Persistent homology for object segmentation in multidimensional grayscale images

•Demonstration of the potential of the algebraic topology in performing object segmentation tasks.•New combination between the topological constructions and superpixels of images.•Insensitivity of the proposed method to continuous deformations and stability against perturbations of the input function.•Capability to be applied on multidimensional images and to perform object segmentation without the need of prior parameters. [Display omitted] In this paper, we develop a methodology originating from algebraic topology, and we demonstrate its capability of performing multidimensional object segmentation without the need of prior parameters. Persistent homology is a method used in algebraic topology to study qualitative features of data that persist across varying scales. The construction of a topological complex on the image is followed by a filtration scheme that consists of composing a nested sequence of cell complexes on which the persistent homology is computed. The most persistent homology classes are extracted by identifying 1D and 2D chains with large lifespans, which allows salient objects in 2D and 3D images to be segmented and detected. A comparison between this method and other segmentation techniques on a synthetic image shows the advantages of the proposed method. The strength of this technique is reflected in its insensitivity to continuous deformations and perturbations of the input function and in its independence of prior parameters. The results obtained on real and biomedical 2D and 3D images also demonstrate the potential of this method.