André Bleau

Watershed-Based Segmentation and Region Merging

In recent years, the watershed line has emerged as the primary tool of mathematical morphology for image segmentation. Several very efficient algorithms have been devised for the determination of watersheds. Nevertheless, the application of watershed algorithms to an image is often disappointing: the image is oversegmented into a large number of tiny, shallow watersheds, where one wanted to obtain only a few deep ones. This paper presents a novel approach to watershed merging. Mainly, it addresses the following question: given an image, what is the closest image that has a simpler watershed structure? The basic idea is to replicate the process of watershed merging that takes place when rain falls over a real landscape: smaller watersheds progressively fill until an overflow occurs. The water then flows to a nearby, larger or deeper watershed, in which the overflown watersheds are merged. The methods presented in this paper apply the minimum extensive modifications possible to a given image to obtain a new one that has many fewer watersheds but is still “close” to the original. Their usefulness is demonstrated for several biomedical applications.

A new set of fast algorithms for mathematical morphology I: idempotent geodesic transforms

Abstract This paper generalizes the geodesic transforms used in mathematical morphology for binary image processing by introducing the concept of morphological operations constrained by an initial set and a transformable set. These new operations allow the efficient extension of geodesic constraints to grayscale image processing as they can be implemented with simple algorithms. They also make possible the application of new constraints, leading to new transforms with new properties. Two particular cases of these new transforms are then studied thoroughly: erosion and dilation operations constrained by an initial set and a transformable set that are iterated until idempotence is reached, or idempotent geodesic transforms (IGT). A sequential local transform (SLT) algorithm is presented that greatly speeds up the computation of IGT; the conditions for convergence for the algorithm and the relation between speed of convergence and the complexity of the initial set and the transformable set are investigated.

A new set of fast algorithms for mathematical morphology II: identification of topographic features on grayscale images

Abstract New algorithms for morphological image processing are presented. These algorithms are based on recursive idempotent geodesic transforms using a pixel-dependent structuring element. Such transforms are used as building blocks to construct new, fast algorithms for the location of topographic features on grayscale images. This approach is first used for the location of regional extrema and then for watershed and water parting determination. The new algorithms are compared to previously known ones in terms of speed and results quality. The same basic transforms are also used to build evaluation tools for measuring the relative importance of watersheds and water partings. The usefulness of the new approach is illustrated by application examples on a biomedical image.