Harris Corner Detection Algorithm at Sub-pixel Level and Its Application Yuanfeng Han a, Peijiang Chen b * and Tian Meng c

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1 Iteratioal Coferece o Computatioal Sciece ad Egieerig (ICCSE 015) Harris Corer Detectio Algorithm at Sub-pixel Level ad Its Applicatio Yuafeg Ha a, Peijiag Che b * ad Tia Meg c School of Automobile, Liyi Uiversity, Shadog, 76000, Chia a hyf @163.com, b * chepeijiag@163.com, c @qq.com Keywords: Harris corer, Sub-pixel, Gaussia surface, Image matchig Abstract. The corer is oe of the most importat features of image ad the corer detectio plays a importat role i digital image processig techology. The performace of Harris corer detectio algorithm is stable ad it is widely applied, but the corer locatio is pixel level which affects the subsequet image processig. I order to improve the performace of corer detectio, the harris algorithm is improved. O the basis of aalyzig the priciple of Harris corer detectio algorithm, the sub-pixel level corer positio based o the Gauss surface method is extracted. The extracted corers is applied i images matchig. The experimetal results show that the Harris corer detectio algorithm ca extract high accurate corers. At the same time, the image matchig based o this algorithm has higher precisio. Itroductio The corer reflects the characteristics of image s essece which brightess chages strogly [1]. The real corer ca effectively simplifies the iformatio amout of data processig. The, it sigificatly improves the speed of image processig ad matchig accuracy ad realizes the efficiecy of image processig. Therefore, i the etire image processig process, corer extractio is particularly importat. Further, corer extractio is more accurate ad more coducive to aalyze ad process image iformatio []. At the same time, corer extractio plays a crucial role i determiig the object i the real eviromet, eve it is sigificat for stereo matchig view. Harris algorithm is a classical corer detectio method. Its comprehesive effect is good ad it is widely applied, but there are also may limitatios. For example, it ca be oly applied i a sigle scale, ad it is difficult to implemet multi-scale corer detectio. Ad the threshold value should be give maually, i additio, the threshold value directly affects the effect of corer extractig. Harris algorithm extracts corer based o pixel level, which has bee uable to meet the requiremet for precisio. With the rapid developmet of computer techology, the sub-pixel corer detectio has become a importat part of the computer image processig. I this project, aimig at the shortcomigs of the Harris algorithm, first of all, usig Harris detectio algorithm extracts the feature poits, the, adoptig Gaussia surface fittig improves the accuracy of the extracted feature poits, which would lay a foudatio for the stereo matchig of feature poits, ad it is applied to the image matchig. Harris corer detectio The algorithms of corer detectio Over the years, the sciece researchers have bee committed to the corer detectio field. The corer detectio plays a importat role i the field of image processig. At preset, the corer detectio methods are maily divided ito two categories: based o image edge iformatio ad based o image gray scale iformatio [3]. The corer detectio i image processig has the followig requiremets. (1) Stability. The corer detectio algorithm has strog adaptability to gray scale images, lies ad brightess, which ca make proper adjustmet automatically, ad the detected corer umber ad positio are stable The authors - Published by Atlatis Press 133

2 () Resistace for oise. Durig a certai amout of oise, the algorithm ca weake or elimiate the oise, ad it has strog ability of corer detectio. (3) Accuracy. It ca fid the accurate coordiates of corers. (4) Efficiecy. The method is fast eough ad it saves ruig time. The priciple of Harris corer detectio Harris algorithm basically meets the requiremets of the corer detectio, thus it has quite ideal effect, ad it is widely applied. It uses a certai threshold to extract the feature poits by the aalysis of image gray s chage. The color image is trasformed ito a gray image. Differetial operator ca reflect the chage of pixel gray level i ay directio, thus effectively distiguish the corers ad edge poits [4]. The chage of gray itesity ca be determied by aalyzig the movig pixels i ay directio. Harris corer detectio is maily to use gray iformatio to detect corers ad its priciple is the image gray scale average differece which is caused by the image widow deviatig i ay directio. The auto-correlatio equatio is expressed, as show i Eq. 1. E x y w I I (1),, m x m, y x, y m, Where, w is the image widow fuctio. E( x, y ) ca be approximately expressed, as show i Eq.. E x, y Ax By Cxy () Where, A X w, B Y w, C XY w, w ca select the Gaussia smoothig fuctio, X ad Y are first order directioal derivatives. x A C x E x, y x ym x y y C B y (3) Matrix M is approximately the Hessia matrix of autocorrelatio fuctio, the judgmet fuctio ca be defied, as show i Eq. 4. R x, y det[ M ( x, y)] k trace [ M ( x, y)] (4) Where, det() is the determiat of the matrix, ad trace () is its trace. If the R( x, y ) of a poit is greater tha certai threshold, it ca be made as a corer. From the algorithm s operatio, the threshold settig is a very critical problem. The threshold settig determies the effect of corer extractio, the value of threshold depeds o the huma experiece [5]. If the threshold is too large, it is easy to lose corers, ad if the threshold is too small, it is easy to extract false corers. The threshold settig greatly depeds o the ature of the real image, especially whe the image color chages, the threshold is more difficult to choose [6]. I additio, there are some problems such as the detected corers are pixel level, which affects the followig accuracy of image processig. The Sub-pixel corer detectio of Harris algorithm The Harris algorithm extracts corers at pixel level, the positioig precisio is low. I order to improve the precisio of Harris corer, the sub-pixel detectio methods are used [7]. Now, these methods are maily divided ito three categories: iterpolatio method, momet method ad fittig method. The fittig method is widely used i the field of digital image processig. There are various kids of surface fittig, such as Gaussia surface fittig, polyomial fittig method, ellipse fittig method. This project focuses o the Gaussia surface fittig algorithm, which ca realize the positioig precisio at level of the sub-pixel. First of all, usig the Harris operator ca carry out coarse positio of corers at pixel level. The, the coarse positioig pixel is made as the ceter. The appropriate widow is selected to get the 134

3 correspodig iformatio of grey value. Fially, the corers at the level of sub-pixel ca be gotte, which ca improve the extractio precisio of image corers [8]. The equatio of Gaussia surface ca be expressed, as show i Eq. 5. z e (5) Where, ρ x x0 ( y y0). Take the logarithm o both sides. x x x0 y y y0 l z x y x y Where, 0, 1,, 3 are udetermied parameters, l( ) l 0 x y, x 0 1, y0, 1 3. Accordig to the least squares priciple, the parameters ca be gotte, ad the corer positio ca be obtaied, as show i Eq x, y,, e (7) The, ( x0, y0) is the Gaussia surface extreme value poit positio. I the project, the corers of two automobile image are detected by Harris algorithm combiig with the Gaussia surface method, as show i Fig 1. The false corers are little ad they have high precisio. (6) (a) Left image (b) Right image Fig. 1 The detected corers of two automobiles Image matchig based o Harris corers Image matchig is the process of lookig for similar image or sub-image i a image with a give target image [9]. The techology belogs to the key cotet i the field of computer visio. Due to ucotrollable factors, such as oise, light wave iterferece, the feature poits o the two cameras of the same calibratio object will be differet. I additio, the feature poits o left ad right image may be o loger the mappig relatioship of oe-to-oe. A feature o the left imagig plae may correspod to several characteristics o the right imagig plae. I order to make image matchig more accurate, it is usually to set a variety of costraits o them. 135

4 (1) The cadidate matchig based o correlatio theory Usually, makig a feature poit of the image as the ceter, a sub-image widow is selected as the eighborhood widow of the feature poit. The similarity would be compared betwee the left eighborhood widow of a give feature poit i the left image ad each right eighborhood widow of feature poit i the right image. Accordig to the ormalized formula of correlatio coefficiet at gray-level, the calculatio of similarity ca be described, as show i Eq. 8. S( x, y) 1 m1 y ' 0 x' 0 ( T ( x ', y ') T )( I ( x x ', y y ') I) 1 m1 1 m1 ( T ( x ', y ') T) ( I( x x ', y y ') I) y ' 0 x' 0 y ' 0 x' 1 Where, S( x, y ) is the similarity of two correspodig eighborhood widow, I is gray scale value of target image, I is the average gray scale value of eighborhood widow i the target image; T is the gray scale value of source image, T is average gray scale value of eighborhood widow i the source image. () Matchig stregth calculatio of correspodig poits based o disparity gradiet Cadidate matchig based o correlatio meas are more cocetrated. Because of the brightess ad evirometal coditios, a certai feature poit i oe image may have may similar poits i aother image. The disparity gradiet ca be used to detect the cosistecy degree of matched poits [10]. (3) Calculatig the fudametal matrix based o cadidate matched poits The liearity of fudametal matrix ca be estimated by usig the ormalized coordiates of correspodig poits. Before the calculatio, the correspodig coordiates of feature poits ca be processed by ormalizatio. The ormalizatio matrix is obtaied by usig least square method. After the adjustmet based o rak- costrait, the fudametal matrix ca be gotte. Accordig to the fudametal matrix, it ca elimiate most false matchig, so the matched corers has high registratio precisio. For the tow automobile images as show i Fig. 1, the detected Harris corers are matched based o the above method, the corer matchig results are give, as show i Fig.. The matchig result of the detected Harris corers has higher accuracy. (8) Fig. The corer matchig results of the two automobile images Coclusios O the basis of Harris algorithm, the Gaussia surface fittig is used to extract the the sub-pixel corers i this project. The experimetal results show that extracted corers are more accurate, ad the experimets of image matchig ca also verify the effectiveess. It ca be used i some 136

5 applicatios with higher demad of positioig precisio. Of course, there are also somethig eed to be improved. For example, the Harris algorithm uses certai threshold to detect the corers, which affects the uiversality of the algorithm may brig certai difficulty for subsequet precisio positioig. The related research eeds to be cotiued to improve the practicability of the corer detectio method. Ackowledgemets This study is sposored by the Natioal Udergraduate Traiig Programs for Iovatio ad Etrepreeurship (No ) ad the Sciece ad Techology Developmet Plaig Project of Shadog Provice (No. 013YD05004), People s Republic of Chia. Refereces [1] F. Bellavia, D. Tegolo, C. Valeti, Improvig Harris Corer Selectio Strategy. IEF Computer Visio. 5() (011) [] Y. Bastalar, Y. Yardimci, Corer Validatio Based O Extracted Comer Properties. Computer Visio ad Image Uderstadig. 5(3) (008) [3] W. Zhao, S. Gog, C. Liu, X. She, Adaptive Harris Corer Detectio Algorithm. Computer Egieerig. 34(10) (008) [4] X. Wag, Z. Wag, F. Wu, Harris Correlatio ad Feature Matchig. Patter Recogitio ad Artificial Itelligece. (4) (009) [5] D. G. Lowe, Distictive Image Features From Scale-Ivariat Key-Poits. Iteratioal Joural of Computer Visio. 60() (004) [6] Y. Li, R. Xia, Sub-pixel Edge Detectio Algorithm Based o Curve Fittig Method. Trasactio of Chogqig College of Techology. (10) (008) [7] Z. M. Liag, H. M. Gao, Z. J. Wag, L. Wu, Sub-pixels Corer Detectio for Camera Calibratio. Trasctios-Chia Weldig Istitutio. 7() (006) [8] D. Zhao, D. Liu, Y. Yag, A New Stereo Matchig Method Based O Sub-pixel Corer Detectio. Iteratioal Coferece o Computer Sciece ad Software Egieerig. () (008) [9] Q. Zhu, B. Wu, N. Wa, A Sub-pixel Locatio Method for Iterest Poits By Meas of the Harris Iterest Stregth. The Photogrammetric Record. (10) (007) [10] A. Trujillo-Pio, K. Krissia, M. Alema-Flores, D. Sataa-Cedres, Accurate Sub-pixel Edge Locatio Based O Partial Area Effect. Image ad Visio Computig. 31(1) (013)