Pierre Soille

Watersheds in digital spaces: an efficient algorithm based on immersion simulations

A fast and flexible algorithm for computing watersheds in digital gray-scale images is introduced. A review of watersheds and related motion is first presented, and the major methods to determine watersheds are discussed. The algorithm is based on an immersion process analogy, in which the flooding of the water in the picture is efficiently simulated using of queue of pixel. It is described in detail provided in a pseudo C language. The accuracy of this algorithm is proven to be superior to that of the existing implementations, and it is shown that its adaptation to any kind of digital grid and its generalization to n-dimensional images (and even to graphs) are straightforward. The algorithm is reported to be faster than any other watershed algorithm. Applications of this algorithm with regard to picture segmentation are presented for magnetic resonance (MR) imagery and for digital elevation models. An example of 3-D watershed is also provided. >

Constrained connectivity for hierarchical image partitioning and simplification

This paper introduces an image partitioning and simplification method based on the constrained connectivity paradigm. According to this paradigm, two pixels are said to be connected if they satisfy a series of constraints defined in terms of simple measures such as the maximum gray-level differences over well-defined pixel paths and regions. The resulting connectivity relation generates a unique partition of the image definition domain. The simplification of the image is then achieved by setting each segment of the partition to the mean value of the pixels falling within this segment. Fine to coarse partition hierarchies (and, therefore, images of increasing degree of simplification) are produced by varying the threshold value associated with each connectivity constraint. The paper also includes a generalization to multichannel images, application examples, a review of related image segmentation techniques, and pseudocode for an implementation based on queue and stack data structures.

Directional morphological filtering

We show that a translation invariant implementation of min/max filters along a line segment of slope in the form of an irreducible fraction dy/dx can be achieved at the cost of 2+k min/max comparisons per image pixel, where k=max(|dx|,|dy|). Therefore, for a given slope, the computation time is constant and independent of the length of the line segment. We then present the notion of periodic moving histogram algorithm. This allows for a similar performance to be achieved in the more general case of rank filters and rank-based morphological filters. Applications to the filtering of thin nets and computation of both granulometries and orientation fields are detailed. Finally, two extensions are developed. The first deals with the decomposition of discrete disks and arbitrarily oriented discrete rectangles, while the second concerns min/max filters along gray tone periodic line segments.

Morphological segmentation of binary patterns

This paper presents a method for segmenting binary patterns into seven mutually exclusive categories: core, islet, loop, bridge, perforation, edge, and branch. This is achieved by applying a series of morphological transformations such as erosions, geodesic dilations, reconstruction by dilation, anchored skeletonisation, etc. The proposed method depends on a single parameter only and can be used for characterising binary patterns with emphasis on connections between their parts as measured at varying analysis scales. This is illustrated on two examples related to land cover maps and circuit board defect detection.

A Global Human Settlement Layer From Optical HR/VHR RS Data: Concept and First Results

A general framework for processing high and very-high resolution imagery in support of a Global Human Settlement Layer (GHSL) is presented together with a discussion on the results of the first operational test of the production workflow. The test involved the mapping of 24.3 million km2 of the Earth surface spread in four continents, corresponding to an estimated population of 1.3 billion people in 2010. The resolution of the input image data ranges from 0.5 to 10 meters, collected by a heterogeneous set of platforms including satellite SPOT (2 and 5), CBERS 2B, RapidEye (2 and 4), WorldView (1 and 2), GeoEye 1, QuickBird 2, Ikonos 2, and airborne sensors. Several imaging modes were tested including panchromatic, multispectral and pan-sharpened images. A new fully automatic image information extraction, generalization and mosaic workflow is presented that is based on multiscale textural and morphological image features extraction. New image feature compression and optimization are introduced, together with new learning and classification techniques allowing for the processing of HR/VHR image data using low-resolution thematic layers as reference. A new systematic approach for quality control and validation allowing global spatial and thematic consistency checking is proposed and applied. The quality of the results are discussed by sensor, band, resolution, and eco-regions. Critical points, lessons learned and next steps are highlighted.

Recursive implementation of erosions and dilations along discrete lines at arbitrary angles

Van Herk (1992) has shown that the erosion/dilation operator with a linear structuring element of an arbitrary length can be implemented in only three min/max operations per pixel. In this paper, the algorithm is generalized to erosions and dilations along discrete lines at arbitrary angles. We also address the padding problem; so that the operation can be performed in place without copying the pixels to and from an intermediate buffer. Applications to image filtering and to radial decompositions of discs are presented.

On the Validity of Fractal Dimension Measurements in Image Analysis

Abstract Fractal dimension is a parameter frequently used to analyze textures at different scales. There are several alternative definitions of the fractal dimension and consequently many algorithms have been proposed to determine its value. In this paper, we assess the robustness of all these algorithms. This is achieved by comparing their respective behavior under linear transformations of the image intensity values. A theoretical comparison shows that algorithms invariant to these transformations are restricted to Flat Structuring Element, Variogram, and Power Spectrum methods. This comparison is illustrated by experiments performed on simulated and natural images.

Morphological image compositing

Image mosaicking can be defined as the registration of two or more images that are then combined into a single image. Once the images have been registered to a common coordinate system, the problem amounts to the definition of a selection rule to output a unique value for all those pixels that are present in more than one image. This process is known as image compositing. In this paper, we propose a compositing procedure based on mathematical morphology and its marker-controlled segmentation paradigm. Its scope is to position seams along salient image structures so as to diminish their visibility in the output mosaic even in the absence of radiometric corrections or blending procedures. We also show that it is suited to the seamless minimization of undesirable transient objects occurring in the regions where two or more images overlap. The proposed methodology and algorithms are illustrated for the composition of satellite images minimizing cloud cover

Generalized geodesy via geodesic time

Abstract The time necessary to cover a path on a grey-scale image is the sum of the grey-level values along the path. The geodesic time between two points in a grey-scale image is defined as the smallest amount of time allowing to link these points. The geodesic time allows the definition of generalized geodetic distances, erosions, dilations, and skeletons by influence zones. An application to minimal path extraction on grey-scale images is presented.

On morphological operators based on rank filters

Rank order morphological operators have been designed to better cope with shape variations and noise than the corresponding operators with plain structuring elements. In this paper, starting from a brief historical overview of rank order filters and erosions/dilations in digital image processing, rank order based morphological operators are surveyed. We also highlight the relations between these operators and show that many are similar if not equivalent. An extensive bibliography is provided.