Jianning Xu

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.

Morphological decomposition of 2-D binary shapes into conditionally maximal convex polygons

Mathematical morphology is an approach to image analysis based on the geometric concept of shape and size. Naturally, it provides a very effective tool for shape analysis. In this paper we present a morphological shape segmentation algorithm that decomposes a 2-D (two-dimensional) binary shape into a collection of restricted convex polygons. We use simple morphological operations to extract shape information from different skeleton subsets to form a group of conditionally maximal convex polygonal shape components. Then a set of more meaningful and natural convex polygonal components are constructed from these maximal components. The resulting algorithm is very simple and the decomposition is always unique. The components produced have well-defined mathematical characterizations and they seem to be in good agreement with the nature structures of the given shapes. The shape segments produced can be used to construct structural shape description and for other shape analysis purposes.

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.

Morphological decomposition of 2-D binary shapes into convex polygons: a heuristic algorithm

In many morphological shape decomposition algorithms, either a shape can only be decomposed into shape components of extremely simple forms or a time consuming search process is employed to determine a decomposition. In this paper, we present a morphological shape decomposition algorithm that decomposes a two-dimensional (2-D) binary shape into a collection of convex polygonal components. A single convex polygonal approximation for a given image is first identified. This first component is determined incrementally by selecting a sequence of basic shape primitives. These shape primitives are chosen based on shape information extracted from the given shape at different scale levels. Additional shape components are identified recursively from the difference image between the given image and the first component. Simple operations are used to repair certain concavities caused by the set difference operation. The resulting hierarchical structure provides descriptions for the given shape at different detail levels. The experiments show that the decomposition results produced by the algorithm seem to be in good agreement with the natural structures of the given shapes. The computational cost of the algorithm is significantly lower than that of an earlier search-based convex decomposition algorithm. Compared to nonconvex decomposition algorithms, our algorithm allows accurate approximations for the given shapes at low coding costs.

Hierarchical representation of 2-D shapes using convex polygons: A morphological approach

This paper presents a structural shape representation scheme in which a binary shape is represented by a number of convex polygons organized into a hierarchical tree structure. Morphological operations are used in the implementation of the scheme. The representation scheme provides natural and effective descriptions of binary shapes and has simple and efficient implementations.

Morphological decomposition of 2-D binary shapes into simpler shape parts

This paper presents a simple and efficient morphological shape segmentation algorithm that is based on morphological skeleton transform. This algorithm decomposes a binary shape into simpler shape segments that not only appear to be quite natural, but also have well defined mathematical characterizations.

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

Efficient morphological shape representation by varying overlapping levels among representative disks

Abstract 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 without searching

This paper proposes a new morphological shape representation algorithm that does not require searching. A theoretical analysis as well as experimental results are presented to compare the algorithm with two leading morphological shape representation schemes: the morphological skeleton transform (MST) and the morphological shape decomposition (MSD). Our algorithm combines the advantages of the MST and MSD. In our scheme, a binary shape is decomposed into a union of disks of different sizes. The number of disks used is close to that by the MST and the reconstruction cost is close to that by the MSD.

Shape matching using morphological structural shape components

A morphological shape decomposition algorithm was recently introduced that allows a shape to be represented as a collection of modestly overlapped disk components. In this paper, we present a shape matching algorithm that is based on this decomposition algorithm. The matching algorithm matches two shapes by matching their disk components. A local descriptor that contains both geometric and structural information is built for each disk component. Such descriptors are used to determine the matching of disk components from two shapes. The overall similarity score is established by combining scores from matching individual disk components. The experiments show that the algorithm is tolerant to scale and rotation changes. An advantage of the algorithm is that the matching can be done at different levels of details.