Abderrahim Elmoataz

Graph-based tools for microscopic cellular image segmentation

We propose a framework of graph-based tools for the segmentation of microscopic cellular images. This framework is based on an object oriented analysis of imaging problems in pathology. Our graph tools rely on a general formulation of discrete functional regularization on weighted graphs of arbitrary topology. It leads to a set of useful tools which can be combined together to address various image segmentation problems in pathology. To provide fast image segmentation algorithms, we also propose an image simplification based on graphs as a pre processing step. The abilities of this set of image processing discrete tools are illustrated through automatic and interactive segmentation schemes for color cytological and histological images segmentation problems.

Multi-resolution graph-based analysis of histopathological whole slide images: Application to mitotic cell extraction and visualization

In this paper, we present a graph-based multi-resolution approach for mitosis extraction in breast cancer histological whole slide images. The proposed segmentation uses a multi-resolution approach which reproduces the slide examination done by a pathologist. Each resolution level is analyzed with a focus of attention resulting from a coarser resolution level analysis. At each resolution level, a spatial refinement by label regularization is performed to obtain more accurate segmentation around boundaries. The proposed segmentation is fully unsupervised by using domain specific knowledge.

Eikonal equation adaptation on weighted graphs: fast geometric diffusion process for local and non-local image and data processing

In this paper we propose an adaptation of the Eikonal equation on weighted graphs, using the framework of Partial difference Equations, and with the motivation of extending this equation’s applications to any discrete data that can be represented by graphs. This adaptation leads to a finite difference equation defined on weighted graphs and a new efficient algorithm for multiple labels simultaneous propagation on graphs, based on such equation. We will show that such approach enables the resolution of many applications in image and high dimensional data processing using a unique framework.

Automated region of interest retrieval and classification using spectral analysis

Efficient use of whole slide imaging in pathology needs automated region of interest (ROI) retrieval and classification, through the use of image analysis and data sorting tools. One possible method for data sorting uses Spectral Analysis for Dimensionality Reduction. We present some interesting results in the field of histopathology and cytohematology.In histopathology, we developed a Computer-Aided Diagnosis system applied to low-resolution images representing the totality of histological breast tumour sections. The images can be digitized directly at low resolution or be obtained from sub-sampled high-resolution virtual slides. Spectral Analysis is used (1) for image segmentation (stroma, tumour epithelium), by determining a «distance» between all the images of the database, (2) for choosing representative images and characteristic patterns of each histological type in order to index them, and (3) for visualizing images or features similar to a sample provided by the pathologist.In cytohematology, we studied a blood smear virtual slide acquired through high resolution oil scanning and Spectral Analysis is used to sort selected nucleated blood cell classes so that the pathologist may easily focus on specific classes whose morphology could then be studied more carefully or which can be analyzed through complementary instruments, like Multispectral Imaging or Raman MicroSpectroscopy.

Partial Difference Equations over Graphs: Morphological Processing of Arbitrary Discrete Data

Mathematical Morphology (MM) offers a wide range of operators to address various image processing problems. These processing can be defined in terms of algebraic set or as partial differential equations (PDEs). In this paper, a novel approach is formalized as a framework of partial difference equations (PdEs) on weighted graphs. We introduce and analyze morphological operators in local and nonlocal configurations. Our framework recovers classical local algebraic and PDEs-based morphological methods in image processing context; generalizes them for nonlocal configurations and extends them to the treatment of any arbitrary discrete data that can be represented by a graph. It leads to considering a new field of application of MM processing: the case of high-dimensional multivariate unorganized data.

On the

In this paper we introduce a new family of partial difference operators on graphs and study equations involving these operators. This family covers local variational

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-Laplacian and

-Laplacian,

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-Laplacian on Graphs with Applications in Image and Data Processing

-Laplacian, nonlocal