Efficient algorithms for motion and deformation recovery with biological applications

Determining the motion and deformation of genomic structures, such as chromosome territories, chromatin domains, and DNA replication and transcription sites, in living cells is a fundamental and challenging problem in research of the genomic organization and function of the cell nucleus. Due to a number of limitations, current techniques for microscopic imaging and labeling cannot yet provide the necessary spatial and temporal resolutions for tracking the rather complicated DNA dynamics. Significant amount of information between two consecutive reference frames or images could be lost, thus preventing most of the existing approaches from yielding satisfactory solutions. In this paper, we present a geometric-techniques-based approach for solving this problem. Our techniques can effectively recover rather complicated motion including non-uniform translation, rotation, scaling, and deformation represented by a sequence of microscopic images, and has a very low time complexity which is particularly desired by many biological applications in which an enormous amount of DNA need to be processed. Our techniques can also be used to reconstruct the 3-D surfaces of large genomic structures, such as chromosome territories, and are readily applicable to images in other formats for recovering motion and reconstructing surfaces of deformable objects.