Perspectives in Science (2016) 8, 488—491

Available online at www.sciencedirect.com

ScienceDirect journal homepage: www.elsevier.com/pisc

HPV guided object tracking: Theoretical advances on fast pattern matching technique夽 Deep Suman Dev a, Dakshina Ranjan Kisku b,∗ a

Department of Information Technology, Neotia Institute of Technology, Management and Science, Diamond Harbour Rd., Sarisha Hat, Sarisha 743368, West Bengal, India b Department of Computer Science and Engineering, National Institute of Technology Durgapur, Durgapur 713209, Burdwan, West Bengal, India Received 6 February 2016; received in revised form 19 April 2016; accepted 8 June 2016 Available online 1 July 2016

KEYWORDS Pattern matching; Haar transform; Image integral; Arithmetic operations

Summary Pattern matching is a fundamental machine vision problem that deals with searching an object in a comparatively large scene. It can use to solve many vision problems ranging from typical human detection to searching defective parts in industrial automation. This paper reports a fast pattern matching technique which makes use of cumulative subtraction and cumulative division operations based on Image Integral model. The idea is to use both the cumulative subtraction and division operations to evaluate the image values on a very small rectangular region of the image scene as well as on the input pattern to be searched for. Image values are transformed to Haar Projection Values (HPVs) using Haar transform in order to achieve pattern matching on sliding window of the image scene. Computation of HPV needs seven arithmetic operations, including two addition and five subtraction operations, which are found to be same as that of Image Integral technique. Besides, the proposed pattern matching technique is identified as computationally effective in terms of both time and memory. © 2016 Published by Elsevier GmbH. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Introduction

夽 This article belongs to the special issue on Engineering and Material Sciences. ∗ Corresponding author. E-mail addresses: [email protected] (D.S. Dev), [email protected] (D.R. Kisku).

Pattern matching problem (Lewis, 1995; Ouyang et al., 2010) can be thought as the matching of feature points representing an object or a pattern to an instance of that object given in a scene. It has extensive applications in object tracking and detection (Viola and Jones, 2001), shape matching (Lampert et al., 2008), image retrieval and industrial applications in automotive machine vision. For example, pattern

http://dx.doi.org/10.1016/j.pisc.2016.06.005 2213-0209/© 2016 Published by Elsevier GmbH. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

HPV guided object tracking

489

Figure 2 Figure 1 An example of scene of various objects from COIL100 database (http://www.cs.columbia.edu/CAVE/databases/) is shown.

matching can be used for finding a pattern in a scene contains large number of objects, finding a particular face in a scene of crowd face images, finding a missing part of an object in some industrial products by inspecting on assembly line, etc. In those applications, a priori information about the target pattern is determined in the form of deformable shape, texture, boundary information, etc. The task of pattern matching is to find the pattern in the scene with some priori information. Moreover, the features which constitute the target pattern make the correspondence with features determined from a window in a scene by maximizing the similarity function. Fig. 1 shows an example of a scene where the input pattern to be searched. There exist many pattern matching algorithms which claim to reduce computational complexity by finding the target pattern in the scene. Considering speed constraint, the set of algorithms can roughly be divided into two groups — full search algorithms and fast pattern matching algorithms. Most of the cases it has been seen that, fast pattern matching algorithms outperform full search algorithms. The similarity between a target pattern and a sliding window decides the pattern to be searched in the given scene. A large number of similarity based fast pattern matching algorithms can be found in Lewis (1995), Stefano and Mattoccia (2003), Pele and Werman (2008) and Lowe (2004). Some algorithms use normalized correlation based similarity approach to pattern matching problems in Lewis (1995) and Stefano and Mattoccia (2003). Use of Hamming distance can be found in Pele and Werman (2008). The pattern matching algorithms which use Sum of Squared Differences (SSDs) based similarity can be found in Ouyang et al. (2010). Other than similarity, dissimilarity scores can also be used to find the input pattern in the scene and few works on dissimilarity are available in Lowe (2004) and Mikolajczyk and Schmid (2005) as part of fast pattern matching algorithms. In this paper, we are interested to develop a pattern matching algorithm which would be computationally efficient as well as it would find the target pattern as an instance in the given scene in faster way. In order to accomplish this task, the proposed algorithm uses Image Integral model (Ouyang et al., 2010) as Haar transform manipulator. As most of the pattern matching algorithms are not proved to be memory efficient, therefore large memory space requirement could be disastrous and at the same time performance can be degraded. Though the authors of Ouyang et al. (2010)

Rectangle Rect in image g(H, W).

use Haar like features to compute Haar Projection Values (HPVs) and for cumulative computation, Image Integral and Image Square Sum techniques are used. This particular combination (Ouyang et al., 2010) achieves the desired results and behaves like fast pattern matching algorithms. However in our paper, cumulative computation is performed using arithmetic operations, such as subtraction and division. Rectangle sum (Ouyang et al., 2010) and Haar like features (Ouyang et al., 2010) are successfully applied in object detection (Viola and Jones, 2001), object classification (Lampert et al., 2008) and pattern matching (Tombari et al., 2009) problems. On the other hand, Integral Image (Ouyang et al., 2010) can be used to find rectangle sum and the corresponding Haar Projection Values (HPVs) (Ouyang et al., 2010) from an image using Haar wavelets. This paper suggests a novel pattern matching algorithm with two different variants to find the rectangle sum and HPVs using Image Cumulative Subtraction and Image Cumulative Division operations. Prior to apply cumulative operations, Haar like features are applied to both target pattern and windows of given scene to determine HPVs separately. The rest of the paper is organized as follows. Section ‘Pattern matching techniques’ discusses the proposed pattern matching algorithm with two different variants. Concluding remarks are made in the last section.

Pattern matching techniques Image Cumulative Subtraction To compute HPVs (Ouyang et al., 2010) from both the target pattern and the candidate window, we apply Image Cumulative Subtraction (ICS) method. HPVs for any spatial location (x, y) can be computed using ICS method is shown in Fig. 2 where the updated value (after cumulative subtraction) of spatial location (x − 1, y) and HPVs of all the spatial locations from (x, 0) to (x, y − 1) are subtracted from the HPV of (x, y). The Image Cumulative Subtraction algorithm is shown in Fig. 3. After computing HPVs, a correlation based metric is used to find a correspondence between the input pattern and a candidate window, and a predefined threshold decides whether the candidate window to be accepted or rejected. The cumulative subtraction operation is expressed by the following equation: ICS(x, y) = (g(x, y) − ICS(x − 1, y)) −

y−1  i=0

g(x, i)

(1)

490

D.S. Dev, D.R. Kisku

Algorithm 1 Image Cumulative Subtraction (ICS) Algorithm

Algorithm 2 Image Cumulative Division (ICD) Algorithm 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

Let, ICS(0, 0) = g(0, 0) and d, c are two matrices having all zeros with size h × w. for x = 0 to h – 1 do for y = 0 to w – 1 do b(x,y) = g(x,y); end for end for for x = 1 to h – 1 do Compute ICS(x, 0) = g(x, 0) –ICS(x – 1, 0); end for for y = 1 to w – 1 do for k = 0 to y – 1 do d(0, y) = b(0, k) – d(0, y); end for Compute ICS(0, y) = g(0, y) – d(0, y); end for for x = 1 to h – 1do for y = 0 to w – 1 do for k = 0 to y – 1do c(x, y) = b(x, k) – c(x, y); end for ICS(x, y) = (g(x, y) – ICS(x – 1, y)) – c(x, y); end for 23. end for

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

Figure 3

Image Cumulative Subtraction algorithm.

In the following algorithm, h and w represent the height and width of both the input pattern and the candidate window respectively. The ICS is calculated by varying the x and y coordinates from 1 to h and from 1 to w respectively. We compute the rectangle sum using ICS method. The symbols and expressions those of which are used in the algorithm are self-explanatory.

Figure 4

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

Let, ICS(0, 0) = g(0, 0) and d, c are two matrices having all zeros with size h × w. for x = 0 to h − 1 do for y = 0 to w − 1 do b(x,y) = g(x,y); end for end for for x = 1 to h − 1 do Compute ICS(x, 0) = g(x, 0) − ICS(x − 1, 0); end for for y = 1 to w − 1 do for k = 0 to y − 1 do d(0, y) = b(0, k) − d(0, y); end for Compute ICS(0, y) = g(0, y) − d(0, y); end for for x = 1 to h − 1 do for y = 0 to w − 1 do for k = 0 to y − 1do c(x, y) = b(x, k) − c(x, y); end for ICS(x, y) = (g(x, y) − ICS(x − 1, y)) − c(x, y); end for end for

Image Cumulative Division In this section, we present another method that calculates HPVs by computing rectangle sum and we call this method Image Cumulative Division (ICD) as it uses arithmetic division operation. HPV calculation at any spatial location (x, y) using cumulative division method is shown in Fig. 2 where

Image Cumulative Division algorithm.

the HPV at (x, y) is divided by updated HPV (computed using cumulative division) of the spatial location (x − 1, y) and also divided by the values of all the locations from (x, 0) to (x, y − 1). The algorithm is given in Fig. 4. The cumulative division operation is expressed by the following equation ICD(x, y) =

(g(x, y)/ICD(x − 1, y)) , g(x, i)

where i = 0, 1, . . ., y − 1

Algorithm 1 (Image Cumulative Subtraction (ICS) algorithm.). 1.

Let, ICD(0, 0) = g(0, 0) and d, c are two matrices having all ones with size h × w. for x = 0 to h – 1 do for y = 0 to w – 1do b(x, y) = g(x, y); end for end for for x = 1 to h – 1 do Compute ICD(x, 0) = g(x, 0) /ICD(x – 1, 0); end for for y = 1 to w – 1 do for k = 0 to y – 1do d(0, y) = b(0, k) /d(0, y); end for Compute ICD(0, y) = g(0, y) / d(0, y); end for for x = 1 to h – 1 do for y = 0 to w – 1 do for k = 0 to y – 1 do c(x, y) = b(x, k)/c(x, y); end for ICD(x, y) = (g(x, y) / ICD(x – 1, y)) / c(x, y); end for end for

(2)

Algorithm 2 (Image Cumulative Division (ICD) algorithm.). 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

Let, ICD(0, 0) = g(0, 0) and d, c are two matrices having all ones with size h × w. for x = 0 to h − 1 do for y = 0 to w − 1do b(x, y) = g(x, y); end for end for for x = 1 to h − 1 do Compute ICD(x, 0) = g(x, 0)/ICD(x − 1, 0); end for for y = 1 to w − 1 do for k = 0 to y − 1do d(0, y) = b(0, k)/d(0, y); end for Compute ICD(0, y) = g(0, y)/d(0, y); end for for x = 1 to h − 1 do for y = 0 to w − 1 do for k = 0 to y − 1 do c(x, y) = b(x, k)/c(x, y); end for ICD(x, y) = (g(x, y)/ICD(x − 1, y))/c(x, y); end for end for

The rectangle sum is computed using Image Cumulative Subtraction (ICS) can be expressed by Rect(ICS) = ICS(x + h, y + w) + ICS(x, y) − ICS(x, y + w) − ICS(x + h, y) and rectangle sum using Image Cumulative Division (ICD) can

HPV guided object tracking be expressed by Rect(ICD) = ICD(x + h, y + w) + ICD(x, y) − ICD(x, y + w) − ICD(x + h, y), where 0 ≤ x, x + h ≤ H − 1, 0 ≤ y, y + w ≤ W − 1, h > 0, w > 0. To compute rectangle sum, both the cumulative operations need two subtractions and one addition. Further, HPV needs one more subtraction between two rectangle sums. Finally, the algorithm needs seven operations which include five subtractions and two additions.

Conclusion This paper has presented a novel pattern matching algorithm which uses two different variants, such as Image Cumulative Subtraction (ICS) and Image Cumulative Division (ICD). The aim of these two methods is to compute rectangle sum using arithmetic operations. Further, in order to obtain HPVs from Haar like features, rectangle sum is found very effective method. Cumulative operations ICS and ICD can be used to compute orthogonal Haar transform (OHT) and then OHT is used as HPVs for equivalent pattern matching where ICS and ICD methods represent input image in small values compared to values calculated by cumulative sum in image integral. Moreover, the rectangle sum of a particular rectangle region calculated by cumulative sum for image integral is much higher than the rectangle sum calculated by the proposed cumulative operations.

491

References Lampert, C., Blaschko, M., Hofmann, T., 2008. Beyond sliding windows: object localization by efficient subwindow. In: CVPR, pp. 1—8. Lewis, J., 1995. Fast template matching. In: Proc. Vision Interface, pp. 120—123. Lowe, D.G., 2004. Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60 (2), 91—110. Mikolajczyk, K., Schmid, C., 2005. A performance evaluation of local descriptors. IEEE Trans. Pattern Anal. Mach. Intell. 27 (October (10)), 1615—1630. Ouyang, W., Zhang, R., Cham, W.K., 2010. Fast pattern matching using orthogonal Haar transform. In: Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), pp. 3050—3057. Pele, O., Werman, M., 2008. Robust real-time pattern matching using Bayesian sequential hypothesis testing. IEEE Trans. Pattern Anal. Mach. Intell. 30 (August (8)), 1427—1443. Stefano, L.D., Mattoccia, S., 2003. Fast template matching using bounded partial correlation. J. Mach. Vis. Appl. 13, 213—221. Tombari, F., Mattoccia, S., Stefano, L.D., 2009. Full search equivalent pattern matching with incremental dissimilarity approximations. IEEE Trans. Pattern Anal. Mach. Intell. 31 (January (1)), 129—141. Viola, P., Jones, M., 2001. Rapid object detection using a boosted cascade of simple features. In: CVPR, I:511—I:518.

HPV guided object tracking: Theoretical advances on ...

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