Eric Backer

Resolving motion correspondence for densely moving points

Studies the motion correspondence problem for which a diversity of qualitative and statistical solutions exist. We concentrate on qualitative modeling, especially in situations where assignment conflicts arise either because multiple features compete for one detected point or because multiple detected points fit a single feature point. We leave out the possibility of point track initiation and termination because that principally conflicts with allowing for temporary point occlusion. We introduce individual, combined, and global motion models and fit existing qualitative solutions in this framework. Additionally, we present a tracking algorithm that satisfies these-possibly constrained-models in a greedy matching sense, including an effective way to handle detection errors and occlusion. The performance evaluation shows that the proposed algorithm outperforms existing greedy matching algorithms. Finally, we describe an extension to the tracker that enables automatic initialization of the point tracks. Several experiments show that the extended algorithm is efficient, hardly sensitive to its few parameters, and qualitatively better than other algorithms, including the presumed optimal statistical multiple hypothesis tracker.

A maximum variance cluster algorithm

We present a partitional cluster algorithm that minimizes the sum-of-squared-error criterion while imposing a hard constraint on the cluster variance. Conceptually, hypothesized clusters act in parallel and cooperate with their neighboring clusters in order to minimize the criterion and to satisfy the variance constraint. In order to enable the demarcation of the cluster neighborhood without crucial parameters, we introduce the notion of foreign cluster samples. Finally, we demonstrate a new method for cluster tendency assessment based on varying the variance constraint parameter.

Genetic network modeling

The inference of genetic interactions from measured expression data is one of the most challenging tasks of modern functional genomics. When successful, the learned network of regulatory interactions yields a wealth of useful information. An inferred genetic network contains information about the pathway to which a gene belongs and which genes it interacts with. Furthermore, it explains the function of the gene in terms of how it influences other genes and indicates which genes are pathway initiators and therefore potential drug targets. Obviously, such wealth comes at a price and that of genetic network modeling is that it is an extremely complex task. Therefore, it is necessary to develop sophisticated computational tools that are able to extract relevant information from a limited set of microarray measurements and integrate this with different information sources, to come up with reliable hypotheses of a genetic regulatory network. Thus far, a multitude of modeling approaches have been proposed for discovering genetic networks. However, it is unclear what the advantages and disadvantages of each of the different approaches are and how their results can be compared. In this review, genetic network models are put in a historical perspective that explains why certain models were introduced. Various modeling assumptions and their consequences are also highlighted. In addition, an overview of the principal differences and similarities between the approaches is given by considering the qualitative properties of the chosen models and their learning strategies.

A Clustering Performance Measure Based on Fuzzy Set Decomposition

Clustering is primarily used to uncover the true underlying structure of a given data set and, for this purpose, it is desirable to subject the same data to several different clustering algorithms. This paper attempts to put an order on the various partitions of a data set obtained from different clustering algorithms. The goodness of each partition is expressed by means of a performance measure based on a fuzzy set decomposition of the data set under consideration. Several experiments reported in here show that the proposed performance measure puts an order on different partitions of the same data which is consistent with the error rate of a classifier designed on the basis of the obtained cluster labelings.

Finding point correspondences using simulated annealing

Abstract Identifying corresponding points between two recordings of a point set has always been an important problem in stereo vision applications. We describe this matching problem in terms of cost minimization and present an algorithm to approach the minimal cost mapping using simulated annealing. The algorithm calculates the costs to match all possible point pairs and tries to minimize the sum of the costs of all matched points. Starting from an initial mapping, it uses a random rearrangement scheme to alter the mapping towards the optimal (minimal cost) mapping.

Image sharpening by morphological filtering

Abstract This paper introduces a class of iterative morphological image operators with applications to sharpen digitized gray-scale images. It is proved that all image operators using a concave structuring function have sharpening properties. By using a Laplacian property, we introduce the underlying partial differential equation that governs this class of iterative image operators. The parameters of the operator can be determined on the basis of an estimation of the amount of blur present in the image. For discrete implementations of the operator class it is shown that operators using a parabolic structuring function have an efficient implementation and isotropic sharpening behavior.

A cellular coevolutionary algorithm for image segmentation

Clustering is inherently a difficult problem, both with respect to the definition of adequate models as well as to the optimization of the models. We present a model for the cluster problem that does not need knowledge about the number of clusters a priori. This property is among others useful in the image segmentation domain, which we especially address. Further, we propose a cellular coevolutionary algorithm for the optimization of the model. Within this scheme multiple agents are placed in a regular two-dimensional (2-D) grid representing the image, which imposes neighboring relations on them. The agents cooperatively consider pixel migration from one agent to the other in order to improve the homogeneity of the ensemble of the image regions they represent. If the union of the regions of neighboring agents is homogeneous then the agents form alliances. On the other hand, if an agent discovers a deviant subject, it isolates the subject. In the experiments we show the effectiveness of the proposed method and compare it to other segmentation algorithms. The efficiency can easily be improved by exploiting the intrinsic parallelism of the proposed method.

Segmentation of Muscle Cell Pictures: A Preliminary Study

This paper describes a procedure for segmenting muscle cell pictures. The segmentation procedure is broken into two logical parts. The first part segments the picture into regions composed of cells or clumps of cells using a number of low-level operations. The second part of the procedure involves the segmentation of the cell clumps into individual cells. This is done by using a hierarchical clustering algorithm to group together those boundary points of a cell clump that belong to the same globally convex sections of the boundary. The dissimilarity measure used by the clustering algorithm is based only on information about the shape of the boundary, where this information is derived from line segments interior to the boundary. This procedure has given us satisfactory results on a number of test pictures.

Multi-criterion optimization for genetic network modeling

A major problem associated with the reverse engineering of genetic networks from micro-array data is how to reliably find genetic interactions when faced with a relatively small number of arrays compared to the number of genes. To cope with this dimensionality problem, it is imperative to employ additional (biological) knowledge about real genetic networks, such as limited connectivity, redundancy, stability and robustness, to sensibly constrain the modeling process. In previous work (Proceedings of the 2001 IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, Baltimore, MA, June 2001; Proceedings of the Second International Conference on Systems Biology, Pasadena, CA, November 2, pp. 222-230), we have shown that by applying single constraints, the inference of genetic interactions under realistic conditions can be significantly improved. Recently (Proceedings of the SPIE, San Jose, CA, January 2002), we have made a preliminary study on how these approaches based on single constraints solve the underlying bi-criterion optimization problem. In this paper, we study the problem of how multiple constraints can be combined by formulating genetic network modeling as a multi-criterion optimization problem. Results are shown on artificial as well as on a real data example.

Motion tracking as a constrained optimization problem

In this paper we pose the problem of tracking of a varying number of points through an image sequence as a multi-objective optimization problem with additional hard constraints. One of the objectives is to find smooth tracks based on second-order motion characteristics optimized over several frames. The corresponding optimization algorithm we present is a sequential heuristic search algorithm that adequately prunes the search tree in such a way that its exponential order remains low. When the algorithm is compared to other tracking algorithms, it turns out that the proposed algorithm is easier to tune and generally more efficient and more accurate.