Performance of three recursive algorithms for fast space-variant Gaussian filtering

A Computational Framework for Realistic Retina Modeling

Computational simulations of the retina have led to valuable insights about the biophysics of its neuronal activity and processing principles. A great number of retina models have been proposed to reproduce the behavioral diversity of the different visual processing pathways. While many of these models share common computational stages, previous efforts have been more focused on fitting specific retina functions rather than generalizing them beyond a particular model. Here, we define a set of computational retinal microcircuits that can be used as basic building blocks for the modeling of different retina mechanisms. To validate the hypothesis that similar processing structures may be repeatedly found in different retina functions, we implemented a series of retina models simply by combining these computational retinal microcircuits. Accuracy of the retina models for capturing neural behavior was assessed by fitting published electrophysiological recordings that characterize some of the best-known phenomena observed in the retina: adaptation to the mean light intensity and temporal contrast, and differential motion sensitivity. The retinal microcircuits are part of a new software platform for efficient computational retina modeling from single-cell to large-scale levels. It includes an interface with spiking neural networks that allows simulation of the spiking response of ganglion cells and integration with models of higher visual areas.

A frequency averaging framework for the solution of complex dynamic systems

A frequency averaging framework is proposed for the solution of complex linear dynamic systems. It is remarkable that, while the mid-frequency region is usually very challenging, a smooth transition from low- through mid- and high-frequency ranges is possible and all ranges can now be considered in a single framework. An interpretation of the frequency averaging in the time domain is presented and it is explained that the average may be evaluated very efficiently in terms of system solutions.

Fast space-variant elliptical filtering using box splines

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying size, elongation and orientation using a fixed number of computations per pixel. The associated algorithm, which is based upon a family of smooth compactly supported piecewise polynomials, the radially-uniform box splines, is realized using preintegration and local finite-differences. The radially-uniform box splines are constructed through the repeated convolution of a fixed number of box distributions, which have been suitably scaled and distributed radially in an uniform fashion. The attractive features of these box splines are their asymptotic behavior, their simple covariance structure, and their quasi-separability. They converge to Gaussians with the increase of their order, and are used to approximate anisotropic Gaussians of varying covariance simply by controlling the scales of the constituent box distributions. Based upon the second feature, we develop a technique for continuously controlling the size, elongation and orientation of these Gaussian-like functions. Finally, the quasi-separable structure, along with a certain scaling property of box distributions, is used to efficiently realize the associated space-variant elliptical filtering, which requires O(1) computations per pixel irrespective of the shape and size of the filter.

Accurate and efficient method for smoothly space-variant Gaussian blurring

This paper presents a computationally efficient algorithm for smoothly space-variant Gaussian blurring of images. The proposed algorithm uses a specialized filter bank with optimal filters computed through principal component analysis. This filter bank approximates perfect space-variant Gaussian blurring to arbitrarily high accuracy and at greatly reduced computational cost compared to the brute force approach of employing a separate low-pass filter at each image location. This is particularly important for spatially variant image processing such as foveated coding. Experimental results show that the proposed algorithm provides typically 10 to 15 dB better approximation of perfect Gaussian blurring than the blended Gaussian pyramid blurring approach when using a bank of just eight filters.

Virtual Retina: a biological retina model and simulator, with contrast gain control

We propose a new retina simulation software, called Virtual Retina, which transforms a video into spike trains. Our goal is twofold: Allow large scale simulations (up to 100,000 neurons) in reasonable processing times and keep a strong biological plausibility, taking into account implementation constraints. The underlying model includes a linear model of filtering in the Outer Plexiform Layer, a shunting feedback at the level of bipolar cells accounting for rapid contrast gain control, and a spike generation process modeling ganglion cells. We prove the pertinence of our software by reproducing several experimental measurements from single ganglion cells such as cat X and Y cells. This software will be an evolutionary tool for neuroscientists that need realistic large-scale input spike trains in subsequent treatments, and for educational purposes.