Authors: Peng He, Na Wang, Cheng Lin Wang

Abstract: An improved corner detection algorithm for medical image based on USAN is proposed in this paper. The algorithm firstly defines the concept of end line which through the core of the circular template, and analyses the number of end lines in the corner point, thus obtains an initial response function of the corner. Then puts forward a non-maxima suppression method by defining the concept of uniformity coefficient of the non-end line. Finally, compared with existing algorithms, experiments indicates that the improved algorithm has the fast and accurate advantages. I.IntroductionCorner detection based on grayscale images has been widely used in medical image registration. Medical image registration techniques can be divided into two categories, which is based on pixels (voxels) and the feature-based methods. Feature-based registration method is matched by extracting the structural features of different images (the common features including points, contours, curves and surfaces, etc.) , in which the registration based on feature points is the most widely applied method[1]. Corner points as the feature of image has rich information content and a little calculation, matching simple and rotation, translation, scaling invariant properties. In recent years, some improved methods for Harris algorithm[2,3] and USAN (Univalue Segment Assimilating Nucleus, with the value of the shrinking core) algorithm[4] method have been applied in image registration. In 2002, Zhou Peng, etc. developed a new corner detection method based on the model proposed in the USAN[5].Experimental results show that image registration based on the method without restrictions on the rotation of the image, it improves the registration accuracy and has less computation. In 2006, Rae etc. built a new multi-scale Harris corner detection algorithm[6]. The new corner-detection method can obtain corner points at different scales corner, improved the detection performance of detection operators, advanced the registration accuracy of corner-based image registration algorithm. In 2007, Huashun Gang, etc. absorbed and improved the SUSAN , proposed a dense image matching algorithm[7], using Sobel operator and the feature similarity to initially match the corner on the left and right image, achieved dense matching of all the pixels of two images which without calibration. At present, image corner detection based on gray, in particular the method based on template made great development. However, the accuracy of these methods are mostly poor, algorithm complexity, time-consuming, so have some limits in real-time applications. Based on the USAN, a new improved algorithm was proposed and has been applied to medical image corner detection, the new algorithm in terms of speed and accuracy has a larger increase.II.Susan Corner Detection PrincipleSUSAN algorithm [4] defines a circular template, as shown in Fig. 1, the center of circular template is called the core, if some pixel's brightness of the circular template is the same or similar to the core, the region composed with these pixels will be defined USAN region ,at the corner point and non-corner point, USAN region area is different, and the USAN area of the corner point is the smallest.Fig. 1 The circular template of SUSAN algorithmDoing the specific defection, a circular template with 37 pixel will be used to scan the entire image, and to calculate the gray intensity’s minus between each pixel and the core of the template, if the absolute value is less than the given threshold t ,which will be considered to belong to USAN ,the commonly used similarity comparison function is as follows: (1)in this formula,is the discriminate result，is the gray value of the core of circular template， is the gray value of the arbitrary pixel in addition to the core of the template.Apply the formula (1) to each pixel, then the size of the USAN area can be expressed as: (2)In this formula, is the circular template whose core is [8].After getting the USAN area of all the pixels, then according to the following corner response function to generate the initial corner response: (3)In this formula, g is the geometric threshold value of the noise suppression, which decides the maximum value of output corners’ USAN area.SUSAN algorithms do not need the beforehand edge detection, which avoid the calculation of the gradient and not depend on the results of image segmentation, with integral characteristics, good anti-noise performance, and is not influenced by the type of the corner point, so it is widely used in image processing. However, a fixed threshold value will also make the positioning accuracy is not satisfactory, easy to produce pseudo-response, or easy to lose the true corner point, the process of integration has also led to more time-consuming.III.Description of the Improved AlgorithmA. Corner Detection Based On Non-end LineUse the circular template in SUSAN algorithm ,in the circular template start a axle-box whose origin is the core, if the pixels at the axis positive direction are all located in the USAN outside, there is the pixels within the USAN in the negative direction, state the core as the end point at the direction of the axis ,state the axis as the end line of the core, otherwise state it as the non-end line, as shown in Fig. 2,is the end point at the direction of ,is the end line. Due to that there are no pixels at the negative direction of within the USAN, so is not the end point at the direction of ,is non-end line, as the same, is not the end point at the direction of , , , is non-end line ,is the end point at the direction of , but is not the end point at the direction of , is the end line, is the non-end line.By analysing of the fig.2, we can get the following laws: there are numerous end lines and non-end lines inner the circular template whose core is the corner point; there are numerous end lines inner the circular template whose core is the edge point; but there is only one non-end line, which is the axis down the direction of USAN area edge; there are numerous non-end lines, but there is no end line inner the circular template whose core is inner point. That is to say, the corner point has numerous end lines and non-end lines; the edge point has numerous end points, but there is only one non-end line; the inner point has numerous non-end line, but no end lines.Fig. 2 The end line and non-end line of the circular templateFig. 3 The corner inspection based on the number of the end linesAccording to the above rules, you can filter out some of the non-corner points by the way of judging the number of the end lines and non-end lines inner the circular mask, and generate an initial response of the corner points. In Fig. 3(a), eight straight lines which pass through the circle are distributed in the circular mask, it can be respectively stated as , it is the USAN area shown by the shaded area, Stated from the Fig., the number of the end lines and non-end lines are respectively five and three, according the above rules, we can judge O is the corner point . In actual detections, considering of a circular template including 37 pixels, shown in Fig.3(b), each edge pixel and the pixel on the symmetry of the core constitute a line straight passing through the core. for example, the two pixels numbered g constitute the straight line g-g, the same as Fig.3(a), all pixels were composed of eight straight lines. Using a circular template to scan the entire image, to calculate the number of the end lines and non-end lines in each template to produce a candidate corner points.In Fig. 3 (a) , the line constituted by two symmetrical edge pixels is (), the collection of the end lines within the round templates is and the collection of the non-end lines is , then the judging formula of the end line is: (4)In this formula, 、 respectively stands for the similarity values of the two symmetrical edge pixels with the core ,and is the non-end line rejection threshold. For easy to calculate, the definition of the degree of the end line is: (5)Then the number of end line within a circular template is: (6)So the initial response function of the corner point is: (7)In this formula, is the geometric threshold for restraining edge points.Only the relationship between the edge pixel and the core is considered in the introduction of the new algorithms, which will generate some pseudo-response at the corner points, a number of suppression methods should be adopted to filter, but based on that the calculation amount can be greatly reduced because of the edge points’ initial response, which makes it more applicable for real-time applications.B. Non-maxima Suppression Based on Non-end Line’s uniformity coefficientAs a result of adapting the similarity between the edge pixels and core to generate the initial response of the corner points, pseudo-response will be produced in a certain range near the corner, as shown in Fig. 4, in the circular template 1, A corner points can be got by, , in the circular template 2, B corner points can be got by, , apparently B is a pseudo-response. The following non-maxima suppression method based on the non-end line’s uniformity can be adopted to filter the false responses.Fig. 4 The uniformity degree of the non-end lineAccording to Section 3.1, non-end line has two forms, the one is the direction line which is not passing through the USAN area (assuming that a small neighbor area near the core of the USAN area is negligible), the other is the direction line which is passing through the USAN area but the two intersection with the circular template is located outside USAN area. If a non-end lines do not pass through USAN region, we call it is uniform, or else call it a non-uniform, and according to the length of the segment inner USAN area to define the degree of non-uniform, the longer is, the greater the degree of non-uniform is, shown in Fig. 4, the degree of non-uniform 、 is greater than 、(, is uniform), it is easy to prove, the degree of non-uniform at the corner point is the greatest, but the degree of non-uniform at the non-corner point is the smallest, so according to this feature, pseudo-response suppression can be operated.While actually use it, first use the judging formula of the end lines to get the non-end lines, then through calculating the length of the line segment in the USAN region to get the degree of non-uniform, suppose the degree of non-uniform of the non-end line as ,so (8) is the non-end line which is passing through the core of the circular template, thus, the degree of non-uniform of all the non-end lines that have passed through is :(9)represent all the non-end lines that passes through the core of the circular template. Finally, the non-maxima suppression function is as follows: (10) in this formula, is the geometric value of pseudo-response suppression, which determines the sharp degree of the output corner points.IV. Experimental VerificationTo test the effectiveness of the new algorithm, this paper compared the improved algorithm with the present algorithm in accuracy and computational complexity .First, through adopting artificial typical corner-point image to test, shown as Fig. 5, (a) is the initial image, (b)~(d) is the effective image which respectively adopted Harris algorithm, SUSAN algorithm and the improved algorithm, through analysing, Harris algorithm has positioning bias in some corner points, there is also a small amount of pseudo-response, while SUSAN and the improved algorithm has greater effect. (a) Initial image (b) Harris (c) SUSAN (d) Improved algorithmFig. 5 The detection results in artificial corner detection of the improved algorithm and the initial algorithmFig. 6 is the detection test results of the three kinds of algorithm in medical image, you can see, Harris has stronger ability to process actual image processing ,but has a large number of pseudo-response points and there are few undetected corner. SUSAN has not very good processing effect to process actual image and has a lot of pseudo-response points. The new algorithm also has a little pseudo-response points, but on the whole there is a better detection result than the SUSAN algorithm .TableⅠ shows the average detection rate of the three algorithms in a variety samples. (a) Initial image (b) Harris (c) SUSAN (d) Improved algorithmFig. 6 The test results of the improved algorithm and the initial algorithm in medical imageTABLEⅠTHE AVERAGE DETECTION RATE OF THE THERE ALGORITHMWe can know from the former analysis of the algorithm, the improved algorithm do the complex calculations only on the most likely place for the corner points, but do little calculations on the easily judge where is the non-corner points, and the new algorithm is not based on a very abstract theory, which makes that the improved algorithm simple and easy to understand, with low computational complexity. The author adapted a variety samples to add up the detection time of the three algorithm using own computer, shown in the TableⅡ, we can know, the detection time of the improved algorithm is significantly lower than other algorithm.TABLEⅡ THE AVERAGE DETECTION TIME OF THE THERE ALGORITHMV.ConclusionsIn order to improve detection speed, the improved algorithm uses a progressive layer by layer mechanism, the basic idea is: first, through the most simple calculation to exclude certain non-corner points, followed the possible areas for the corner point will be implement the more sophisticated detection algorithm, due to the proportion of the corner point in image is small, this mechanism greatly increased the detection rate. For the pre-processing of the exclusion of the non-corner point, this paper proposed a method based on the smallest circular template with small amount of calculation, and can retain all the characteristics of corner points. In the corner detection algorithm, using the number characteristics of the corner points’ end line, and according to the non-end lines’ uniformity coefficient to perform non-maxima suppression, experiments show that the improved algorithm is effective in the speed and accuracy of calculation is better than the SUSAN method .ReferencesVanden P, Evert Jan D P, Viergever M, ”Medical image matching-a review with classification,” IEEE Engineering in Medicine and Biology, vol.12, no.1, pp. 26-39, January 1993.Jianhui Hou, Yi Lin, ” Harris checkerboard corner detection algorithm with self-adapting,”Computer Engineering and Design, vol.30, no.20, pp.4741 -4743, October 2009Harris C, Stephens M. A Combined Corner and Edge Detector. In Proceedings of the 4^{th }Alvey Vision Conference, pp. 147-151,1988.Smith S M, Brady M. 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