Energy Minimization Strategy Research Articles

Author Index for Volume 76

This paper presents an original method for analyzing, in an unsupervised way, images supplied by high resolution sonar. We aim at segmenting the sonar image into three kinds of regions: echo areas (due to the reflection of the acoustic wave on the object), shadow areas (corresponding to a lack of acoustic reverberation behind an object lying on the sea-bed), and sea-bottom reverberation areas. This unsupervised method estimates the parameters of noise distributions, modeled by a Weibull probability density function (PDF), and the label field parameters, modeled by a Markov random field (MRF). For the estimation step, we adopt a maximum likelihood technique for the noise model parameters and a least-squares method to estimate the MRF prior model. Then, in order to obtain an accurate segmentation map, we have designed a two-step process that finds the shadow and the echo regions separately, using the previously estimated parameters. First, we introduce a scale-causal and spatial model called SCM (scale causal multigrid), based on a multigrid energy minimization strategy, to find the shadow class. Second, we propose a MRF monoscale model using a priori information (at different level of knowledge) based on physical properties of each region, which allows us to distinguish echo areas from sea-bottom reverberation. This technique has been successfully applied to real sonar images and is compatible with automatic processing of massive amounts of data.

Three-Class Markovian Segmentation of High-Resolution Sonar Images

This paper presents an original method for analyzing, in an unsupervised way, images supplied by high resolution sonar. We aim at segmenting the sonar image into three kinds of regions: echo areas (due to the reflection of the acoustic wave on the object), shadow areas (corresponding to a lack of acoustic reverberation behind an object lying on the sea-bed), and sea-bottom reverberation areas. This unsupervised method estimates the parameters of noise distributions, modeled by a Weibull probability density function (PDF), and the label field parameters, modeled by a Markov random field (MRF). For the estimation step, we adopt a maximum likelihood technique for the noise model parameters and a least-squares method to estimate the MRF prior model. Then, in order to obtain an accurate segmentation map, we have designed a two-step process that finds the shadow and the echo regions separately, using the previously estimated parameters. First, we introduce a scale-causal and spatial model called SCM (scale causal multigrid), based on a multigrid energy minimization strategy, to find the shadow class. Second, we propose a MRF monoscale model using a priori information (at different level of knowledge) based on physical properties of each region, which allows us to distinguish echo areas from sea-bottom reverberation. This technique has been successfully applied to real sonar images and is compatible with automatic processing of massive amounts of data.

A comparative study of existing and new design techniques for protein models

We present a detailed study of the performance and reliability of design procedures based on energy minimization. The analysis is carried out for model proteins where exact results can be obtained through exhaustive enumeration. The efficiency of design techniques is assessed as a function of protein length and the number of classes into which amino acids are coarse grained. It turns out that, while energy minimization strategies can identify correct solutions in most circumstances, it may be impossible for numerical implementations of design algorithms to meet the efficiency required to yield correct solutions in realistic contexts. Alternative design strategies based on an approximate treatment of the free energy are shown to be much more efficient than energy-based methods while requiring nearly the same CPU time. Finally, we present a novel iterative design strategy that incorporates negative design with the use of selected decoy structures that compete significantly with the target native state in housing the designed sequences. This procedure allows one to identify systematically all sequences that fold on a given target structure.

Molecular Mechanics Calculations of Proteins. Comparison of Different Energy Minimization Strategies

A general strategy for performing energy minimization of proteins using the SYBYL molecular modelling program has been developed. The influence of several variables including energy minimization procedure, solvation, dielectric function and dielectric constant have been investigated in order to develop a general method, which is capable of producing high quality protein structures. Avian pancreatic polypeptide (APP) and bovine pancreatic phospholipase A2 (BP PLA2) were selected for the calculations, because high quality X-ray structures exist and because all classes of secondary structure are represented in the structures. The energy minimized structures were evaluated relative to the corresponding X-ray structures. The overall similarity was checked by calculating RMS distances for all atom positions. Backbone conformation was checked by Ramachandran plots and secondary structure elements evaluated by the length on hydrogen bonds. The dimensions of active site in BP PLA2 is very dependent on electrostatic interactions, due to the presence of the positively charged calcium ion. Thus, the distances between calcium and the calcium-coordinating groups were used as a quality index for this protein. Energy minimized structures of the trimeric PLA2 from Indian cobra (N.n.n. PLA2) were used for assessing the impact of protein-protein interactions. Based on the above mentioned criteria, it could be concluded that using the following conditions: Dielectric constant ϵ = 4 or 20; a distance dependent dielectric function and stepwise energy minimization, it is possible to reproduce X-ray structures very accurately without including explicit solvent molecules.