Noise adaptive matrix edge field analysis of small sized heterogeneous onion layered textures for characterizing human embryonic stem cell nuclei

We present a methodology for characterizing small size heterogeneous textures that are hard to analyze in general due to the paucity of pixels and textural heterogeneity. The methodology overcomes the limitation for a large class of heterogeneous textures that exhibit onion layer type textural variation, where we may assume that within a layer the behavior is homogeneous, but may vary from layer to layer. The shape of the onion layers is data dependent; radial symmetry is not required. We use an energy functional approach for simultaneous smoothing and segmentation that relies on two key innovations: a matrix edge field, and adaptive weighting of the measurements relative to the smoothing process model. The matrix edge function adaptively and implicitly modulates the shape, size, and orientation of smoothing neighborhoods over different regions of the texture. It thus provides directional information on the texture that is not available in the more conventional scalar edge field based approaches. The adaptive measurement weighting varies the weighting between the measurements at each pixel. Image based analysis of human embryonic stem cells is the motivating application for this new approach, and we show how the features extracted using this approach can be used to automate the classification of pluripotent vs. differentiated stem cell nuclei based on confocal images of fluorescent GFP-labeled chromatin.