Sumit Kumar Nath

Cell segmentation using coupled level sets and graph-vertex coloring

Current level-set based approaches for segmenting a large number of objects are computationally expensive since they require a unique level set per object (the N-level set paradigm), or [log2N] level sets when using a multiphase interface tracking formulation. Incorporating energy-based coupling constraints to control the topological interactions between level sets further increases the computational cost to O(N2). We propose a new approach, with dramatic computational savings, that requires only four, or fewer, level sets for an arbitrary number of similar objects (like cells) using the Delaunay graph to capture spatial relationships. Even more significantly, the coupling constraints (energy-based and topological) are incorporated using just constant O(1) complexity. The explicit topological coupling constraint, based on predicting contour collisions between adjacent level sets, is developed to further prevent false merging or absorption of neighboring cells, and also reduce fragmentation during level set evolution. The proposed four-color level set algorithm is used to efficiently and accurately segment hundreds of individual epithelial cells within a moving monolayer sheet from time-lapse images of in vitro wound healing without any false merging of cells.

Quantitative cell motility for in vitro wound healing using level set-based active contour tracking

Quantifying the behavior of cells individually, and in clusters as part of a population, under a range of experimental conditions, is a challenging computational task with many biological applications. We propose a versatile algorithm for segmentation and tracking of multiple motile epithelial cells during wound healing using time-lapse video. The segmentation part of the proposed method relies on a level set-based active contour algorithm that robustly handles a large number of cells. The tracking part relies on a detection-based multiple-object tracking method with delayed decision enabled by multi-hypothesis testing. The combined method is robust to complex cell behavior including division and apoptosis, and to imaging artifacts such as illumination changes

Moving object segmentation using the flux tensor for biological video microscopy

Time lapse video microscopy routinely produces terabyte sized biological image sequence collections, especially in high throughput environments, for unraveling cellular mechanisms, screening biomarkers, drug discovery, image-based bioinformatics, etc. Quantitative movement analysis of tissues, cells, organelles or molecules is one of the fundamental signals of biological importance. The accurate detection and segmentation of moving biological objects that are similar but nonhomogeneous is the focus of this paper. The problem domain shares similarities with multimedia video analytics. The grayscale structure tensor fails to disambiguate between stationary and moving features without computing dense velocity fields (i.e. optical flow). In this paper we propose a novel motion detection algorithm based on the flux tensor combined with multi-feature level set-based segmentation, using an efficient additive operator splitting (AOS) numerical implementation, that robustly handles deformable motion of non-homogeneous objects. The flux tensor level set framework effectively handles biological video segmentation in the presence of complex biological processes, background noise and clutter.

Adaptive robust structure tensors for orientation estimation and image segmentation

Recently, Van Den Boomgaard and Van De Weijer have presented an algorithm for texture analysis using robust tensor-based estimation of orientation. Structure tensors are a useful tool for reliably estimating oriented structures within a neighborhood and in the presence of noise. In this paper, we extend their work by using the Geman-McClure robust error function and, developing a novel iterative scheme that adaptively and simultaneously, changes the size, orientation and weighting of the neighborhood used to estimate the local structure tensor. The iterative neighborhood adaptation is initialized using the total least-squares solution for the gradient using a relatively large isotropic neighborhood. Combining our novel region adaptation algorithm, with a robust tensor formulation leads to better localization of low-level edge and junction image structures in the presence of noise. Preliminary results, using synthetic and biological images are presented.

Robust tracking of migrating cells using four-color level set segmentation

Understanding behavior of migrating cells is becoming an emerging research area with many important applications. Segmentation and tracking constitute vital steps of this research. In this paper, we present an automated cell segmentation and tracking system designed to study migration of cells imaged with a phase contrast microscope. For segmentation the system uses active contour level set methods with a novel extension that efficiently prevents false-merge problem. Tracking is done by resolving frame to frame correspondences between multiple cells using a multi-distance, multi-hypothesis algorithm. Cells that move into the field-of-view, arise from cell division or disappear due to apoptosis are reliably segmented and tracked by the system. Robust tracking of cells, imaged with a phase contrast microscope is a challenging problem due to difficulties in segmenting dense clusters of cells. As cells being imaged have vague borders, close neighboring cells may appear to merge. These false-merges lead to incorrect trajectories being generated during the tracking process. Current level-set based approaches to solve the false-merge problem require a unique level set per object (the N-level set paradigm). The proposed approach uses evidence from previous frames and graph coloring principles and solves the same problem with only four level sets for any arbitrary number of similar objects, like cells.

Fast graph partitioning active contours for image segmentation using histograms

We present a method to improve the accuracy and speed, as well as significantly reduce the memory requirements, for the recently proposed Graph Partitioning Active Contours (GPACs) algorithm for image segmentation in the work of Sumengen and Manjunath (2006). Instead of computing an approximate but still expensive dissimilarity matrix of quadratic size, , for a 2D image of size and regular image tiles of size , we use fixed length histograms and an intensity-based symmetric-centrosymmetric extensor matrix to jointly compute terms associated with the complete dissimilarity matrix. This computationally efficient reformulation of GPAC using a very small memory footprint offers two distinct advantages over the original implementation. It speeds up convergence of the evolving active contour and seamlessly extends performance of GPAC to multidimensional images.

Accurate spatial neighborhood relationships for arbitrarily-shaped objects using Hamilton-Jacobi GVD

Many image segmentation approaches rely upon or are enhanced by using spatial relationship information between image regions and their object correspondences. Spatial relationships are usually captured in terms of relative neighborhood graphs such as the Delaunay graph. Neighborhood graphs capture information about which objects are close to each other in the plane or in space but may not capture complete spatial relationships such as containment or holes. Additionally, the typical approach used to compute the Delaunay graph (or its dual, the Voronoi polytopes) is based on using only the point-based (i.e., centroid) representation of each object. This can lead to incorrect spatial neighborhood graphs for sized objects with complex topology, eventually resulting in poor segmentation. This paper proposes a new algorithm for efficiently, and accurately extracting accurate neighborhood graphs in linear time by computing the Hamilton-Jacobi generalized Voronoi diagram (GVD) using the exact Euclidean-distance transform with Laplacian-of-Gaussian, and morphological operators. The algorithm is validated using synthetic, and real biological imagery of epithelial cells.