Curvature Scale Space Based Image Corner Detection Farzin Mokhtarian and Riku Suomela Centre for Vision, Sp eech, and Signal Pro cessing Department of Electronic and Electrical Engineering University of Surrey, Guildford, England GU2 5XH, UK e-mail: [email protected]. uk ABSTRACT quality of its results. Note however that the Canny de- tector is not a critical part of our corner detector: it can This pap er describ es a new metho d for image corner b e replaced with another edge detector if the new edge detection based on the curvature scale space (CSS) rep- detector is b elieved to p erform b etter. resentation. The rst step is to extract edges from the Section 2 gives a brief overview of the CSS metho d original image using a Canny detector. The Canny de- and section 3 describ es the prop osed corner detector. tector sometimes leaves a gap in T-junctions so during The p erformance of a corner detector is b est evaluated edge extraction, the gaps are examined to lo cate the with real test images and in section 4 the results of the T-junction corner p oints. The corner p oints of an im- CSS corner detector are presented. Four images with age are de ned as p oints where image edges have their di erent prop erties are used in the exp eriments. maxima of absolute curvature. The corner p oints are de- tected at a high scale of the CSS and the lo cations are 2 The curvature scale space technique tracked through multiple lower scales to improve lo caliz- ation. The nal stage is to compare T-junction corners The curvature scale space technique is suitable for re- to CSS corners and remove duplicates. This metho d covering invariant geometric features (curvature zero- is very robust to noise and we b elieve that it p erforms crossing p oints and/or extrema) of a planar curve at b etter than the existing corner detectors. multiple scales. To compute it, the curve is rst para- metrized by the arc length parameter u: 1 Intro duction (u)=(x(u);y(u)): Corner detection is an imp ortant task in various ma- chine vision and image pro cessing systems. Applications An evolved version of can then b e computed [10]: include motion tracking, ob ject recognition, and stereo matching. It is a fundamental problem and several dif- =(X(u; );Y (u; )) ferent algorithms have b een prop osed. Corner detection should satisfy a numb er of criteria in order to p erform where satisfactorily. We prop ose the following criteria: X (u; )=x(u) g(u; ) All the true corners should b e detected Y (u; )=y(u) g(u; ) Corner p oints should b e well lo calized where is the convolution op erator and g (u; ) denotes No false corners should b e detected a Gaussian of width . Note that is also referred to as the scale parameter. The pro cess of generating evolved Corner detector should b e robust to noise versions of as increases from 0 to 1 is referred to as the evolution of . This technique is suitable for Corner detector should b e ecient removing noise from and smo othing a planar curve as This pap er prop oses a new corner detection metho d well as gradual simpli cation of its shap e [7, 9]. based on the curvature scale space (CSS) technique. The In order to nd curvature zero-crossings or extrema CSS technique is suitable for extraction of curvature fea- from evolved versions of the input curve, one needs to tures from an input contour at a continuum of scales. compute curvature accurately and directly on an evolved This corner detection metho d requires edge contours of version of that curve. Curvature on is given by: the real image. In the implementation of the CSS de- X (u; )Y (u; ) X (u; )Y (u; ) u uu uu u tector a Canny edge detector was used [1]. The Canny (u; )= 1:5 2 2 detector was selected since we were satis ed with the (X (u; ) + Y (u; ) ) u u (a) Africa (b) =4 Figure 2: Curvature Scale Space image of Africa (c) =8 (d) =16 As the contour evolves, the actual lo cations of the corners change. If the detection is achieved at a large scale the lo calization of the corners will be p o or. To Figure 1: Evolution of Africa overcome this problem tracking is intro duced in the de- tection. The corners are lo cated at a high scale , hig h where this assures that the corner detection is not a ected by noise. Then sigma is reduced and the same corner p oints @ X (u; )= (x(u) g(u; )) = x(u) g (u; ) are examined at lower scales. As a result, lo cation of u u @u corners may be up dated. This is continued until the 2 scale is very low and the op eration is very lo cal. This @ X (u; )= (x(u) g(u; )) = x(u) g (u; ) uu uu improves lo calization and the computational cost is not 2 @u high, as curvature values at scales lower than do hig h Y (u; )=y(u) g (u; ) u u not need to b e computed at every contour p oint but only in a small neighb ourho o d of the detected corners. and There are lo cal maxima on the evolved contours due Y (u; )=y(u) g (u; ): uu uu to rounded corners. These can be removed by intro- The function de ned implicitly by (u; ) = 0 is the ducing a threshold value. The curvature of a sharp CSS image of . Figure 1 shows an example of contour corner is higher than that of a rounded corner. There evolution. Figure 2 shows the CSS image of the contour is one nal addition to the corner candidate declara- shown in gure 1. tion. Each lo cal maximum of curvature is compared to its two neighb ouring lo cal minima. The curvature of a 3 CSS corner detection metho d corner p oint has to b e 2 times higher than the curvature of a neighb oring extremum. This is necessary since if 3.1 Overview the contour is continuous and round, the curvature val- The corners are de ned as the lo cal maxima of the abso- ues are well ab ove the threshold value and false corners lute value of curvature. Atavery ne scale there exists would b e declared. many such maxima due to noise on the digital contour. As the scale is increased, the noise is smo othed away and 3.2 Outline only the p eaks corresp onding to the real corners remain. The pro cess of CSS image corner detection is as follows: The CSS corner detection metho d nds the corners at Utilize the Canny edge detector to extract edges these lo cal maxima. The problem is to nd the right from the original image scale where the corners are to b e detected. Figure 3: Arti cial test image with noise Extract the edge contours from the edge image { Fill the gaps in the edge contour Figure 4: Blo cks image { Find T-junctions and mark them as T-corners the images increases, the p erformance of the CSS image Compute the curvature at highest scale and hig h corner detector was not a ected much. Due to shortage determine the corner candidates by comparing the of space, only the results for the CSS detector are shown maxima of curvature to the threshold t and the here (see gures 3-6). neighb oring lo cal minima. All the detectors were implemented in C++, and had Track the corners to the lowest scale to improve rather similar sp eeds. Tests showed that ab out 85% of lo calization the time used by the CSS detector is sp ent in the edge detection stage. Compare the T-corners to the corners found using The CSS corner detector uses only two imp ortant the curvature pro cedure and remove corners which parameters. Exp eriments showed that = 4 gave hig h are to o close. good results with almost all images. The threshold t dep ends on the value of and with = 4 the hig h hig h 4 Exp erimental results and discussion threshold can b e set to 0.03. Other values of are hig h The CSS corner detector was tested using four di er- also p ossible and for a very noisy image = 8 and hig h ent images and the results were compared to the output threshold t =0:02 can b e used. Starting with = hig h of three other corner detectors: Kitchen and Rosenfeld 4, tracking can be accomplished at = 2, = 1 and [5], Susan [15] and Plessey [4] corner detectors. Other = 0.7. The nal scale should b e as lo cal as f inal f inal corner detectors [3, 17,13,2, 11, 14,8,6,12,16]were p ossible to ensure go o d lo calization. It was found that also considered. Note that we attempted to obtain the the results were not sensitive to the exact values of the b est p ossible results for each corner detector tested by parameters, and that the same values worked well for searching for parameter values that app eared to yield the di erent test images used except for one that was the b est results. The rst test image is an arti cially cre- very noisy byintention.