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 lowrank thermal representations for each case. Then, we embed lowrank 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 (crossvalidated accuracy of 71.36% (69.42%-73.3%)).

Thermal imagery for monitoring of body temperature provides a powerful tool to decrease health risks (e.g., burning) for patients during medical imaging (e.g., magnetic resonance imaging). The presented approach discusses an experiment to simulate radiology conditions with infrared imaging along with an automatic thermal monitoring/tracking system. The thermal tracking system uses an incremental low-rank noise reduction applying incremental singular value decomposition (SVD) and applies color based clustering for initialization of the region of interest (ROI) boundary. Then a particle filter tracks the ROI(s) from the entire thermal stream (video sequence). The thermal database contains 15 subjects in two positions (i.e., sitting, and lying) in front of thermal camera. This dataset is created to verify the robustness of our method with respect to motion-artifacts and in presence of additive noise (2–20%—salt and pepper noise). The proposed approach was tested for the infrared images in the dataset and was able to successfully measure and track the ROI continuously (100% detecting and tracking the temperature of participants), and provided considerable robustness against noise (unchanged accuracy even in 20% additive noise), which shows promising performance.

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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.