Morphological Skeleton Transform Research Articles

A generalized morphological skeleton transform using both internal and external skeleton points

The morphological skeleton transform (MST) is a leading morphological shape representation scheme. In the MST, a given shape is represented as the union of all the maximal disks contained in the shape. The concept of external skeleton points and external maximal disks has been used for shape description and characterization purposes. In this paper, we develop a generalized morphological skeleton transform that combines the concepts of internal and external maximal disks into a unified framework. In this framework, a shape is described in terms of disk components that need to be added as well as disk components that need to be removed. The procedures and formulae describing the extraction of the disk components and the reconstruction of the original shape from these components are developed. The correctness of the procedures and formulae is established. This new framework seems to provide a more powerful and more natural way of modeling the approximation and reconstruction of binary shapes using primitive shape components.

Efficient morphological shape representation with overlapping disk components

This paper proposes a new morphological shape representation algorithm, in which a two-dimensional (2-D) binary shape is represented as a union of certain disks contained in the given shape. The representative disks of different sizes may overlap. But excessive overlapping between them is avoided. The algorithm combines the advantages of the morphological skeleton transform (MST) and the morphological shape decomposition (MSD). The representative disks have simple and well-defined mathematical characterizations. The algorithm is simple and efficient to implement. The experimental results show that the number of representative disks used by our algorithm is significant lower than that used by the MSD. The overlapping level between the representative disks is much lower than that of the MST. A simple procedure can be used to combine the representative disks into more meaningful shape components. These shape components seem to correspond better to the natural shape parts than those generated by the MSD. It is also possible to build a good approximation for a given shape using only a small number of major components.

Binary object representation and recognition using the Hilbert morphological skeleton transform

Abstract A binary shape representation called the Hilbert Morphological Skeleton Transform ( HMST ) is introduced. This representation combines the Morphological Skeleton Transform ( MST ) with the clustering capabilities of the Hilbert transform. The HMST preserves the skeleton properties including information preservation, progressive visualization and compact representation. Then, an object recognition algorithm, the Hilbert Skeleton Matching Algorithm ( HSMA ), is introduced. This algorithm performs a single sweep over the HMST s and renders the similarity between them as a distance measure. Testing the HSMA against the Skeleton Matching algorithm ( SMA ) and invariant moments revealed that the HSMA algorithm achieves slightly better object recognition rates while substantially reducing the complexity. In an experiment of 14,400 shape matches, the HSMA achieved a 90.36% recognition rate as opposed to 89.76% for the SMA and 89.49% for invariant moments. On the other hand, the HSMA improved the SMA processing more than 40%.

Digital image compression in astronomy morphology or wavelets

A wide-field astronomical image is often considered as a set of quasi point-like sources spread on a slow-varying backgound. With this model, the image is described as a set of connected fields. We have to code the field positions, the field boundaries and their pixel values. It exists different methods for coding this information, they are mainly connected to the Mathematical Morphology. The fields may be coded from their contours, their binary skeletons or the grey-tone ones. The morphological skeleton transformation in general gives us the best results. The H-transform is a two-dimensional generalization of the Haar transform often used for compressing astronomical images. Blocking effects appear in the restored image. The quality of the restoration is improved by introducing an a priori knowledge on the solution. These two different approaches lead to high compression rates on classical astronomical images. The best compression technique is directly connected to the image modelling.

RECONSTRUCTABLE PARALLEL THINNING

This paper describes a reconstructable thinning process which is based on one-pass parallel thinning and the morphological skeleton transformation. It reduces a binary digital pattern into a unit-width connected skeleton enabling perfect reconstruction of the original pattern. The process uses thinning templates to iteratively remove boundary pixels and structuring templates of the morphological skeleton transformation to retain critical feature pixels for reconstruction. The thinning templates together with the extracted feature pixels ensure skeletal connectivity, unit width, and reconstructability. These essential properties are guaranteed regardless of the chosen structuring templates used in the morphological skeleton transformation. The thinning process is analyzed and results are presented. A number of implementation issues, such as the choice of structuring templates, the computational model, noise filtering, and computational efficiency, are also addressed.

SEGMENTATION OF BILEVEL IMAGES USING MATHEMATICAL MORPHOLOGY

This paper presents the results of a study on the use of morphological skeleton transformation to segment gray-scale images into bilevel images. When a bilevel image (such as printed texts and machine tools) is digitized, the result is a gray-scale image due to the point spread function of digitizer, non-uniform illumination and noise. Our method can recover the original bilevel image from the gray-scale image. The theoretical basis of the algorithm is the physical structure of the skeleton set. A connectivity property of the gray-scale skeleton transformation is used to separate and remove the background terrain. The object pixels can then be obtained by applying a global threshold. Experimental results are given.

Analysis and implementation of morphological skeleton transforms

This paper presents the analysis and the implementation algorithms of the morphological skeleton transform (MST) of binary images. A general MST algorithm is provided from which different subclasses of MSTs can be derived by choosing different structuring elements. Three subclasses of MSTs are discussed in this paper: the uniform-step-distance MST (USDMST), the periodically-uniform-step-distance MST (PUSDMST) and the pseudo-Euclidean MST (PEMST). A general discrete distance called morphological distance relates distance measures to the definitions of structuring elements. The PEMST is proposed which uses isotropic discrete structuring elements called quasi-circular structuring elements (QCSE). The QCSEs of all integer sizes are composed by a dilation interpolation method so that they can be decomposed into simplest elements in order to reduce computation. The PEMST has better performance in terms of rotation-invariance than any existing MSTs. The algorithm has an approximately linear computational complexity. Finally, the implementation of the three MSTs are discussed.

Astronomical image data compression by morphological skeleton transformation

Astronomical instruments currently provide a large amount of data. Nowadays, a large part of these data are image frames obtained with receivers of increasing size. The scan of large astronomical plates using fast microdensitometers gives image frames of over 30000×30000 pixels. More and more often, images are transmitted over a network in order to control the observations, to process the data, and to examine or to fill a data bank. The time taken for archiving, the cost of communication, the available memory given by magnetic tapes, and the limited bandwidth of transmission lines are reasons which lead us to examine the data compression of astronomical images. The astronomical image has the characteristic of being a set of astronomical sources in the sky background whose values are not zero. We are, in fact, only interested in the astronomical sources. Once a suitable detection is made, we generally want a compression without any distorsion. In this paper, we present a method which can be adapted for this purpose. It is based on morphological skeleton transformations. The experimental results show that it can give us an efficient compression. Moreover, the flexibility of choosing a structure element adapted to different images and the simplicity of implementation are other advantages of this method. Because of these characteristics, different compression applications may be treated.