Michael H. F. Wilkinson

Connected Shape-Size Pattern Spectra for Rotation and Scale-Invariant Classification of Gray-Scale Images

In this paper, we describe a multiscale and multishape morphological method for pattern-based analysis and classification of gray-scale images using connected operators. Compared with existing methods, which use structuring elements, our method has three advantages. First, in our method, the time needed for computing pattern spectra does not depend on the number of scales or shapes used, i.e., the computation time is independent of the dimensions of the pattern spectrum. Second, size and strict shape attributes can be computed, which we use for the construction of joint 2D shape-size pattern spectra. Third, our method is significantly less sensitive to noise and is rotation-invariant. Although rotation invariance can also be approximated by methods using structuring elements at different angles, this tends to be computationally intensive. The classification performance of these methods is discussed using four image sets: Brodatz, COIL-20, COIL-100, and diatoms. The new method obtains better or equal classification performance to the best competitor with a 5 to 9-fold speed gain

A comparison of algorithms for connected set openings and closings

The implementation of morphological connected set operators for image filtering and pattern recognition is discussed. Two earlier algorithms based on priority queues and hierarchical queues, respectively, are compared to a more recent union-find approach. Unlike the earlier algorithms which process regional extrema in the image sequentially, the union-find method allows simultaneous processing of extrema. In the context of area openings, closings, and pattern spectra, the union-find algorithm outperforms the previous methods on almost all natural and synthetic images tested. Finally, extensions to pattern spectra and the more general class of attribute operators are presented for all three algorithms, and memory usages are compared.

CPM: a deformable model for shape recovery and segmentation based on charged particles

A novel, physically motivated deformable model for shape recovery and segmentation is presented. The model, referred to as the charged-particle model (CPM), is inspired by classical electrodynamics and is based on a simulation of charged particles moving in an electrostatic field. The charges are attracted towards the contours of the objects of interest by an electrostatic field, whose sources are computed based on the gradient-magnitude image. The electric field plays the same role as the potential forces in the snake model, while internal interactions are modeled by repulsive Coulomb forces. We demonstrate the flexibility and potential of the model in a wide variety of settings: shape recovery using manual initialization, automatic segmentation, and skeleton computation. We perform a comparative analysis of the proposed model with the active contour model and show that specific problems of the latter are surmounted by our model. The model is easily extendable to 3D and copes well with noisy images.

Shape Preserving Filament Enhancement Filtering

Morphological connected set filters for extraction of filamentous details from medical images are developed. The advantages of these filters are that they are shape preserving and do not amplify noise. Two approaches are compared: (i) multi-scale filtering (ii) single-step shape filtering using connected set (or attribute) thinnings. The latter method highlights all filamentous structure in a single filtering stage, regardless of the scale. The second approach is an order of magnitude faster than the first, filtering a 2563 volume in 41.65 s on a 400 MHz Pentium II.

Mask-Based Second-Generation Connectivity and Attribute Filters

Connected filters are edge-preserving morphological operators, which rely on a notion of connectivity. This is usually the standard 4 and 8-connectivity, which is often too rigid since it cannot model generalized groupings such as object clusters or partitions. In the set-theoretical framework of connectivity, these groupings are modeled by the more general second-generation connectivity. In this paper, we present both an extension of this theory, and provide an efficient algorithm based on the max-tree to compute attribute filters based on these connectivities. We first look into the drawbacks of the existing framework that separates clustering and partitioning and is directly dependent on the properties of a preselected operator. We then propose a new type of second-generation connectivity termed mask-based connectivity which eliminates all previous dependencies and extends the ways the image domain can be connected. A previously developed dual-input max-tree algorithm for area openings is adapted for the wider class of attribute filters on images characterized by second-generation connectivity. CPU-times for the new algorithm are comparable to the original algorithm, typically deviating less than 10 percent either way

Efficient 2-D Grayscale Morphological Transformations With Arbitrary Flat Structuring Elements

An efficient algorithm is presented for the computation of grayscale morphological operations with arbitrary 2D flat structuring elements (S.E.). The required computing time is independent of the image content and of the number of gray levels used. It always outperforms the only existing comparable method, which was proposed in the work by Van Droogenbroeck and Talbot, by a factor between 3.5 and 35.1, depending on the image type and shape of S.E. So far, filtering using multiple S.E.s is always done by performing the operator for each size and shape of the S.E. separately. With our method, filtering with multiple S.E.s can be performed by a single operator for a slightly reduced computational cost per size or shape, which makes this method more suitable for use in granulometries, dilation-erosion scale spaces, and template matching using the hit-or-miss transform. The discussion focuses on erosions and dilations, from which other transformations can be derived.

Shape representation and recognition through morphological curvature scale spaces

A multiscale, morphological method for the purpose of shape-based object recognition is presented. A connected operator similar to the morphological hat-transform is defined, and two scale-space representations are built, using the curvature function as the underlying one-dimensional signal. Each peak and valley of the curvature is extracted and described by its maximum and average heights and by its extent and represents an entry in the top or bottom hat-transform scale spaces. We demonstrate object recognition based on hat-transform scale spaces for three large data sets, a set of diatom contours, the set of silhouettes from the MPEG-7 database and the set of two-dimensional views of three-dimensional objects from the COIL-20 database. Our approach outperforms other methods for which comparative results exist.

Concurrent Computation of Attribute Filters on Shared Memory Parallel Machines

Morphological attribute filters have not previously been parallelized, mainly because they are both global and non-separable. We propose a parallel algorithm which achieves efficient parallelism for a large class of attribute filters, including attribute openings, closings, thinnings and thickenings, based on Salembiers Max-Trees and Min-trees. The image or volume is first partitioned in multiple slices. We then compute the Max-trees of each slice using any sequential Max-Tree algorithm. Subsequently, the Max-trees of the slices can be merged to obtain the Max-tree of the image. A C-implementation yielded good speed-ups on both a 16-processor MIPS 14000 parallel machine, and a dual-core Opteron-based machine. It is shown that the speed-up of the parallel algorithm is a direct measure of the gain with respect to the sequential algorithm used. Furthermore, the concurrent algorithm shows a speed gain of up to 72% on a single-core processor, due to reduced cache thrashing.

Morphological hat-transform scale spaces and their use in pattern classification

In this paper we present a multi-scale method based on mathematical morphology which can successfully be used in pattern classification tasks. A connected operator similar to the morphological hat-transform is defined, and two scale-space representations are built. The most important features are extracted from the scale spaces by unsupervised cluster analysis, and the resulting pattern vectors provide the input of a decision tree classifier. We report classification results obtained using contour features, texture features, and a combination of these. The method has been tested on two large sets, a database of diatom images and a set of images from the Brodatz texture database. For the diatom images, the method is applied twice, once on the curvature of the outline (contour), and once on the grey-scale image itself.

Optimizing edge detectors for robust automatic threshold selection: coping with edge curvature and noise

The Robust Automatic Threshold Selection algorithm was introduced as a threshold selection based on a simple image statistic. The statistic is an average of the grey levels of the pixels in an image weighted by the response at each pixel of a specific edge detector. Other authors have suggested that many edge detectors may be used within the context of this method instead. A simple proof of this is given, including an extension to any number of image dimensions, and it is shown that in noiseless images with straight line edges these statistics all yield an optimum threshold. Biases caused by curvature of edges and by noise (uniform Gaussian and Poisson) are explored theoretically and on synthetic 2-D images. It is shown that curvature bias may be avoided by proper selection of the edge detector, and a comparison of two noise bias reduction schemes is given. Criteria for optimizing edge detectors are given and the performances of eight edge detectors are investigated in detail. The best results were obtained using two edge detectors which compute an approximation of the square of the gradient. It is shown that this conclusion can be extended to 3-D. Least sensitivity to noise was obtained when using 3 x 3 Sobel filter kernels to approximate partial derivatives in x and y