Julio Esclarín

Image quantization using reaction-diffusion equations

In this paper we present an image quantization model based on a reaction-diffusion partial differential equation. The quantized image is given by the asymptotic state of this equation. Existence and uniqueness of the solution are proved in the framework of viscosity solutions. We introduce an

Semi-automatic segmentation and detection of aorta dissection wall in MDCT angiography.

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Invertibility and Estimation of Two-Parameter Polynomial and Division Lens Distortion Models

stable algorithm in order to compute numerically the solution of the equation, and some experimental results are shown. A new energy functional based on the classical Lloyd method is used to compute the quantizer codewords.

An Iterative Optimization Algorithm for Lens Distortion Correction Using Two-Parameter Models

Aorta dissection is a serious vascular disease produced by a rupture of the tunica intima of the vessel wall that can be lethal to the patient. The related diagnosis is strongly based on images, where the multi-detector CT is the most generally used modality. We aim at developing a semi-automatic segmentation tool for aorta dissections, which will isolate the dissection (or flap) from the rest of the vascular structure. The proposed method is based on different stages, the first one being the semi-automatic extraction of the aorta centerline and its main branches, allowing an subsequent automatic segmentation of the outer wall of the aorta, based on a geodesic level set framework. This segmentation is then followed by an extraction the center of the dissected wall as a 3D mesh using an original algorithm based on the zero crossing of two vector fields. Our method has been applied to five datasets from three patients with chronic aortic dissection. The comparison with manually segmented dissections shows an average absolute distance value of about half a voxel. We believe that the proposed method, which tries to solve a problem that has attracted little attention to the medical image processing community, provides a new and interesting tool to isolate the intimal flap that can provide very useful information to the clinician.

Fast and accurate circle tracking using active contour models

In this paper, we study lens distortion for still images considering two well-known distortion models: the two-parameter polynomial model and the two-parameter division model. We study the invertibility of these models, and we mathematically characterize the conditions for the distortion parameters under which the distortion model defines a one-to-one transformation. This ensures that the inverse transformation is well defined and the distortion-free image can be properly computed, which provides robustness to the distortion models. A new automatic method to correct the radial distortion is proposed, and a comparative analysis for this method is extensively performed using the polynomial and the division models. With the aim of obtaining an accurate estimation of the model, we propose an optimization scheme which iteratively improves the parameters to achieve a better matching between the distorted lines and the edge points. The proposed method estimates two-parameter radial distortion models by detecting...

Tracking the Aortic Lumen Geometry by Optimizing the 3D Orientation of Its Cross-sections

We present an algorithm to automatically estimate two-parameter radial polynomial and division distortion models in images. The method first detects the longest distorted lines within the image by applying the Hough transform enriched with a radial distortion parameter. Once we have obtained a valid initial solution, a two-parameter model is embedded into an iterative nonlinear optimization schema to improve the solution. The minimization aims at reducing the distance from the points to the lines, adjusting two distortion parameters as well as the coordinates of the center of distortion. Furthermore, this allows us to detect more points on the distorted lines in the image, so that the Hough transform is iteratively repeated to extract a better set of lines until no improvement is achieved. We present some experiments on real images with significant distortion to show the ability of the proposed approach to automatically correct this type of distortion as well as a comparison between the polynomial and division models.

Image quantization by nonlinear smoothing

In this paper, we deal with the problem of circle tracking across an image sequence. We propose an active contour model based on a new energy. The center and radius of the circle is optimized in each frame by looking for local minima of such energy. The energy estimation does not require edge extraction, it uses the image convolution with a Gaussian kernel and its gradient which is computed using a GPU–CUDA implementation. We propose a Newton–Raphson type algorithm to estimate a local minimum of the energy. The combination of an active contour model which does not require edge detection and a GPU–CUDA implementation provides a fast and accurate method for circle tracking. We present some experimental results on synthetic data, on real images, and on medical images in the context of aorta vessel segmentation in computed tomography (CT) images.

Affine Invariant Distance Using Multiscale Analysis

We propose a fast incremental technique to compute the 3D geometry of the aortic lumen from a seed point located inside it. Our approach is based on the optimization of the 3D orientation of the cross-sections of the aorta. The method uses a robust ellipse estimation algorithm and an energy-based optimization technique to automatically track the centerline and the cross sections. In order to perform the optimization, we consider the size and the eccentricity of the ellipse which best fit the contour of the aorta on each cross-sectional plane. The method works directly on the original image and does not require a prior segmentation of the aortic lumen. We present some preliminary results which show the accuracy of the method and its ability to cope with challenging real CT (computed tomography) images of aortic lumens with significant angulations due to severe elongations.

Estimation of the Lens Distortion Model by Minimizing a Line Reprojection Error

We present a quantization technique based on the partial differential equation (∂u/∂t) = g(||∇(Gσ * u)||) |∇u|div(∇u/|∇u|) + f(u, t) where |∇u|div(∇u/|∇u|) represents the derivative of the function u in the direction orthogonal to the gradient, Gs is a linear convolution kernel, g is a decreasing function and f(s, t) is a lipschitz function. We assume that when t tends to +∞, f(s,t) tends uniformly to a function f∞(s) which has a finite number of zeros with negative derivative which act as attractors in the system and represent the quantization levels. The location of the zero-crossing of the function f∞s(s) depends on the histogram of the initial image given by u0. We introduce a new energie based in the Lloyd model to compute the quantizer levels. We develop a numerical scheme to discretize the above equation and we present some experimental results.

Automatic correction of perspective and optical distortions

In this paper we introduce an affine invariant distance definition from a