Skeletonization Algorithm Research Articles

GRAY IMAGE SKELETONIZATION WITH HOLLOW PREPROCESSING USING DISTANCE TRANSFORMATION

This paper presents a gray-scale skeletonization algorithm based on the gray weighted distance transformation (GWDT). The proposed algorithm is conceptually simple and could be used to process nonuniformly distributed gray-scale images. The algorithm can detect the hollows on the gray-scale image, a feature that is often ignored in other skeletonization algorithms, and improves the quality of the skeleton.

Mending broken handwriting with a macrostructure analysis method to improve recognition

Broken characters always create problems in handwriting recognition systems, especially those using boundary and/or skeleton information. This paper presents a macrostructure analysis (MSA) mending method based on skeleton and boundary information and an MSA that investigates the stroke tending direction and other properties of handwritings. A new skeleton end extension algorithm is introduced, which compensates the defectiveness of the skeletonization algorithm and obtains a satisfactory skeleton. When combined with suitable parameters, improved performance from a handwriting classifier is achieved. The experimental results from over 13 000 numerals show the efficiency and robustness of the proposed method, raising recognition rates by over 10% for broken handwritten digits, from 74.8% to 86.4%.

A SIMPLE AND ROBUST THINNING ALGORITHM

In this paper a new thinning algorithm is presented. It is simple yet robust, and can maintain the same advantages of other key skeletonization algorithms. In this new algorithm, only a very small set of rules of criteria for deleting pixels is used. It is faster and easier to implement. Its advantages and limitations are discussed and compared with others. Several examples are illustrated.

Skeletonization algorithm based on cross segment analysis

Skeletonization algorithm based on cross segment analysis

Finding shape axes using magnetic fields

This paper presents a novel method, based on magnetic field principles, for obtaining the axes of shapes. The method is based on directional information of the shape's boundary. By simulating a parallel algorithm, we are able to generate the inner as well as the outer axes (axes of concavities) of the shape. The preprocessing phase for this algorithm involves obtaining the shape's gradient. Each point of the gradient is substituted by a minute magnetic dipole. The cumulative magnetic field due to these dipoles is accumulated at all points in the image in a one-pass algorithm. The magnitude of the final magnetic vector field has valleys that are created from mutual and directionally balanced cancellations of opposing boundary segments. These valleys signify the axes of the shape. The axes are obtained by performing a valley search. The magnetic field modeling (MFM) method has an advantage over previous approaches since it utilizes not only the location information of the boundary, but also its directional information. As demonstrated, experimental results of the MFM method are much improved, compared to other skeletonization algorithms which tend to generate spurious and noisy axes.

Efficient Skeletonization of Volumetric Objects.

Skeletonization promises to become a powerful tool for compact shape description, path planning, and other applications. However, current techniques can seldom efficiently process real, complicated 3D data sets, such as MRI and CT data of human organs. In this paper, we present an efficient voxel-coding based algorithm for Skeletonization of 3D voxelized objects. The skeletons are interpreted as connected centerlines. consisting of sequences of medial points of consecutive clusters. These centerlines are initially extracted as paths of voxels, followed by medial point replacement, refinement, smoothness, and connection operations. The voxel-coding techniques have been proposed for each of these operations in a uniform and systematic fashion. In addition to preserving basic connectivity and centeredness, the algorithm is characterized by straightforward computation, no sensitivity to object boundary complexity, explicit extraction of ready-to-parameterize and branch-controlled skeletons, and efficient object hole detection. These issues are rarely discussed in traditional methods. A range of 3D medical MRI and CT data sets were used for testing the algorithm, demonstrating its utility.

Skeletonisation: An electrostatic field-based approach

Skeleton representation of an object is a powerful shape descriptor that captures both boundary and region information of the object. The skeleton of a shape is a representation composed of idealized thin lines that preserve the connectivity or topology of the original shape. Although the literature contains a large number of skeletonisation algorithms, many open problems remain. In this paper, we present a new skeletonisation approach that relies on the Electrostatic Field Theory (EFT). Many problems associated with existing skeletonisation algorithms are solved using the proposed approach. In particular, connectivity, thinness and other desirable features of a skeleton are guaranteed. It also captures notions of corner detection, multiple scale, thinning, and skeletonisation all within one unified framework. The performance of the proposed EFT-based algorithm is studied extensively. Using the Hausdorf distance measure, the noise sensitivity of the algorithm is compared to two existing skeletonisation techniques. In addition, the experimental results also demonstrate the multiscale property of the proposed approach.

Pruning Medial Axes

The medial axis is an attractive shape feature; however, its high sensitivity to boundary noise hinders its use in many applications. In order to overcome the sensitivity problem some regularization has to be performed. Pruning is a family of medial axis regularization processes, incorporated in most skeletonization and thinning algorithms. Pruning algorithms usually appear in a variety of application-dependent formulations. Inconsistent terminology used until now prevented analysis and comparison of the various pruning methods. Indeed many seemingly different algorithms are in fact equivalent. In this paper we suggest the rate pruning paradigm as a standard for pruning methods. The proposed paradigm is a framework in which it is easy to analyze, compare, and tailor new pruning methods. We analyze existing pruning methods, propose two new methods, and compare the methods via a model-based analysis. The theoretical analysis is supported by simulation results of the various pruning methods.

Morphological Models for the Collapse of Area Features in Digital Map Generalization

“Collapse” is an essential operation for the manipulation of area features in digital data generalization. This operation can be categorized into two types: complete collapse and partial collapse. The former is composed of another two types: area-to-point and area-to-line collapse. In this paper, a set of algebraic models built upon the operators in mathematical morphology is described for the area-to-line collapse and partial collapse operations. For the area-to-line collapse operation, a modified skeleton algorithm is presented. For the partial collapse operation, a procedure is designed which consists of a set of operations, i.e., the skeletonization, separation of areal and linear parts, simplification of areas and an overlay operation. These models are tested using real map data sets.

A fast Parallel Skeletonization Algorithm on Block Represented Binary Images

This paper describes a binary image representation scheme, which is called Image Block Representation and presents a new skeletonization algorithm, which is fast implemented on block represented binary images. The main purpose of the Image Block Representation is to provide an efficient binary image representation that permits the execution of operations on image areas instead of image points. The skeletonization algorithm operates in four subiterations: each subiteration deletes the north, the south, the west and the east boundary points, respectively. Due to the substitution of the boundary points by the blocks' boundary points, the relevant operations are performed fast, while preserving the end points and the object connectivity. Keywords: Image Block Representation, Skeletonization, Thinning.

The Curve Axis

In this paper we examine various aspects of the medial axis representation of shapes, resulting in a novel, highly accurate skeletonization algorithm suitable for shapes with parametrically described boundaries such as, for example, polygons or “spline”-gons. The medial axis representation is first shown to be efficient in calculating local boundary features. Then the problem of deciding whether an axis-like function is indeed an axis of a shape is addressed, and two necessary and locally sufficient restrictions on axis functions are derived. The proposed skeletonization approach is based on another result which shows that the medial axis is the solution of a system of first order differential equations. The new skeletonization algorithm provides a discrete parametric representation of the axis for smooth shapes, the input to the algorithm being a parametric description of the shape boundary. Skeletonization examples using the proposed algorithm are presented.

Skeletonization algorithm running on path-based distance maps

A new skeletonization algorithm is introduced which runs on the distance map of a digital figure, computed according to any among four commonly used path-based distance functions. The skeletonization algorithm has a number of features: it is reversible, since it detects the centres of the maximal disks; it is nearly invariant under figure rotation (when the adopted distance function provides a reasonably good approximation to the Euclidean distance); it includes two steps (pruning and beautifying), which allow us to simplify skeleton structure according to the user's needs, as well as to improve skeleton aesthetics; and its computational load is limited, whatever the size of the figure to be skeletonized.

Number of branches in diffusion-limited aggregates: The skeleton.

We develop the skeleton algorithm to define the number of main branches $N_b$ of diffusion-limited aggregation (DLA) clusters. The skeleton algorithm provides a systematic way to remove dangling side branches of the DLA cluster and has successfully been applied to study the ramification properties of percolation. We study the skeleton of comparatively large ($\approx 10^6$ sites) off-lattice DLA clusters in two, three and four spatial dimensions. We find that initially with increasing distance from the cluster seed the number of branches increases in all dimensions. In two dimensions, the increase in the number of branches levels off at larger distances, indicating a fixed number of $N_b = 7.5\pm 1.5$ main branches of DLA. In contrast, in three and four dimensions, the skeleton continues to ramify strongly as one proceeds from the cluster center outward, and we find no indication of a constant number of main branches. Likewise, we find no indication for a fixed $N_b$ in a study of DLA on the Cayley tree. In two dimensions, we find strong corrections to scaling of logarithmic character, which can help to explain recently reported deviations from self-similar behavior.

Skeletonization for fuzzy degraded character images

Most skeletonization algorithms are operated on binary images. To avoid information loss and distortion, a topography-based approach is proposed to apply directly on fuzzy or gray scale images. A membership function is used to indicate the degree of membership of each ridge point with respect to the skeleton. Significant ridge points are linked to form strokes of skeleton. Experimental results show that our algorithm can reduce deformation of junction points anti correctly extract the whole skeleton, although a character may be broken into pieces. For merged characters, the breaking positions can be located by searching for the saddle points. A multiple context confirmation is used to increase the reliability of breaking hypotheses.

Design of an ASIC Chip for Skeletonization of Graylevel Digital Images

This paper describes the design of an ASIC chip for thinning of graylevel images. The chip implements a Min-Max skeletonization algorithm and is based on a pipeline architecture where each stage of the pipeline performs masking operations on the graylevel images. The chip operates in real time at a frequency of 8 MHz and utilizes about 321 mils × 410 mils of silicon area.

Skeletonization via Distance Maps and Level Sets

The medial axis transform (MAT) of a shape, better known as its skeleton, is frequently used in shape analysis and related areas. In this paper a new approach for determining the skeleton of an object is presented. The boundary is segmented at points of maximal positive curvature and a distance map from each of the segments is calculated. The skeleton is then located by applying simple rules to the zero sets of distance map differences. A framework is proposed for numerical approximation of distance maps that is consistent with the continuous case and hence does not suffer from digitization bias due to metrication errors of the implementation on the grid. Subpixel accuracy in distance map calculation is obtained by using gray-level information along the boundary of the shape in the numerical scheme. The accuracy of the resulting efficient skeletonization algorithm is demonstrated by several examples.

TWO METHODOLOGIES TO IMPLEMENT 3D THINNING ALGORITHMS ON DISTRIBUTED MEMORY MACHINES

Our goal is to implement skeletonization algorithms on distribution memory mechines. This implementation is not trivial, because we cannot apply locally thinning operators based on 26-neighborhood, sequentially or simultaneously on all the points of the image. After summarizing the problem, we describe two methodologies to implement these algorithms on MIMD machines, one based on the decomposition of the thinning operator into sub-operators, and the other based on the decomposition of the study domain (image) into sub-domains.

A Parallel Skeletonization Algorithm Based on Two-Dimensional Cellular Automata and its VLSI Implementation

This paper presents a new parallel algorithm for binary object skeletonization and its implementation in VLSI. The proposed skeletonization algorithm is based on a digital geometry concept known as the 'Voronoi diagram, which is established, after an edge detection pre-processing step, through the time evolution of Cellular Automata. The proposed algorithm is both space and time efficient, since it does not require any distance calculations and ordering of distances as in the case of other skeletonization algorithms nor the application of complex 'template' criteria to guarantee object connectiveness as in the case of thinning algorithms. Additionally, the proposed Cellular Automaton architecture achieves high frequency of operation and it is especially suited for VLSI implementation due to its inherent parallelism, structural locality, regularity and modularity. A set of quantitative measures was defined in this paper in order to evaluate the performance of the proposed algorithm. It was found that the proposed algorithm for pattern skeletonization outperforms already existing algorithms, with respect to these measures.

A Computerized Method for Determination of Microvascular Density

Currently accepted stereological methods for vascular density measurements involve manual counting of labeled vessels with a grid image overlay and determination of vessel-grid intersections. This method both is tedious and may be prone to error; therefore, our laboratory has developed a method for computer-automated determination of microvascular density using digital image processing techniques. An image of the microvasculature is acquired using computer videomicroscopy. The image is processed in three general steps, involving (1) background correction, (2) thresholding of the gray level image to create a binary image, and (3) processing of the binary image using erosion, dilation, and skeletonization algorithms. Testing of this procedure was performed on 328 typical images of skeletal muscle tissue sections taken from the hindlimb of Sprague-Dawley rats and quantitated by both traditional measures and our new computer method. Results from this comparison reveal that the automated vessel counting is highly correlated ( r 2 = 0.71) and decreased analysis time from 15 min/image to 30 sec/image when compared with manual counting methods. Our computer-based method also appears to be superior to the traditional method due to the unbiased and nonsubjective nature of determining vessel-grid intersections.

A skeletonization algorithm by maxima tracking on Euclidean distance transform

A simple and efficient algorithm using the maxima tracking approach on Euclidean distance transform to detect skeleton points is presented. The advantages of the skeleton obtained are: (1) connectivity preservation; (2) single-pixel in width; and (3) its locations as close as to the most symmetrical axes. Besides, the condition of the least slope change of skeleton is used to ensure the fairness of the digital medial axes. With the least effort, the algorithm can be modified to eliminate non-significant short skeletal branches originating from the object contour while the critical shape-informative medial axes are preserved.