2D partially occluded object recognition using curve moment invariants

2D PARTIALLY OCCLUDED OBJECT RECOGNITION USING CURVE MOMENT INVARIANTS ZHENG HAO (B.Eng., TIANJIN UNIVERSITY) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2005 ACKNOWLEDGEMENTS Many people have provided advice, support, and encouragement to the author, during the research which led to this thesis. Here I would like to express my sincere appreciation to the people below: First, my sincerely thanks go to Associate Professor Lim Kah Bin, my supervisor who patiently and intellectually guided me through all the research work; his insightful advice, clear vision, many suggestions, and endless efforts to be available for many educational discussions, were invaluable. I also appreciate his friendliness and eagerness. Special thanks must also go to assistance received from technical staff of the Control & Mechatronics Laboratory 2. I would like to acknowledge the financial assistance received from Nationa l University of Singapore for the duration of this project. I also wish to express my sincerely gratitude to my senior colleagues: Mr. Du TieHua. And other colleagues: Mr. Ning Yu, Mr. Lv Zhe, Mr. Wang WenHui, Mr. Xiao Yong, and Mr. Yu WeiMiao. Finally, I would like to express my heartfelt appreciation to my parents, Zheng Lanjin and Luan Min, who first taught me the importance of education. i TABLE OF CONTENTS ACKNOWLEDGEMENTS .i TABLE OF CONTENTS ii SUMMARY v LIST OF FIGURES vi LIST OF TABLES viii CHAPTER INTRODUCTION 1.1 Background 1.2 Definition of the problem .1 1.3 Literature reviews 1.3.1 Contour-based vs Region-based .3 1.3.2 Global approaches vs Structural approaches 1.3.3 Partially occluded object recognition 1.4 Our scheme 1.5 Organization of the thesis 10 1.6 Our contributions .10 CHAPTER .12 THEORY OF CURVE MOMENT INVARIANTS 12 2.1 Introduction 12 2.2 Traditional moment invariants .14 2.3 Curve moment invariants .17 2.3.1 Shape representation of curve moments .18 ii 2.3.2 Curve moment invariants 20 2.3.3 Analysis and solution of curve moment invariants as the feature 23 CHAPTER .25 RECOGNITION ALGORITHM USING CURVE MOMENT INVARIANTS 25 3.1 Image pre-processing .27 3.1.1 Noise Removal 27 3.1.2 Binarizing an image 29 3.1.3 Edge detection .32 3.1.4 Boundary tracking .33 3.2 Boundary segmentation .40 3.2.1 Smoothing the boundary .40 3.2.2 Extracting the corner point 45 3.2.3 Partitioning the boundary 46 3.3 Feature matrix of object .47 3.3.1 Organization of feature matrix of object .47 3.3.2 Model database construction .49 3.4 Object matching .50 3.4.1 Segment matching .50 3.4.2 Matching criterion .53 CHAPTER EXPERIMENTAL RESULTS .56 4.1 Description of system configuration 56 4.1.1 Hardware .56 4.1.2 Software 57 4.1.3 Image data .57 4.2 Constructing the model database .58 iii 4.3 Standalone object recognition 61 4.4 Noise insensitivity 65 4.5 Occluded object recognition 68 4.5.1 Experiment .69 4.5.2 Experiment .74 4.5.3 Experiment .77 CHAPTER CONCLUSION .81 BIBLIOGRAPHY 83 APPENDIX A .90 Algorithm for image thresholding 90 APPENDIX B .91 Algorithm for edge detection in binary images .91 APPENDIX C .92 Algorithm for boundary tracking .92 iv SUMMARY This project presents a novel approach for the recognition of 2D partially occluded objects using the curve moment invariants as the features. Curve moment can uniquely characterize the geometric features of object boundary. It not only inherits the similarity transform invariance properties from conventional region-based moment, but also has many advantages which are especially promising for our research project. We have adopted successfully the curve moment invariants as our features for recognition of partially occluded object. In the recognition approach, the boundary of object of interest is first extracted after image pre-processing. Then corner points were used to partition the boundary into curve segments consisted of consecutive corners. Subsequently, seven different order moment descriptors are computed as feature vectors for each segment. Finally, feature matching between the object of interest in the scene and the model is performed hierarchically. From the experimental results, the proposed recognition algorithm was found to be robust to similarity transform, noise and partial occlusion, and computational efficient. v LIST OF FIGURES Figure 1. Objects under similarity transformation and partial occlusion Figure 1. Recognition system .8 Figure 3. The flowchart of recognition process 26 Figure 3. An example: the pair of pliers .26 Figure 3. The histogram of the pliers 31 Figure 3. The shape boundary concept .32 Figure 3. Result of edge detection 33 Figure 3. 4-neighbor tracking diagram .34 Figure 3. 8-neighbour tracking diagram .34 Figure 3. Schemes illustrating the boundary tracking algorithm 36 Figure 3. Positions already verified by the initial scanning line search 37 Figure 3. 10 Parametric contour representation of pliers shown in Figure 3.2 .40 Figure 3. 11 Single object: the wrench .43 Figure 3. 12 Point curvatures of a wrench outline smoothed by a Gaussian filter with different widths 44 Figure 3. 13 Result of corner point extraction 46 Figure 3. 14 The result of boundary segmentation of the pliers .47 Figure 3. 15 Segment matching diagram 51 Figure 3. 16 Hierarchical matching process 53 Figure 4. Objects for the Experiments 57 vi Figure 4. The result of corner point extraction of a scissor in Figure 4.1(II) .58 Figure 4. The result of corner point extraction of flower in Figure 4.1(IV) .59 Figure 4. The result of corner point extraction of Figure 4.1(VIII) 60 Figure 4. Single scene object 62 Figure 4. The result of corner point extraction of single scene object 62 Figure 4. The result of adding noise .66 Figure 4. The result of corner point after adding noise .66 Figure 4. Occluded objects 68 Figure 4. 10 Result of corner point extraction of Figure 4.9(a) 69 Figure 4. 11 The result of corner points extraction of Figure 4.9(d) 75 Figure 4. 12 Result of corner point extraction of Figure 4.9(f) 78 vii LIST OF TABLES Table 3. The invert function 38 Table 3. Feature matrix of pliers .48 Table 4. The feature matrix of Figure 4.1(II) 59 Table 4. The feature ma trix of Figure 4.1(IV) 59 Table 4. The feature matrix of Figure 4.1(VIII) .60 Table 4. Feature matrix of single scene object 63 Table 4. Matching result of scene object with the model object 63 Table 4. Feature matrix after adding no ise .67 Table 4. Final matching result of φ1 of noised pliers .67 Table 4. Feature matrix of Figure 4.9(a) .70 Table 4. Matching process of Figure 4.9 (a) with Figure 4.1(VIII) 71 Table 4. 10 The feature matrix of Figure 4.9(d) .76 Table 4. 11 Final matching result of φ1 between Figure 4.10 (d) and flower 77 Table 4. 12 Feature matrix of scene object in Figure 4.9(f) .78 Table 4. 13 The final matching result .79 Table 4. 14 Rate and time of recognition process .80 viii CHAPTER INTRODUCTION 1.1 Background Object recognition has been one of the most challenging problems in computer vision for several decades, and has been used for a variety of tasks in industrial, military and medical applications. It can also be used as the key technique for the solution of the correspondence problem in stereo vision or motion analysis. Since, in general, recognition is performed by modeling the target object using a set of primitives or features that describe the characteristic of the object, extraction of the features in a scene is a very important problem for reliable matching. However, all the features of the object are not always visible in the scene, due to occlusion, noise, and inaccurate low-level feature extracting process, and so forth. Therefore, most of the existing recognition methods assume that the objects to be matched are non-occluded. As a result, the performance would be degraded in circumstances involving object occlusion. 1.2 Definition of the problem In general, the shape-based recognition of objects can be divided into two classes. One is the recognition of single object with complete shapes, and the other is the recognition of multiple objects with partia l occlusion. The former, which has been Figure 4. 12 Table 4. 12 Result of corner point extraction of Figure 4.9(f) Feature matrix of scene object in Figure 4.9(f) log(φ1 ) log(φ ) log(φ ) log(φ ) log(φ ) log(φ ) log(φ ) Segment1 -2.5165 -5.0459 -12.458 -13.786 -2.7668 -6.0548 -8.9854 -11.019 -17.085 -14.7 + 3.1416i -27.298 Segment2 -27.214 -21.74 + 3.1416i Segment3 -2.7964 -5.7977 -10.381 -11.569 -22.798 -14.946 Segment4 -3.5058 -7.7294 -10.772 -11.927 -23.32 -15.833 Segment5 -3.5939 -8.0548 -11.058 -12.214 Segment6 -2.9853 -6.9703 -9.2429 -11.519 -23.96 -21.901 + 3.1416i -16.349 -15.017 + 3.1416i Segment7 -2.7288 -5.7005 -9.5903 -10.978 -21.646 -14.396 Segment8 -2.6996 -5.6403 -9.4745 -11.032 Segment9 -3.0711 -7.7289 -9.4028 -11.527 -21.983 -22.002 + 3.1416i -14.885 -15.395 + 3.1416i Segment10 -3.1609 -6.5873 -10.384 -11.023 -21.73 -14.319 Segment11 -3.1345 -8.404 -10.678 -12.102 Segment12 Segment13 -2.8374 -2.7721 -5.7691 -5.7427 -10.43 -10.607 -10.924 -12.04 -23.545 + 3.1416i -21.603 -23.891 -16.382 + 3.1416i -13.827 -15.657 Segment14 -2.7787 -5.8936 -9.5516 -11.158 -22.049 -14.766 Segment15 -2.5247 -5.0621 -12.327 -13.318 -26.238 -16.197 Segment16 -3.8648 -7.7668 -24.718 -23.784 -48.217 -27.74 -21.156 -23.006 + 3.1416i -24.511 + 3.1416i -24.655 -25.269 -21.575 + 3.1416i -21.428 -24.004 -24.153 + 3.1416i -24.64 -24.495 -23.577 -21.723 + 3.1416i -27.007 + 3.1416i -48.628 + 3.1416i 78 Table 4. 13 d (i , j ) j=1 d (i , j ) j=1 i=1 5.29e-16 The final matching result - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - i=9 10 11 12 13 14 15 16 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1.75e-16 - - - - - - - - 4.59e-16 Table 4.13 shows that segments in Figure 9(f) match with the screwdriver in Figure 4.1(II).The number of segment of the screwdriver is 7. So the minimum recognition threshold is 3. According to the criterion of Equation 3.18, nMatched=3, which is equal to the minimum recognition threshold, 3. Hence, we conclude that the screwdriver in Figure 4.1(II) is present in Figure 4.9(f). We have also done experiments to test the performance of our recognition system on many other samples shown in Figure 4.9, the result of which are too lengthy to be included here. Table 4.14 shows the rate and time for recognizing objects in the figure 4.9. The time is obtained from Matlab 6.5 in Intel Pentium III PC (450MHz), memory size 512M. 79 Table 4. 14 Rate and time of recognition process a b c d e f Object in scene image Pliers and wrench Part of pliers Part of screwdriver Saw and flower Screwdriver and scissors Screwdriver and wrench Image Size (pixel *pixel) 512*512 340*300 419*429 380*337 512*512 512*512 Number of boundary segments 15 21 20 16 Recognized object Pliers Pliers Screwdriver Saw, flower Screwdriver, scissors Screwdriver Time (s) 0.659 0.381 0.402 0.549 0.705 0.618 From the Table 4.14, it is shown that the time is mainly decided by the image size, the number of boundary segments in scene and the number of boundary segments of matched objects. Our recognition system is proven to be robust and efficient, both on non-occlude object recognition and partially occluded object recognition. We have presented part of our experience results in the seventh IASTED international conference (Computer graphics and imaging) [27]. 80 CHAPTER CONCLUSION In this thesis, a novel technique for the recognition of non-occluded and partially occluded objects using curve moment is developed and presented. This technique has been shown to recognize unknown objects which have been rotated, translated, scaled, and even partially occluded by other objects. Firstly, the related works for object recognition have reviewed, especially those focused on partial occluded object recognition. The merits and drawbacks have been discussed. Existing object recognition algorithms have their limitation in some way or another in the recognition of partial occluded objects. Secondly, we studied and analyzed the theory and property of curve moment invariants, represented the physical interpretation of curve moments of an image, and proved that curve moments of curve segment are invariants to similarity transformation. The advantages of curve moment invariants serve as the object features for solving partial occlusion problem are shown. After that, a novel object representation technique based on curve moment is developed and presented. Then, a series of object recognition algorithms are addressed. The partial occlusion problem is presented. The recognition procedure includes preprocessing, segmentation, feature extraction and matching has been described step by step. 81 Extensive experiments have been done to test the performance of our recognition system in three aspects: 1. Invariant to similarity transform; 2. Tolerant to noise; 3. Robust to partial occlusion. Experimental results showed that our recognition system can successfully recognize not only standalone object but also partial occluded object. It can also handle similarity transform and noise. Overall, our proposed recognition system is a novel approach for solving partial occlusion problem and it outperforms some traditional algorithms. However, there are several possible works need to be done in future research to improve our recognition algorithm. 1. In our recognition system, the partition algorithm is not strictly scale invariant, a more stable segmentation algorithm need to be developed in future. 2. Currently, the threshold value is obtained experimentally, an optimum threshold value with theoretical support need to be developed in the future. 3. 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Algorithm: Edge Detection in Binary Images For each pixel p(x, y) let h (x, y) be a white pixel If p (x, y) is a black pixel If ( p (x, y+1) is a white pixel OR p(x, y-1) is a white pixel OR p(x+1, y ) is a white pixel OR p(x-1,y) is a white pixel ) h (x, y) = black pixel 91 APPENDIX C Algorithm for boundary tracking The boundary tracking algorithm may be summarized as follows: Algorithm: Boundary tracking Find E[n] in scanning line; /* starting pixel */ n = 2; let next_pixel be the second boundary pixel found as section 3.1.3; let d cn be the direction from E[1] to next_pixel; while ( next_pixel ≠ E[1] ) E[n] = next_pixel; d pc = d cn ; find_next ( E[n] , d pc , next_pixel, d cn ); n = n + 1; 92 Algorithm: Find next boundary pixel find_next ( Pc , d pc , Pn , d cn ) d cp = invert ( d pc ) ; found = 0; For r = to d = mod ( d cp + r , 8); P = chainpoint ( Pc , d ); If ( ( P is a black pixel ) and ( found =0 ) ) then Pn = P; d cn = d; found = 1; The function chainpoint( P, d) simply returns the coordinates of the neighbor pixel of P in the direction d. 93 [...]... have been used Therefore not only the non -partially- occluded objects, but also the partially occluded objects can be recognized The final representation is usually a string or a graph, the similarity measure is done by string matching or graph matching 1.3.3 Partially occluded object recognition The main objective of this thesis is the recognition of occluded objects A study on previous attempts is introduced... properties make curve moment a potential descriptor for object recognition involving partial occlusion problem In our research, we have developed a methodology to solve object recognition involving partial occlusion problem based on curve moment descriptors In this thesis, we use curve moment invariants as the feature of object to recognize the objects We first preprocess the image and extract object boundary... our research, we understand that the curve moment have transformation invariance not only for the curve but also for the curve segment The followings are the definition of curve moment, whose invariants we are going to use as object feature We modified the moment definition in equation (2.1) using the shape boundary only For a curve or curve segment C, its curve moments of order (p, q)th is defined... smooth curve in the plane and C ′ is the curve obtained by rotating C an angle θ clockwise, then φ k′ = φ k for 1 ≤ k ≤ 7 (2.16) 21 where φ k′ is the curve moment invariants of the curve C ′ , φ k is the curve moment invariants of the curve C They both are defined as in equation (2.6) by using normalized central curve moment η pq in equation (2.11) for p + q = 2,3, Proof Suppose u ′pq is the central moment. .. approaches, and are not applicable for the recognition of partially occluded object recognition In this project, we will define the new curve moment and apply the curve moment invariants to the structural approach 2.2 Traditional moment invariants Let image intensity function f ( x , y ) be 1 over a closed and bounded region R and 0 otherwise Define the (p, q)th moment as m pq = ∫∫ x p y q f ( x, y )dxdy... continuous one These problems will influence the effect of curve moment invariants as the object features 24 CHAPTER 3 RECOGNITION ALGORITHM USING CURVE MOMENT INVARIANTS The shape representation characteristics of moment functions have been effectively used in recognizing object features from images The most common method adopted in moment based recognition algorithms is the comparison of feature vectors... of two-dimensional partially occluded object recognition in the following aspects: 1 We have analyzed the useful properties and advantages of the curve moment invariants which can serve as the robust features for our specific recognition system 2 We also developed a recognition system which can effectively and efficiently recognize not only standalone but also partially occluded objects 10 3 Advantages... presented another improved moment invariants -curve moment invariants, they are quite similar to Hu’s area moment invariants, but require only the computations along shape boundaries, which tremendously reduces computational efforts However, so far all pattern recognition applications using moments and curve moments rely on the entire region or the boundary of the object of interest Therefore, they... particular view of an object, irrespective of the distance between the camera and the object, as well as the pan and roll angles of the camera The next section describes the invariant functions of curve moments 19 2.3.2 Curve moment invariants Functions of curve moments which are invariant with respect to image-plane transformations are very useful in object identification and pattern recognition applications... to object recognition using Zernike moment invariants in 1990 Super [48] represented a new approach of extraction of shape information from texture using local spectral moments in 1995 R Mukundan and S H Ong [49] also introduced Tchebichef moments, a new set of orthogonal 13 moment functions based on the discrete Tchebichef polynomials in 2001 Chen [50] and Andrzej [51] presented another improved moment . Traditional moment invariants 14 2.3 Curve moment invariants 17 2.3.1 Shape representation of curve moments 18 iii 2.3.2 Curve moment invariants 20 2.3.3 Analysis and solution of curve moment invariants. approach for the recognition of 2D partially occluded objects using the curve moment invariants as the features. Curve moment can uniquely characterize the geometric features of object boundary 2D PARTIALLY OCCLUDED OBJECT RECOGNITION USING CURVE MOMENT INVARIANTS ZHENG HAO (B.Eng., TIANJIN UNIVERSITY)