Surface approximation based image simplification and applications

In this paper, we consider the problems of simplifying microscopic images of cell nucleus and segmenting genomic structures (such as DNA replication/transcription sites or foci and chromatin domains) from such images. DNA foci often have small sizes, and could be hidden by diffuse signals or quasi-foci (fanned by the overlapping of some neighboring foci), making the simplification and segmentation tasks extremely challenging. Existing simplification algorithms often yield large-sized images and take unreasonably long execution time. Available segmentation algorithms either fail reporting all DNA foci or generate incorrect boundaries. Based on an interesting observation on the intensity of microscopic images of cell nucleus, we present in this paper a novel approach for simplifying microscopic images by approximating the intensity surface of images by a set of normal distribution functions. Our technique yields much smaller-sized simplified images and runs in near linear time. With this technique, we further develop an efficient algorithm for segmenting DNA foci. Comparing with existing segmentation algorithms (such as watershed method), our algorithm detects all possible foci and generates much more accurate boundary of the detected foci. Our techniques are readily extendable to other types of images.