Edwin Carlinet

A comparative review of component tree computation algorithms

Abstract

Connected operators are morphological tools that have the property of filtering images without creating new contours and without moving the contours that are preserved. Those operators are related to the max-tree and min-tree repre- sentations of images, and many algorithms have been proposed to compute those trees. However, no exhaustive comparison of these algorithms has been proposed so far, and the choice of an algorithm over another depends on many parameters. Since the need for fast algorithms is obvious for production code, we present an in-depth comparison of the existing algorithms in a unique framework, as well as variations of some of them that improve their efficiency. This comparison involves both sequential and parallel algorithms, and execution times are given with respect to the number of threads, the input image size, and the pixel value quantization. Eventually, a decision tree is given to help the user choose the most appropriate algorithm with respect to the user requirements. To favor reproducible research, an online demo allows the user to upload an image and bench the different algorithms, and the source code of every algorithms has been made available.

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Getting a morphological tree of shapes for multivariate images: Paths, traps and pitfalls

Abstract

The Tree of Shapes is a morphological tree that provides an high-level hierarchical representation of the image suitable for many image processing tasks. This structure has the desirable properties to be self-dual and contrast-invariant and describes the organization of the objects through level lines inclusion. Yet it is defined on gray-level while many images have multivariate data (color images, multispectral images…) where information are split across channels. In this paper, we propose some leads to extend the tree of shapes on colors with classical approaches based on total orders, more recent approaches based on graphs and also a new distance-based method. Eventually, we compare these approaches through denoising to highlight their strengths and weaknesses and show the strong potential of the new methods compared to classical ones.

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Meaningful disjoint level lines selection

Abstract

Many methods based on the morphological notion of shapes (i.e., connected components of level sets) have been proved to be very efficient in shape recognition and shape analysis. The inclusion relationship of the level lines (boundaries of level sets) forms the tree of shapes, a tree-based image representation with a high potential. Numerous applications using this tree representation have been proposed. In this article, we propose an efficient algorithm that extracts a set of disjoint level lines in the image. These selected level lines yields a simplified image with clean contours, which also provides an intuitive idea about the main structure of the tree of shapes. Besides, we obtain a saliency map without transition problems around the contours by weighting level lines with their significance. Experimental results demonstrate the efficiency and usefulness of our method.

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A morphological tree of shapes for color images

Abstract

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A comparison of many max-tree computation algorithms

Abstract

With the development of connected filters in the last decade, many algorithms have been proposed to compute the max-tree. Max-tree allows computation of the most advanced connected operators in a simple way. However, no exhaustive comparison of these algorithms has been proposed so far and the choice of an algorithm over another depends on many parameters. Since the need for fast algorithms is obvious for production code, we present an in depth comparison of five algorithms and some variations of them in a unique framework. Finally, a decision tree will be proposed to help the user choose the most appropriate algorithm according to their requirements.

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A quasi-linear algorithm to compute the tree of shapes of $n$-D images

Abstract

To compute the morphological self-dual representation of images, namely the tree of shapes, the state-of-the-art algorithms do not have a satisfactory time complexity. Furthermore the proposed algorithms are only effective for 2D images and they are far from being simple to implement. That is really penalizing since a self-dual represen- tation of images is a structure that gives rise to many powerful operators and applications, and that could be very useful for 3D images. In this paper we propose a simple-to-write algorithm to compute the tree of shapes; it works for nD images and has a quasi-linear complexity when data quantization is low, typically 12 bits or less. To get that result, this paper introduces a novel representation of images that has some amazing properties of continuity, while remaining discrete.

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