised object recognition method using new global features and inspired by the model of the human primary visual cortex V1 as the semidiscrete roto-translation group SE(2, N ) = Z N ⋊ R 2 . The proposed technique is based on generalized Fourier descriptors on the latter group, which are invariant to natural geometric transformations (rotations, translations). These descriptors are then used to feed an SVM classifier. We have tested our method against the COIL-100 image database and the ORL face database, and compared it with other techniques based on traditional descriptors, global and local. The obtained results have shown that our approach looks extremely efficient and stable to noise, in presence of which it outperforms the other techniques analyzed in the paper.

Visual illusions via neural dynamics: Wilson–Cowan-type models and the efficient representation principle

“…Motivated by neuro-phyisiological evidence, we assume that RPs of different neurons are "deducible" one from the other via a linear transformation. As detailed in Franken, 2010, Prandi andGauthier, 2017], see also [Bertalmío et al, 2019, Section 3.1], this amounts to the fact that the linear operator L : L 2 (Q) → L 2 (Q × [0, π)) is a continuous wavelet transform (also called invertible orientation score transform). That is, there exists a mother wavelet Ψ ∈ L 2 (R 2 ) such that Lf (x, θ) = f * (Ψ * • R −θ ) (x).…”

A Semidiscrete Version of the Citti-Petitot-Sarti Model as a Plausible Model for Anthropomorphic Image Reconstruction and Pattern Recognition

“…This chapter collects the results of numerical testing in image processing applications of the various concepts explained throughout this work. These are mostly taken from the already mentioned papers [42,13,16,12,10].…”

“…We evaluate separately the recognition rate obtained using the four previous invariant descriptors and the combination of the RPS & BS invariants to test their complementarity. Then, we compare their performance with the Hu's moments (HM), the Zernike's moments (ZM), the Fourier-Mellin transform (FM) (see the Appendix in [10]), and the local SIFT and HOG descriptors [25] whose performance under the same conditions has been tested in [20], Since we use the RBF kernel in the SVM classification process, this depends on the kernel size σ . The results presented here are obtained by choosing empirically the value σ opt that provided maximum recognition rate.…”

Highly Corrupted Image Inpainting Through Hypoelliptic Diffusion

“…The starting point of our work is the Citti-Petitot-Sarti model of the primary visual cortex V1 [14,32,33,37], and our recent contributions [5][6][7][8][9]16]. This model has also been deeply studied in [17][18][19]23].…”

“…Image reconstruction methods based upon this principle are presented in detail in the previous works [7,9]. The same techniques are applied to the semi-discrete hypoelliptic evolution associated with the well-known Mumford elastica model in [10] and to image recognition in [5,35]. See [36] for a survey of these methods.…”