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The complexity of branching and curvilinear morphology of a complete mitochondrial network within each cell is challenging to analyze and quantify. To address this challenge, we developed an image analysis technique using persistent homology with a multiparameter filtration framework, combining image processing techniques in mathematical morphology. We show that such filtrations contain both topological and geometric information about complex cellular organelle structures, which allows a software program to extract meaningful features. Using this information, we also develop a connectivity index that describes the morphology of the branching patterns. As proof of concept, we utilize this approach to study how mitochondrial networks are altered by genetic changes in the Optineurin gene. Mutations in the autophagy gene Optineurin (OPTN) are associated with primary open-angle glaucoma (POAG), amyotrophic lateral sclerosis (ALS), and Paget's disease of the bone, but the pathophysiological mechanism is unclear. We utilized the proposed mathematical morphology-based multiparameter filtration and persistent homology approach to analyze and quantitatively compare how changes in the OPTN gene alter mitochondrial structures from their normal interconnected, tubular morphology into scattered, fragmented pieces. [ABSTRACT FROM AUTHOR]

The application of artificial intelligence (AI) to various medical subfields has been a popular topic of research in recent years. In particular, deep learning has been widely used and has proven effective in many cases. Topological data analysis (TDA)—a rising field at the intersection of mathematics, statistics, and computer science—offers new insights into data. In this work, we develop a novel deep learning architecture that we call TopoResNet that integrates topological information into the residual neural network architecture. To demonstrate TopoResNet, we apply it to a skin lesion classification problem. We find that TopoResNet improves the accuracy and the stability of the training process. [ABSTRACT FROM AUTHOR]

The field of mathematical morphology offers well-studied techniques for image processing and is applicable for studies ranging from materials science to ecological pattern formation. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis. We demonstrate that morphological operations naturally form a multiparameter filtration and that persistent homology can then be used to extract information about both topology and geometry in the images as well as to automate methods for optimizing the study and rendering of structure in images. For illustration, we develop an automated approach that utilizes this framework to denoise binary, grayscale, and color images with salt and pepper and larger spatial scale noise. We measure our example unsupervised denoising approach to state-of-the-art supervised, deep learning methods to show that our results are comparable. [ABSTRACT FROM AUTHOR]

Detecting humans in crowded environment is profitable but challenging in video surveillance. We propose an efficient human detection method by combining both motion and appearance clues. Moving pixels are first extracted by background subtraction, and then a filtering step is used to narrow the range for human template matching. We utilize integral images to fast generate shape information from edge maps of each frame and define the matching probability to be capable of detecting both full-body and partial-body. Representative human templates are constructed by sparse contours on the basis of the point distribution model. Moreover, linear regression analysis is also applied to adaptively adjust the template sizes. With the aid of the proposed foreground ratio filtering and the multi-sized template matching techniques, experimental results show that our method not only can efficiently detect humans in a crowded environment, but also largely enhance the resultant detection accuracy. [ABSTRACT FROM AUTHOR]