Embedded Deep Regularized Block HSIC Thermomics for Early Diagnosis of Breast Cancer

Thermography has been used extensively as a complementary diagnostic tool in breast cancer detection. Among thermographic methods matrix factorization (MF) techniques show an unequivocal capability to detect thermal patterns corresponding to vasodilation in cancer cases. One of the biggest challenges in such techniques is selecting the best representation of the thermal basis. In this study, an embedding method is proposed to address this problem and Deep-semi-nonnegative matrix factorization (Deep-SemiNMF) for thermography is introduced, then tested for 208 breast cancer screening cases. First, we apply Deep-SemiNMF to infrared images to extract low-rank thermal representations for each case. Then, we embed low-rank bases to obtain one basis for each patient. After that, we extract 300 thermal imaging features, called thermomics, to decode imaging information for the automatic diagnostic model. We reduced the dimensionality of thermomics by spanning them onto Hilbert space using RBF kernel and select the three most efficient features using the block Hilbert Schmidt Independence Criterion Lasso (block HSIC Lasso). The preserved thermal heterogeneity successfully classified asymptomatic versus symptomatic patients applying a random forest model (cross-validated accuracy of 71.36% (69.42%-73.3%)).

Skeletonization and Reconstruction based on Graph Morphological Transformations

Multiscale shape skeletonization on pixel adjacency graphs is an advanced intriguing research subject in the field of image processing, computer vision and data mining. The previous works in this area almost focused on the graph vertices. We proposed novel structured based graph morphological transformations based on edges opposite to the current node based transformations and used them for deploying skeletonization and reconstruction of infrared thermal images represented by graphs. The advantage of this method is that many widely used path based approaches become available within this definition of morphological operations. For instance, we use distance maps and image foresting transform (IFT) as two main path based methods are utilized for computing the skeleton of an image. Moreover, In addition, the open question proposed by Maragos et al (2013) about connectivity of graph skeletonization method are discussed and shown to be quite difficult to decide in general case.

Mathematical Morphology via Category Theory

Mathematical morphology contributes many profitable tools to image processing area. Some of these methods considered to be basic but the most important fundamental of data processing in many various applications. In this paper, we modify the fundamental of morphological operations such as dilation and erosion making use of limit and co-limit preserving functors within (Category Theory). Adopting the well-known matrix representation of images, the category of matrix, called Mat, can be represented as an image. With enriching Mat over various semirings such as Boolean and (max,+) semirings, one can arrive at classical definition of binary and gray-scale images using the categorical tensor product in Mat. With dilation operation in hand, the erosion can be reached using the famous tensor-hom adjunction. This approach enables us to define new types of dilation and erosion between two images represented by matrices using different semirings other than Boolean and (max,+) semirings. The viewpoint of morphological operations from category theory can also shed light to the claimed concept that mathematical morphology is a model for linear logic.