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.