TopoImages: Incorporating Local Topology Encoding into Deep Learning Models for Medical Image Classification

Topological structures in image data, such as connected components and loops, play a crucial role in understanding image content (e.g., biomedical objects). Despite remarkable successes of numerous image processing methods that rely on appearance information, these methods often lack sensitivity to topological structures when used in general deep learning (DL) frameworks. In this paper, we introduce a new general approach, called TopoImages (for Topology Images), which computes a new representation of input images by encoding local topology of patches. In TopoImages, we leverage persistent homology (PH) to encode geometric and topological features inherent in image patches. Our main objective is to capture topological information in local patches of an input image into a vectorized form. Specifically, we first compute persistence diagrams (PDs) of the patches, and then vectorize and arrange these PDs into long vectors for pixels of the patches. The resulting multi-channel image-form representation is called a TopoImage. TopoImages offers a new perspective for data analysis. To garner diverse and significant topological features in image data and ensure a more comprehensive and enriched representation, we further generate multiple TopoImages of the input image using various filtration functions, which we call multi-view TopoImages. The multi-view TopoImages are fused with the input image for DL-based classification, with considerable improvement. Our TopoImages approach is highly versatile and can be seamlessly integrated into common DL frameworks. Experiments on three public medical image classification datasets demonstrate noticeably improved accuracy over state-of-the-art methods.