1. INTRODUCTION. Thinning plays a vital role in image processing and computer vision. It

Transcription

1 1 1. INTRODUCTION 1.1 Introduction Thinning plays a vital role in image processing and computer vision. It is an important preprocessing step in many applications such as document analysis, image compression, data compression, fingerprint classification, and pattern recognition. Thinning process transforms an input binary image into skeletons with nearly thin lines, curves and arcs. The main objective of thinning is to preserve the important information such as shape, size and topological properties thereby simplifying the later processing steps like extracting features from patterns. Skeleton, initially termed as medial axis, was first introduced by Blum [Blum, 1964]. During these years, several thinning algorithms are developed to address wide variety of problems. These algorithms are classified into iterative and non-iterative algorithms as shown in figure 1.1. This classification is based on the approaches used for thinning [Lam, Lee & Suen, 1992]. Non-iterative algorithms obtain the skeleton in a single pass using the methodologies like distance transforms and run-length coding. Non-iterative algorithms do not consider the surrounding pixels while making decisions. Iterative algorithms either delete or retain the boundary pixels layer by layer successively until the desired skeleton is obtained. The iterative algorithms are further categorized as sequential (boundary pixels

2 2 are processed one by one, layer by layer) and parallel (all the boundary pixels are processed simultaneously layer by layer). Sequential algorithms consume less amounts of memory. In contrast, parallel algorithms require more memory compared to sequential algorithms but are much faster in processing. Parallel algorithms process all the border pixels at once and hence are order independent. Figure 1.1 Classification of thinning algorithms A good thinning algorithm should possess many properties. First, the result of thinning process should be connected and one pixel width. Second, the skeleton should have minimal deviation from the medial (central) axis.

3 3 Third, skeleton should preserve the topological and geometrical properties of the image to be thinned. Fourth, the skeleton produced should not be affected by the noise near the boundaries (i.e. insensitive to noise). Fifth, the algorithm should be efficient in terms of memory requirements and time. Sixth, the skeleton produced should be invariant to the geometrical transformations like rotation and scaling. Finally, the skeleton obtained should be in such a way that one can able to reconstruct the original image. All algorithms may not satisfy all the above characteristics, but a good algorithm aims at satisfying most of them. A number of thinning algorithms have been proposed during the last four decades. In recent past, newly devised algorithms concentrated either on improving the quality of the skeleton obtained or reducing the execution time of the existing algorithms. The time required for thinning depends on the size and the shape complexity of the given image. 1.2 Importance of thinning Thinning plays a crucial role in image analysis and pattern recognition applications. These applications require extracting features of interest like number of endpoints, junction points etc., to distinguish one object from another. Extracting such features from a thin line-like representation (skeleton) is easier and efficient than extracting from the original input image. In addition, from an artificial intelligence perspective,

4 4 thin line representation is believed to be close to the way humans recognize objects. And finally, by reducing an object to only a skeleton, irrelevant features and image noise can be filtered out. 1.3 Basic terminology In spatial domain, digital image is defined as a two-dimensional object with a finite set of intensity values whose elements are referred as picture elements (pixels). Images whose possible intensity values are only black (foreground) represented as 1 and white (background) represented as 0 are referred as binary images. Representation of English alphabet T as a binary image is illustrated in figure 1.2. Figure 1.2 Image Representation Mask is an array of values specifying the relative importance of sub pixels. Most of the thinning algorithms based on spatial domain processing techniques use masks of size 3x3 as shown in figure 1.3. Pixels P1, P2, P3, P4,

5 5 P5, P6, P7 and P8 are 8-neighbors of the candidate pixel Pi denoted as N8 (Pi). Whereas P2, P4, P6 and P8 are 4-neighbors of Pi denoted as N4 (Pi). Thus N8 (Pi) = {P1, P2, P3, P4, P5, P6, P7, P8} N4 (Pi) = {P2, P4, P6, P8} Figure 1.3 Pixel representation of 3X3 mask The pixel connectivity is a way in which pixels relate to their neighbors. If the pixels are connected horizontally and vertically in terms of pixel coordinates, it is termed as 4-connectivity. In 8-connectivity, pixels are connected diagonally besides horizontal and vertical. Two pixels P and Q are said to be 4-connected, if Q is a 4-neighbor of P or 8-connected, if Q is an 8-neighbor of P. Pixel is said to be 4-simple or 8-simple, if we change the pixel from foreground to background, it does not change the 4- connectivity or 8-connectivity of 1's in its neighborhood respectively. Connected Component is an ordered set of foreground pixels such a way that any two successive pixels should be neighbors of each other. Based on the connectivity of the successive pixels the corresponding connected

6 6 component is referred to as either 4-connected component or 8- connected component. The break point is a foreground pixel which breaks the connectedness of the original object if it is changed to background. An edge or border point is a pixel with at least one background 4-neighbor. Redundant points are pixels that are belonging to the skeleton whose removal doesn t affect the pixel connectivity. Iteration refers to processing of all the border pixels which belong to a single layer. Scan (pass or cycle) refers to processing of all the border pixels layer by layer until no more pixels are deleted. By placing a 3x3 mask on the foreground (black) pixel of an image, one can define three spatial domain operators on the 8-Neighborhood of Pi. The first spatial domain operator denoted by BP is the number of foreground pixel in the neighborhood of the candidate pixel. The second operator denoted by AP is the number of 4-connected components (4-CC) in the neighbourhood of a candidate pixel. The 4-connected component is a group of foreground pixels which are 4-connected in clock-wise order of {P1, P2... P8, P1}. One can easily compute the 4-connected component by calculating the number of zero-to-one or one-to-zero transitions. Third operator denoted by CP is the number of 8-connected components (8-CC)

7 7 count in the neighbourhood of the candidate pixel. The sequence of foreground pixels where any two successive pixels are 8-connected is referred to as 8-connected component. A 4-connected component is also an 8-connected component but the converse is not true. The three spatial domain operators BP, AP and CP are illustrated in the example figures 1.4 (a), (b) and (c). Figure 1.4 Illustration of BP, AP and CP values Based on the definitions of BP, AP and CP, an end point can be defined as a pixel whose (BP = 1) or (BP = 2 and AP = 1) or (BP = 2 and AP = 2 and CP = 1) as illustrated in the following figure 1.5 (a), (b) and (c) respectively.

8 8 Figure 1.5 Example end point cases 1.4 Principles of thinning Binary image thinning algorithms based on the assumption that images to be thinned have only two possible intensity values 0 and 1. Hence all the input images have more than two intensity levels (gray or color) need to be converted to binary images. Normally thresholding technique is used as a preprocessing step to convert the images into binary. If a pixel in the image has intensity less than the threshold value, the corresponding pixel in the resultant image is set to black (1). If the pixel intensity is greater than or equal to the threshold intensity, the resulting pixel is set to white (0). The input images need to be transformed into skeletons containing essential information. This transformation simplifies further processing in most of the pattern recognition problems. The process of obtaining skeletons referred as skeletonization which is a spatial domain processing technique. The skeletonization operates directly on the aggregate of the pixels that compose the image. Skeletons are usually

9 9 obtained through an iterative reduction using a thinning operator called thinning. In this process, pixels whose removal will not affect the shape and size of the image (simple pixels) are iteratively removed until no more pixels can be deleted. Pixels can be removed either one-by-one (sequential) or layer-by-layer (parallel). The endpoint criteria and different spatial processing operators (BP, AP and CP) discussed in section 1.2 are used to make the decisions about pixel deletions. These combinations can be converted into a set of masks termed as templates which can be matched against the candidate pixel neighborhood. These templates can be rewritten into rules in the form of if the neighborhood matches with the input template, then change it into resultant template. The latter approaches are termed as rule-based approaches. 1.5 Issues involved in thinning The hardest task of thinning algorithms is to obtain the skeleton near the central axis. To tackle this problem, existing algorithms in the literature used the technique of dividing the entire process into sub-cycles (passes). The second major task of thinning is excessive erosion. To overcome this problem, approaches like smoothing templates and flagmap techniques, are used. The third major task is the connectivity preservation. Parallel algorithms are more vulnerable to discontinuities compared to sequential

10 10 algorithms. Thus to preserve connectivity in parallel algorithms, one should adopt a method to retain the pixel that cause discontinuity. Fourth, redundant points do not make contribution to the connectivity and thus should be removed to improve the thinning ratio. Unfortunately, most of the thinning algorithms can not delete all the redundant pixels. The number of redundant pixels in a skeleton is inversely proportional to the quality of the skeleton. The quality of the obtained skeleton can be judged based on how well it enhances the later processing steps. Thus defining the skeleton of an object uniquely is difficult. This vagueness causes difficulties in evaluating and comparing different thinning algorithms. But there are some properties of skeletons such as thinness, connectivity and sensitivity which are measured using mathematical equations. 1.6 Motivation for the present work There are some limitations in existing thinning algorithms. Parallel algorithms use non-isotropic way to find end points that result in producing nearly similar skeletons for specific orientations like multiples of right angles (90 0 ). Whereas for other angles they produce different skeletons which may be with unnecessary information such as spurs or ridges. These are the bottlenecks for the recognition processes. Some thinning algorithms are developed to suit the specific needs (script dependent) of the application where they can be applied but these algorithms fail for other application areas. Within the same application domain, algorithm that works best for

11 11 most of the patterns fails for other types of patterns which are similar in appearance. Sometimes the resultant skeleton may contain more than one pixel and cause discontinuities if it thins further. These limitations motivated us for the further investigation and to find the possible solution to overcome the above limitations. 1.7 Background of the problem In the literature, novel approaches are proposed to improve the performance of the existing thinning methods. Some algorithms result in good skeletons for specialized patterns they are concentrating on, but produce poor skeletons for other types of patterns. For example, thinning algorithms for patterns containing only straight lines may not be suitable for thinning patterns composed of only curves (Telugu Handwritten Characters). Further the finger print patterns require specialized algorithms as the small ridges and furrows can influence the recognition process. Devising a generalized thinning algorithm which can produce satisfactory results for all varieties of pattern shapes is very difficult [Fu, Ya- Ching & Pavlidis, 1999]. But the thinning algorithms developed recently [Ahmad and ward, 2002][Peter I,Rocket,2005][Gabor Nemeth and Kalman Palagyi,2009] aimed at more than one application area but are not completely generalized.

12 Problem statement This research work focuses on the development of parallel binary image thinning algorithms which are order independent, rotation invariant and scale invariant. Besides this, they are size and shape preserving. The proposed algorithms produce one pixel wide connected skeletons on a wide variety of image patterns ranging from linear to non-linear. We want to make the thinning algorithm independent of application areas ranging from thinning characters of different languages to finger prints. The performance and results obtained are compared with existing thinning algorithms in terms of excessive erosion, connectivity, thickness and symmetry of the skeletons, endpoint preservation, and visual quality after skeletonization. 1.9 Objective of the work For the task like character recognition, thinning operation is used as a pre-processing step. An effective thinning helps in better recognition performance. In the recent past, most of the researchers have concentrated on reducing the thinning time of the algorithm than the resulting skeleton shape [T.Y.Zhang and C. Y.suen, 1984]. A few of them focused on the quality of the skeleton produced [Gabor Nemeth and Kalman Palagyi, 2009]. It is difficult to produce an algorithm which can simultaneously focus on both thinning time and skeleton quality. Hence, the main objective of the proposed work is to develop a robust thinning algorithm that focuses simultaneously on both these factors. Besides these it also considers the

13 13 order-independent, rotation-invariant properties and preserves topological and geometrical properties of the obtained skeletons Scope of the work The research work carried out in this thesis is not limited to thinning particular types of binary image patterns. The proposed algorithm is generic in nature and considers varieties of image patterns varying from characters of different languages to objects of linear and non-linear shapes and finger print images. Further proposed algorithm considers achieving one pixel wide connected skeletons around the medial axis Organization of the thesis The thesis is organized as follows. Chapters 2 deals with literature survey which reviews the existing iterative and non-iterative thinning algorithms. Chapter 3 gives a detailed description of the implementation of i) an efficient two-pass approach ii) improved two-pass approach and iii) rule based order independent algorithms for binary images. Topology preserving and making the implementation time efficient are also discussed in this chapter. A detailed analysis and comparison of these algorithms is explained in chapter 4. The analysis and comparison are based on the results of both simple input patterns and real images. Finally, the conclusions are summarized in chapter 5.