Topological persistence based on pixels for object segmentation in biomedical images

In this paper, we show that topological persistence can be employed in biomedical image processing to perform object segmentation. First we model the pixels of the image by combinatorial transformation into a cubical complex that we will call the pixels' complex. Then a nested sequence of complexes is built on which the persistent homology is computed. By identifying the 1D chains with large life spans, the most persistent classes are extracted. This allows to segment the salient objects in the biomedical image and to spot their components. An example was applied first on a toy image of coins that demonstrate the applicability of the method. Results on two real biomedical images, the first recorded by a quantitative phase technique and the second represents a classical image of cells show the potential of this technique. The insensitivity to continuous deformations and the independence to prior parameters reveals the strength of this method.