Overview and Comparison of Python Image Processing Tools with Gabor Functions

With the invention and development of digital photography technology, the number of images obtained for various purposes has dramatically increased. So the need arose for efficient methods of processing, transferring and storing them. It is obvious that the methods of working with images should be scientifically grounded and reflect the peculiarities of human visual perception. One of such methods is systems of Gabor functions, which are a basis in the space ${\mathbb{L}}^{\mathrm{2}}\left(\mathbb{R}\right)$. Their construction is based on the application of the wavelet theory and multiresolution analysis presented in this article. The next step after building the necessary mathematical model of images is its efficient and convenient software implementation. Python is a great tool for doing this. The purpose of this article is to provide an overview and comparison of libraries containing ready-made implementations of these functions, both as simple linear filters and as whole wavelet-bases.

Quantum-like signal-tuned approach to V1 modeling

Signal-tuned Gabor functions — Gaussian-modulated sinusoids whose parameters are determined by a spatial or spectral “tuning signal” — have previously been shown to provide a plausible model for the stimulus-dependent receptive fields and responses of the simple and complex cells of the primary visual cortex (V1). The signal-tuned responses obey Schrödinger equations, which has led to the proposal of a quantum-like model for V1 cells: by considering the squared magnitude of a particular signal-tuned wave function as a probability density, one arrives at a Poisson spiking process which appears consistent with the neurophysiological findings. Here, by incorporating Hermite-polynomial factors to the signal-tuned Gabor functions, we obtain a generalized quantum-like signal-tuned model for which further relevant properties are demonstrated, such as receptive-field coding of the stimulus and its derivatives, saturating spatial summation curves and half-wave rectification of the simple cell responses. Although only a one-dimensional approach is considered here, such properties will carry over to a two-dimensional model, in which case, as our preliminary analysis indicates, end-stopping — another important feature of cortical cells — can also be accommodated.

The Two-Dimensional Gabor Function Adapted to Natural Image Statistics: A Model of Simple-Cell Receptive Fields and Sparse Structure in Images

The two-dimensional Gabor function is adapted to natural image statistics, leading to a tractable probabilistic generative model that can be used to model simple cell receptive field profiles, or generate basis functions for sparse coding applications. Learning is found to be most pronounced in three Gabor function parameters representing the size and spatial frequency of the two-dimensional Gabor function and characterized by a nonuniform probability distribution with heavy tails. All three parameters are found to be strongly correlated, resulting in a basis of multiscale Gabor functions with similar aspect ratios and size-dependent spatial frequencies. A key finding is that the distribution of receptive-field sizes is scale invariant over a wide range of values, so there is no characteristic receptive field size selected by natural image statistics. The Gabor function aspect ratio is found to be approximately conserved by the learning rules and is therefore not well determined by natural image statistics. This allows for three distinct solutions: a basis of Gabor functions with sharp orientation resolution at the expense of spatial-frequency resolution, a basis of Gabor functions with sharp spatial-frequency resolution at the expense of orientation resolution, or a basis with unit aspect ratio. Arbitrary mixtures of all three cases are also possible. Two parameters controlling the shape of the marginal distributions in a probabilistic generative model fully account for all three solutions. The best-performing probabilistic generative model for sparse coding applications is found to be a gaussian copula with Pareto marginal probability density functions.

Generalized signal-tuned Gabor approach for signal representation and analysis

The signal-tuned Gabor approach is based on spatial or spectral Gabor functions whose parameters are determined, respectively, by the Fourier and inverse Fourier transforms of a given “tuning” signal. The sets of spatial and spectral signal-tuned functions, for all possible frequencies and positions, yield exact representations of the tuning signal. Moreover, such functions can be used as kernels for space-frequency transforms which are tuned to the specific features of their inputs, thus allowing analysis with high conjoint spatio-spectral resolution. Based on the signal-tuned Gabor functions and the associated transforms, a plausible model for the receptive fields and responses of cells in the primary visual cortex has been proposed. Here, we present a generalization of the signal-tuned Gabor approach which extends it to the representation and analysis of the tuning signal’s fractional Fourier transform of any order. This significantly broadens the scope and the potential applications of the approach.

The Performance of Short-Term Heart Rate Variability in the Detection of Congestive Heart Failure

Congestive heart failure (CHF) is a cardiac disease associated with the decreasing capacity of the cardiac output. It has been shown that the CHF is the main cause of the cardiac death around the world. Some works proposed to discriminate CHF subjects from healthy subjects using either electrocardiogram (ECG) or heart rate variability (HRV) from long-term recordings. In this work, we propose an alternative framework to discriminate CHF from healthy subjects by using HRV short-term intervals based on 256 RR continuous samples. Our framework uses a matching pursuit algorithm based on Gabor functions. From the selected Gabor functions, we derived a set of features that are inputted into a hybrid framework which uses a genetic algorithm andk-nearest neighbour classifier to select a subset of features that has the best classification performance. The performance of the framework is analyzed using both Fantasia and CHF database from Physionet archives which are, respectively, composed of 40 healthy volunteers and 29 subjects. From a set of nonstandard 16 features, the proposed framework reaches an overall accuracy of 100% with five features. Our results suggest that the application of hybrid frameworks whose classifier algorithms are based on genetic algorithms has outperformed well-known classifier methods.

Signal-Tuned Gabor Functions as Models for Stimulus-Dependent Cortical Receptive Fields

We propose and analyze a model, based on signal-tuned Gabor functions, for the receptive fields and responses of V1 cells. Signal-tuned Gabor functions are gaussian-modulated sinusoids whose parameters are obtained from a given, spatial, or spectral “tuning” signal. These functions can be proven to yield exact representations of their tuning signals and have recently been proposed as the kernels of a variant Gabor transform—the signal-tuned Gabor transform (STGT)—which allows the accurate detection of spatial and spectral events. Here we show that by modeling the receptive fields of simple and complex cells as signal-tuned Gabor functions and expressing their responses as STGTs, we are able to replicate the properties of these cells when tested with standard grating and slit inputs, at the same time emulating their stimulus-dependent character as revealed by recent neurophysiological studies.