THIR: Topological Histopathological Image Retrieval

TL;DR

THIR tackles the challenge of efficient, label-free CBMIR in digital pathology by leveraging topological data analysis. It builds a $3R$-dimensional descriptor from cubical persistence across the RGB channels, focusing on the Betti curve for $\beta_1$ and performs retrieval with Euclidean distance in a fully unsupervised, training-free pipeline. On the BreaKHis dataset, THIR delivers state-of-the-art retrieval performance across magnifications while requiring only about 20 minutes of CPU computation and no training, highlighting interpretability and practicality in resource-constrained clinical settings. These results demonstrate the potential of topological signatures as robust, scalable features for histopathological image retrieval and suggest avenues for expanding to higher-dimensional, multi-channel, and whole-slide analyses.

Abstract

According to the World Health Organization, breast cancer claimed the lives of approximately 685,000 women in 2020. Early diagnosis and accurate clinical decision making are critical in reducing this global burden. In this study, we propose THIR, a novel Content-Based Medical Image Retrieval (CBMIR) framework that leverages topological data analysis specifically, Betti numbers derived from persistent homology to characterize and retrieve histopathological images based on their intrinsic structural patterns. Unlike conventional deep learning approaches that rely on extensive training, annotated datasets, and powerful GPU resources, THIR operates entirely without supervision. It extracts topological fingerprints directly from RGB histopathological images using cubical persistence, encoding the evolution of loops as compact, interpretable feature vectors. The similarity retrieval is then performed by computing the distances between these topological descriptors, efficiently returning the top-K most relevant matches. Extensive experiments on the BreaKHis dataset demonstrate that THIR outperforms state of the art supervised and unsupervised methods. It processes the entire dataset in under 20 minutes on a standard CPU, offering a fast, scalable, and training free solution for clinical image retrieval.

Figures (6)

• Figure 1: shows the main workflow of a CBMIR. It contains two main phases, offline and online. The same FE applies in both phases to extract features. Then, the Euclidean distance as a distance measurement function is applied to find the top-3 similar patches. On top of the query image and the retrieved images, their labels are mentioned.
• Figure 2: THIR model. We first generate persistence diagrams for any input images, utilizing the cubical complex on each channel of the images. Next, we derive our topological feature vectors, represented as the Betti curves. The values of this curve are then input into the CBMIR workflow to produce the results of the search engine.
• Figure 3: shows three channels of an RGB image under different $th$ values. These values were defined as a sublevel filtration in [0-1] for the normalized images. Each channel goes through the same $th$ values to illustrate the $th$ impacts on channels.
• Figure 4: shows four random queries and their similar patches. Each row represents a query image (leftmost) followed by its top-3 retrieved images. The true class labels are shown as Query Label and Retrieved Label. Misclassified retrievals are outlined in red.
• Figure 5: shows four panels, each with four concatenated Betti curves for four random images. The label of each image is represented in a small bar on top of each panel. $L = 0$ and $L = 1$ mean "Benign and "Malignant" cases, respectively. This explains how images with the same cancer grade have similar Betti curves. The y-axis illustrates the number of loops at each filtration step, and the x-axis represents the filtration step for each channel. $R = 200$ yields 200 filter steps for each channel, which means 600 filter steps in total for an RGB image.