In analysis of microscopy based images, a major challenge lies in splitting apart cells that appear to overlap because they are too densely packed. This task is complicated by the physics of the image acquisition that causes large variations in pixel intensities. Each image typically contains thousands of cells with each cell having a different orientation, size and intensity histogram. In this paper, a spatial intensity model of a nucleus is incorporated into [1] to aid cell segmentation from microscopy datasets. An energy functional is defined and with it the spatial intensity distribution of a nuclei is modeled as a Gaussian distribution with constant intensity background. Experimental results on a variety of microscopic data validate its effectiveness.

This work presents an algorithm for the segmentation of myocardial regions in echocardiography imaging based on the statistics of the radiofrequency image. We formulate the problem of segmentation in a maximum likelihood framework using the Generalized Gaussian as an a priori distribution. We minimize the resulting functional using a radial basis functions-based multiphase level set model. Numerical results obtained on both simulation and in vivo data demonstrate the capacity of our approach to segment myocardial regions in echocardiography imaging.

We consider a recent parametric level-set segmentation approach where the implicit interface is the zero level of a continuous function expanded onto compactly supported radial basis functions, defined by their centers, coefficients and supports. We propose to introduce prior knowledge of the shape to be recovered by placing the centers quasi-uniformly over an uncertainty area.

The partial differential equation driving level-set evolution in segmentation is usually solved using finite differences schemes. In this paper, we propose an alternative scheme based on radial basis functions (RBFs) collocation. This approach provides a continuous representation of both the implicit function and its zero level set. We show that compactly supported RBFs (CSRBFs) are particularly well suited to collocation in the framework of segmentation. In addition, CSRBFs allow us to reduce the computation cost using a kd-tree-based strategy for neighborhood representation. Moreover, we show that the usual reinitialization step of the level set may be avoided by simply constraining the l1-norm of the CSRBF parameters. As a consequence, the final solution is topologically more flexible, and may develop new contours (i.e., new zero-level components), which are difficult to obtain using reinitialization. The behavior of this approach is evaluated from numerical simulations and from medical data of various kinds, such as 3-D CT bone images and echocardiographic ultrasound images.

We propose a novel method for reconstructing d dimensional signals with irregular samples, without any restriction on their positions. We develop a multi-resolution approximation scheme using compactly supported radial basis functions (CSRBFs). Samples are first clustered using principal component analysis and their centroids define CSRBF centers. The mean square error is minimized by selecting centers where the largest local error at the previous level is. We shall prove the effectiveness of our algorithm in one-and two-dimensional cases with Gaussian noise

We propose a new approach for surface reconstruction from any unorganized point set, with a fixed amount of parameters. First, we consider some local approximations by compactly supported radial basis functions (CSRBFs), then blend them by a partition of unity method (PU). In our scheme, we start by selecting CSRBFs centers, then construct partitions, finally parameters are calculated in order to minimize, on each sub-domain, the mean square error with a regularization constraint. We demonstrate the effectiveness of our approach on several models with different points distributions.

Most of the meshes coming from a variety of source are over sampled and exhibit highly irregular connectivity that prevent efficient wavelet analysis. Remeshing comes as a solution to sampling and connectivity optimization with respect to the geometry. The main drawback of existing subdivision remeshing approaches is the lack of control either on the number of triangles or on the geometrical error. We propose a new remeshing scheme that directly produces wavelet-based multiresolution meshes which does not suffer from the previous limitations. We provide a finer control on the resulting number of triangles by using an adaptive subdivision scheme. We also show a lowering of the local resulting geometrical error by using a new curvature-based subdivision criterion.