Kevin Loquin

Fuzzy Histograms And Density Estimation

The probability density function is a fundamental concept in statistics. Specifying the density function f of a random variable X on Ω gives a natural description of the distribution of X on the universe Ω. When it cannot be specified, an estimate of this density may be performed by using a sample of n observations independent and identically distributed (X1, ..., Xn) of X . Histogram is the oldest and most widely used density estimator for presentation and exploration of observed univariate data. The construction of a histogram consists in partitioning a given reference interval Ω into p bins Ak and in counting the number Acck of observations belonging to each cell Ak. If all the Ak have the same width h, the histogram is said to be uniform or regular. Let 1lAk be the characteristic function of Ak, we have

Non-Additive Approach for Gradient-Based Edge Detection

In this paper, we propose a new method to perform the first derivative estimation of a discrete intensity distribution. This approach is based on a non-additive aggregation process and provides an estimate of the gradient as intervals instead of single values. These intervals are used to threshold a gradient-based edge detection and therefore discard spurious detections due to noise.

Photoreceptor detection in in-vivo Adaptive Optics images of the retina: Towards a simple interactive tool for the physicians

This article presents a novel photoreceptor detection algorithm applied to in-vivo Adaptive Optics (AO) images of the retina obtained from an advanced ophthalmic diagnosis device. Our algorithm is based on a recursive construction of thresholded connected components when the seeds of the recursions are the regional maxima of the image. This algorithm results in a labeling of the AO image which is then used to segment the image with a marker-controlled watershed algorithm. This method has been implemented in a software currently used by medical experts, and preliminary results are very encouraging.

Imprecise Functional Estimation: The Cumulative Distribution Case

In this paper, we propose an adaptation of the Parzen Rosenblatt cumulative distribution function estimator that uses maxitive kernels. The result of this estimator, on every point of the domain of F, the cumulative distribution to be estimated, is interval valued instead of punctual valued. We prove the consistency of our approach with the classical Parzen Rosenblatt estimator, since, according to consistency conditions between the maxitive kernel involved in the imprecise estimator and the summative kernel involved in the precise estimator, our imprecise estimate contains the precise Parzen Rosenblatt estimate.

Automatic photoreceptor detection in in-vivo adaptive optics retinal images: statistical validation

This article presents a photoreceptor detection algorithm applied to in-vivo Adaptive Optics (AO) images of the retina obtained from an advanced ophthalmic diagnosis device. Our algorithm is based on a recursive construction of thresholded connected components when the seeds of the recursions are the regional maxima of the deconvoluted image. This algorithm is validated on a gold standard dataset obtained thanks to manual cones detections made by ophtalmologist physicians.

Kriging with Ill-known variogram and data

Kriging consists in estimating or predicting the spatial phenomenon at non sampled locations from an estimated random function. Although information necessary to properly select a unique random function model seems to be partially lacking, geostatistics in general, and the kriging methodology in particular, does not account for the incompleteness of the information that seems to pervade the procedure. On the one hand, the collected data may be tainted with errors that can be modelled by intervals or fuzzy intervals. On the other hand, the choice of parameter values for the theoretical variogram, an essential step, contains some degrees of freedom that is seldom acknowledged. In this paper we propose to account for epistemic uncertainty pervading the variogram parameters, and possibly the data set, by means of fuzzy interval uncertainty. We lay bare its impact on the kriging results, improving on previous attempts by Bardossy and colleagues in the late 1980s.

Adaptive optics imaging of retinal microstructures: Image processing for medical applications

Adaptive optics (AO) fundus imaging is an optoelectronic technique allowing an improvement of an order of magnitude of lateral resolution of retinal images. Currently, its main applications in ophthalmology span from photoreceptor to retinal pigment epithelial cells and vessels, each of them being affected by specific diseases. Technological and image processing improvements are expanding the scope of its medical applications. Here we will review some of the current and envisioned applications of AO in clinical practice.

Guaranteed reconstruction for image super-resolution

This paper presents a new reconstruction operator to be used in a super-resolution scheme. Here, by reconstruction in super-resolution, we mean the back-projection operation, i.e. the way K low resolution (LR) images are aggregated to obtain a smooth high resolution (HR) image. Within this method, we replace the usual reconstruction procedure by a non-additive reconstruction operation based on the nice properties of fuzzy partitions. This non-additive reconstruction operator represents a convex family of usual additive reconstruction operators. The obtained reconstructed image is thus a convex family of usual reconstructed images. It allows the super-resolution method to be less sensitive to the choice of the reconstruction method. To make the reading of this method easier, it is presented with 1D signals. We present some experiments to illustrate the proved properties of this new operator.

Estimating the Variance of a Kernel Density Estimation

This article proposes an interval-valued extension of kernel density estimation. We show that the imprecision of this interval-valued estimation is highly correlated with the variance of the density estimation induced by the statistical variations of the set of observations.