Elena A. Zhizhina

Object Extraction Using a Stochastic Birth-and-Death Dynamics in Continuum

We define a new birth and death dynamics dealing with configurations of disks in the plane. We prove the convergence of the continuous process and propose a discrete scheme converging to the continuous case. This framework is developed to address image processing problems consisting in detecting a configuration of objects from a digital image. The derived algorithm is applied for tree crown extraction and bird detection from aerial images. The performance of this approach is shown on real data.

A Marked Point Process Model Including Strong Prior Shape Information Applied to Multiple Object Extraction From Images

Object extraction from images is one of the most important tasks in remote sensing image analysis. For accurate extraction from very high resolution VHR images, object geometry needs to be taken into account. A method for incorporating strong yet flexible prior shape information into a marked point process model for the extraction of multiple objects of complex shape is presented. To control the computational complexity, the objects considered are defined using the image data and the prior shape information. To estimate the optimal configuration of objects, the process is sampled using a Markov chain based on a stochastic birth-and-death process on the space of multiple objects. The authors present several experimental results on the extraction of tree crowns from VHR aerial images.

A Marked Point Process Model with Strong Prior Shape Information for the Extraction of Multiple, Arbitrarily-Shaped Objects

We define a method for incorporating strong prior shape information into a recently extended Markov point process model for the extraction of arbitrarily-shaped objects from images. To estimate the optimal configuration of objects, the process is sampled using a Markov chain based on a stochastic birth-and-death process defined in a space of multiple objects. The single objects considered are defined by both the image data and the prior information in a way that controls the computational complexity of the estimation problem. The method is tested via experiments on a very high resolution aerial image of a scene composed of tree crowns.

A Stochastic Model for Automatic Extraction of 3D Neuronal Morphology

Tubular structures are frequently encountered in bio-medical images. The center-lines of these tubules provide an accurate representation of the topology of the structures. We introduce a stochastic Marked Point Process framework for fully automatic extraction of tubular structures requiring no user interaction or seed points for initialization. Our Marked Point Process model enables unsupervised network extraction by fitting a configuration of objects with globally optimal associated energy to the centreline of the arbors. For this purpose we propose special configurations of marked objects and an energy function well adapted for detection of 3D tubular branches. The optimization of the energy function is achieved by a stochastic, discrete-time multiple birth and death dynamics. Our method finds the centreline, local width and orientation of neuronal arbors and identifies critical nodes like bifurcations and terminals. The proposed model is tested on 3D light microscopy images from the DIADEM data set with promising results.

Extraction of arbitrarily shaped objects using stochastic multiple birth-and-death dynamics and active contours.

We extend the marked point process models that have been used for object extraction from images to arbitrarily shaped objects, without greatly increasing the computational complexity of sampling and estimation. The approach can be viewed as an extension of the active contour methodology to an a priori unknown number of objects. Sampling and estimation are based on a stochastic birth-and-death process defined in a space of multiple, arbitrarily shaped objects, where the objects are defined by the image data and prior information. The performance of the approach is demonstrated via experimental results on synthetic and real data.

Gibbs field approach for evolutionary analysis of regulatory signal of gene expression

We propose a new approach to modeling a nucleotide sequence evolution subject to constraints on the secondary structure. The approach is based on the problem of optimizing a functional that involves both standard evolution of the primary structure and a condition of secondary structure conservation. We discuss simulation results in the example of evolution in the case of classical attenuation regulation.

Gibbs Field Approaches in Image Processing Problems

In this paper, we address the problem of image denoising using a stochastic differential equation approach. Proposed stochastic dynamics schemes are based on the property of diffusion dynamics to converge to a distribution on global minima of the energy function of the model, under a special cooling schedule (the annealing procedure). To derive algorithms for computer simulations, we consider discrete-time approximations of the stochastic differential equation. We study convergence of the corresponding Markov chains to the diffusion process. We give conditions for the ergodicity of the Euler approximation scheme. In the conclusion, we compare results of computer simulations using the diffusion dynamics algorithms and the standard Metropolis–Hasting algorithm. Results are shown on synthetic and real data.