|Ph.D Student||Shamai Gil|
|Subject||Topics in Geometry Processing and Computational Pathology|
|Department||Department of Electrical and Computers Engineering||Supervisor||Dr. Ron Kimmel|
|Full Thesis text|
With the recent growth in size of available data, appears the need for simplification and dimensionality
reduction. Real world data typically lay in high dimensional space. Manifold learning is an approach for dimensionality reduction, in which data is assumed to lay on a low dimensional manifold that resides in the high dimensional space. By discovering the structure of such manifolds, data can be significantly simplified, analyzed and understood.
Multidimensional scaling (MDS) is a dimensionality reduction procedure that is applied to manifolds. Its goal is to find an embedding of the manifold points, such that the Euclidean distance between each pair of embedded points is as close as possible to the geodesic distance between their corresponding points on the manifold. The resulting embedding is invariant to isometric deformation of the manifold.
Thus, when dealing with approximately isometric mappings, MDS can be used for significantly simplifying various tasks, such as non-rigid shape correspondence.
MDS requires the computation of all geodesic distances of the manifold it is applied on. Even when using efficient methods for fast geodesics computation, MDS is impractical when dealing with more than 10,000 points. Regardless of MDS, computation of geodesic distances is one of the major keystones in various applications in graphics, computer vision and geometrical image processing.
The first part of our research was devoted to developing two methods, which we termed FMDS and NMDS, for efficient approximation of geodesic distances, and for combining these techniques in order to obtain an efficient MDS procedure.
In the second part, we defined the Geodesic Distance Descriptor (GDD). We showed that it is an effective descriptor of non-rigid shapes, and unlike the MDS embedding, does not suffer from embedding errors. Like MDS, the computation of the GDD relies on geodesic distances. We showed how to efficiently compute the GDD using the FMDS and NMDS. Finally, we showed how to use the GDD in order to obtain state-of-the-art results in non-rigid shape correspondence.
Molecular profiling is a common technique which allows clinicians to determine various characteristics of the cancer. Quick and accurate profiling is crucial for guiding the treatment and estimating prognosis. Current methods are limited to time consuming and costly techniques that require trained pathologists and advanced equipment. Hematoxylin and Eosin (H&E) are the most widely used biopsy stains in medical diagnosis and are routinely used for every specimen. Unlike molecular profiling, H&E is very cheap and widely available. The third and last part of my research was devoted to predicting the molecular profile of the cancer from H&E images using deep neural networks. This has the potential to revolutionize the way molecular pathology operates today, improve its accuracy and significantly reduce the cost of analysis and time consumption.