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The Harris Corner Detection Method Based on Three Scale Invariance Spaces IJCSI International Journal of Computer Science Issues, Vol. 9, Issue 6, No 2, November 2012 ISSN (Online): 1694-0814 www.IJCSI.org 18 The Harris Corner Detection Method Based on Three Scale Invariance Spaces Yutian Wang, Yiqiang Chen, Jing Li, Biming Li Institute of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei Province, 066004, China given, ignoring the role of the differential scales in the Abstract establishing of the scale space image. In order to solve the problem that the traditional Harris comer operator hasn’t the property of variable scales and is sensitive to Aiming at the problem of the traditional Harris detectors noises, an improved three scale Harris corner detection without the property of variable scales and is sensitive to algorithm was proposed. First, three scale spaces with the noises, this paper proposed an improved three scale Harris characteristic of scale invariance were constructed using discrete corner detection method. Three scale spaces were Gaussian convolution. Then, Harris scale invariant detector was used to extract comers in each scale image. Finally, supportable constructed through selecting reasonably the and unsupportable set of points were classified according to parameters , S and t that influence the performance of whether the corresponding corners in every scale image support the Harris scale invariant detector. Harris comers in each that of the original images. After the operations to those scale images were extracted by the Harris scale invariant unsupportable set of points, the noised corners and most of detector and the supportable and unsupportable set of unstable corners could be got rid of. The corners extracted by points were classified according to whether the the three and the original scale spaces also had scale invariant corresponding corners in every scale image support that of property. The experiments results proved that, compared with the scale space on the whole Gaussian pyramid, the utilization the original images. The method could remove the noised factor of the image was increased, the calculation time is corners and most of unstable corners effectively, and decreased, and the image was high recurrence rate and stability. extracted and increased the corners with the characteristic Keywords: Harris corner detect, three scale spaces, scale of scale invariance. invariant feature, Gaussian convolution, improved algorithm 1. Introduction 2. Harris corner detect lgorithm Corners detection is the key step in the image processing, The equation of Harris corner detect algorithm [7] is: and the Harris comer detector is based on the gray scales 2 gx g x g y of images, much sensitive to the change of the image M G() s g g g 2 scale. Based on the Lindberg [1]-[2] theory of the scale x y y (1) automatic selection, Mikolajczyk etc. [3]-[4] studied the construction of Harris scale invariant detector in the scale Where, g x is the gradient in x direction; g y is the space of images. But the Harris scale invariant detector couldn’t provide stable key points. The reference [5] gradient in y direction; sG )( is the Gaussian template. researched systematically the parameter spaces constituted The corner response function of Harris algorithm is: by the parameters capable of affecting the performance of det 2MktrMR (2) the Harris scale invariant detector, and the experiments result corrected the conclusion that the Harris scale Where, R is the response function of the corner required; invariant detector is unstable. The reference [6] det M is the Matrix determinant; tr M is the Matrix trace; constructed multi-scale spaces using different integral k is the default constant, and is generally 0.04-0.06. scales. Combined with the image blocking method, the In the practice, the center value R of an image is Harris comers were extracted, realizing the accurate calculated and if the value is the maximum in the location in small scale and removing false and remaining neighborhood and larger than a given threshold, the point reality in large scale. But the proportional relations is regarded as a corner point. between the integral and the differential scales were not Copyright (c) 2012 International Journal of Computer Science Issues. All Rights Reserved. IJCSI International Journal of Computer Science Issues, Vol. 9, Issue 6, No 2, November 2012 ISSN (Online): 1694-0814 www.IJCSI.org 19 In order that the second moment Matrix to detect Harris Traditional Method of Lowe [9]-[10] realized Harris scale corners in the scale space was adaptable to the change of invariance detector. In the process of establishing the scales, the secondary moment Matrix after scale Gaussian pyramid image, Harris corners of every points in adjustment was adopted expressed followed: every sub-scale space were calculated according to M x,,, y equations (1) and (2) , and compared them with the Harris ID corners of 26 neighborhood points located at 3 adjacent 2 I x,, y Ix I y x,, y D scales. If the Harris corner get the local maximum value 2 g xD DI 2 and larger than a given threshold, it is extracted as the Ix I y x,, y D IyD x,, y key point. (3) Where, I is the integral scale; D is the differential Experiments show that, establishing whole pyramid will cost much time, and the number of Harris corners scale, and = ; S is the constant; I and I is the x y extracted from every image is close related to the R gradient in the x and y direction. max of the image. Generally, if the value of is small in an image, the When Rmazx max(R ) , RR .0 01 max , and the value of R at every point of the image is also small, maximum value of 3 3neighborhood is got, the current impossible to be larger than all the 26 neighborhood point is a corner. It is the gradient that is calculated by points. So a little of the image in the pyramid is Harris operators, so it is changed only in directions, contributed, and the number of the corners extracted is independent of the image brightness, that is, the small. Solving the problem would cost more time to algorithm has the feature of rotational invariance. establish more layers of pyramid. The value of is determined by and S, and to different images, the different value of and S would also increase the 3. Improved Harris corner detect algorithm calculation complex and the time. with three scale invariance spaces In this paper, three Gaussian kernel functions with In order to solve the defects that the traditional Harris comer detector is sensitive to scale spaces and noises, an different scales G1 (,,) x y 1 , G2 (,,) x y 2 and improved three scale Harris corner detection algorithm G3 (,,) x y 3 were established, and the four images in was proposed. their scale spaces including the original image were constructed. The corners of the four images were The theory of the scale space is first used to simulate the 2 multi-scale features of images in the computer vision field. extracted by Harris, where 2 t 1 , 3 t 1 . The Lindeberg etc. demonstrated that the Gaussian kernel unstable and noise corners without scale invariance were function is the only linear kernel. The Gaussian kernel removed. Then the corners calculation was increased, function with the variable scales is [8]: assuring the numbers of the corners extracted. The steps 2 2 2 were: 1 xy /2 G x,, y 2 e (1) Based on the original image L0, three space images 2 (4) L1, L2, L3 with different scales were established by three An image in a scale could be expressed the convolution of Gaussian kernel functions with different scales the image and the variable Gaussian kernel function, and , , . the expression of the LOG operator is: Experiments showed that the suitable value of is 0.6- L x,,,,*, y G x y I x y 1.2 and the t is 1.5-2.5. (5) (2) The Harris corners of the four images were extracted according to the equations (1) and (2). Experiment Where, (,)x y is the space coordinate and the little showed that the suitable value of S is 0.4-1.0. represents the little smoothing of the image, and the (3)If the corner a in the image L0 could be found in corresponding scale is small. Large scales correspond to 0 the general view of images, and small scales correspond other 5 5 neighborhood of other images with different to the details of images. scales, it would be regarded as being supported by corners in other scale spaces and the corner could be reserved. Copyright (c) 2012 International Journal of Computer Science Issues. All Rights Reserved. IJCSI International Journal of Computer Science Issues, Vol. 9, Issue 6, No 2, November 2012 ISSN (Online): 1694-0814 www.IJCSI.org 20 Otherwise, the corner would be removed. The number corners were extracted by the improved Harris algorithm. of the reserved corners was z . We set =0.8, t= 2 , and S=0.8 in the experiments. 1 (4) Corners in the images L1, L2, L3 were separated into The first image series shown in the Fig.1 and the Fig. 2 the corners supporting L0 and the corners not supporting adopted the classical testing image and the corresponding L0. The corners collections not supporting L0 in the three image with additional noises. images L1, L2, L3 were recorded as , , a1[] n 1 a2[] n 2 a3[] n 3 . (5) For the corner a1 in the , if it could be found that at least one corner was the corner in the and with 5 5 neighborhood of images L2, and L3, the corner of the in the image L1 would be regarded as the corner with scale invariance.
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