Morphological Shape Representation Research Articles

An Iterative Morphological Decomposition Algorithm for Reduction Of Skeleton Points

Shape representation is an important aspect in image processing and computer vision. There are several skeleton transforms that lead to morphological shape representation algorithm. One of the main problems with these algorithms is in selecting the skeleton points that represent the shape component. If the numbers of skeleton subsets are reduced then the reconstruction process will be easy and time consuming. The present paper proposes a skeleton scheme that selects skeleton points based on the largest shape element. By this, overall skeleton subsets will be reduced. The present method is applied on various images and is compared with generalized skeleton transform and octagon-generating decomposition algorithm.

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.

Morphological Decomposition of 2-D Binary Shapes Into Modestly Overlapped Octagonal and Disk Components

One problem with several leading morphological shape representation algorithms is the heavy overlapping among the representative disks of the same size. A shape component formed by grouping connected disk centers may use many heavily overlapping disks to represent a simple shape part. Sometimes, these representative disks form complicated structures. A generalized skeleton transform was recently introduced which allows a shape to be represented as a collection of modestly overlapped octagonal shape parts. However, the generalized skeleton transform needs to be applied many times. Furthermore, an octagonal component is not easily matched up with another octagonal component. In this paper, we describe a octagon-fitting algorithm which identifies a special maximal octagon for each image point in a given shape. This transform leads to the development of two new shape decomposition algorithms. These algorithms are more efficient to implement; the octagon-fitting algorithm only needs to be applied once. The components generated are better characterized mathematically. The disk components used in the second decomposition algorithm are more primitive than octagons and easily matched up with other disk components from another shape. The experiments show that the new decomposition algorithms produce as efficient representations as the old algorithm for both exact and approximate cases. A simple shape-matching algorithm using disk components is also demonstrated.

A generalized discrete morphological skeleton transform with multiple structuring elements for the extraction of structural shape components

A common problem shared by several leading morphological shape representation algorithms is that there is much overlapping among the representative disks of the same size. A shape component represented by a group of connected disk centers sometimes uses many heavily overlapping representative disks to represent a relatively simple shape part. A shape component may also contain a large number of representative disks that form a complicated structure. We introduce a generalized discrete morphological skeleton transform that uses eight structuring elements to generate skeleton subsets so that no two skeletal points from the same skeleton subset are adjacent to each other. Each skeletal point represents a shape part that is in general an octagon with four pairs of parallel opposing sides. The number of representative points needed to represent a given shape is significantly lower than that in the standard skeleton transform. A collection of shape components needed to build a structural representation is easily derived from the generalized skeleton transform. Each shape component covers a significant area of the given shape and severe overlapping is avoided. The given shape can also be accurately approximated using a small number of shape components.

Efficient morphological shape representation by varying overlapping levels among representative disks

The morphological skeleton transform, the morphological shape decomposition, and the overlapped morphological shape decomposition are three basic morphological shape representation schemes. In this paper, we propose a new way of generalizing these basic representation algorithms to improve representational efficiency. In all three basic algorithms, a fixed overlapping policy is used to control the overlapping relationships among representative disks of different sizes. In our new algorithm, different overlapping policies are used to generate shape components that have different overlapping relationships among themselves. The overlapping policy is selected dynamically according to local shape features. Experiments show that compared to the three basic algorithms, our algorithm produces more efficient representations with lower numbers of representative points.

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.

Efficient morphological shape representation

Mathematical morphology is well suited to capturing geometric information. Hence, morphology-based approaches have been popular for object shape representation. The two primary morphology-based approaches-the morphological skeleton and the morphological shape decomposition (MSD)-each represent an object as a collection of disjoint sets. A practical shape representation scheme, though, should give a representation that is computationally efficient to use. Unfortunately, little work has been done for the morphological skeleton and the MSD to address efficiency. We propose a flexible search-based shape representation scheme that typically gives more efficient representations than the morphological skeleton and MSD. Our method decomposes an object into a number of simple components based on homothetics of a set of structuring elements. To form the representation, the components are combined using set union and set difference operations. We use three constituent component types and a thorough cost-based search strategy to find efficient representations. We also consider allowing object representation error, which may yield even more efficient representations.

Comparison between the morphological skeleton and morphological shape decomposition

The morphological skeleton and morphological shape decomposition (MSD) are two popular approaches for morphological shape representation. Each method represents an object as an algebraic combination of a number of components, where each component is given by a locus of points dilated by a specified structuring-element homothetic. This correspondence develops a theoretical comparison between the two methods. Combining the theoretical results with several representation cost measures, we make a concrete comparison of the efficiency of the two methods. The results indicate that for complex objects-i.e., objects requiring a full range of homothetic sizes in the morphological skeleton representation-the MSD represents objects more efficiently than the morphological skeleton for three of four suggested cost measures.

Morphological shape representation for very low bit-rate video coding

Abstract Region-based coding schemes are among the most promising compression techniques for very low bit-rate applications. They consist of image segmentation, contour and texture coding. This paper deals with the use of the geodesic skeleton as a morphological tool for contour coding of segmented image sequences. In the geodesic case, already coded and known regions are taken into account for the coding of contours of unknown regions. A new technique is presented for the entropy coding of the coordinates of the skeleton points exploiting their special spatial distribution. Furthermore, a fast algorithm for the reconstruction of the skeleton points is given based on hierarchical queues. In the case of numerous isolated contour arcs (for example error coding in a motion prediction loop), the geodesic skeleton proofs higher efficiency than traditional methods. Results at very low bit-rates are presented and compared to standard methods confirming the validity of the chosen approach.

Morphological shape representation

A new approach for shape representation is described, which provides a general scheme for object description and unifies some of the existing representation techniques. The proposed method has the advantage that it is based on the use of simple geometric objects which are intuitively used by humans in their perception of shapes. Furthermore, its unifying framework can be used both in computer graphics and computer vision, thus providing a tool to close the existing gap between object modeling and object recognition in certain applications.