Image Corner Detection Based on Curvature Scale Space and Adaptive Thresholding
Prof. Mohammad Reza Alsharif , Md. Foisal Hossain and Miyahira Yoshihiko
E-mail: asharif@ie.u-ryukyu.ac.jp, k068661@eve.u-ryukyu.ac.jp, e055760@ie.u-ryukyu.ac.jp
Department of Information Engineering,Ryukyu University
1 Senbaru, Nishihara, Okinawa, 903-0213, Japan

Abstract: Corner detection or the more general terminology interest point detection is an approach usedwithin computer vision systems to extract certain kinds of features and infer the contents of an image. Cornerdetection is frequently used in motion detection, image matching, tracking, image mosaicing, panorama
stitching, 3D modelling and object recognition. It is difficult to detect both fine and coarse features at thesame time using single-scale corner detection whereas multi-scale feature detection is inherently able to solve
this problem. This paper describes a multi-scale image corner detection method based on the curvature scalespace (CSS) representation and adaptive thresholding. This method uses an adaptive local curvature thresholdinstead of a global threshold. To eliminate falsely detected corner, the angles of corners are checked in a
dynamic region of support. The results of the proposed method were compared with the results of some otherpopular corner detection methods. Experimental results show that the proposed corner detection method gives
better results compared to other method.
Keywords: Corner detection, Adaptive thresholding, Curvature Scale Space.

1. Introduction
Corners in images represent critical information indescribing object features that are essential for patternrecognition and identification. Corners in images represent
a lot of useful information and they play an important rolein describing object features for recognition andidentification. There are many applications that are related
to successful detection of corners, including motion
tracking, object recognition, and stereo matching, among
many others. A number of corner detection methods havebeen proposed in [1-4].
Kitchen and Rosenfeld [2] proposed a corner detection
method based on differential operator that determines thefirst and second partial derivatives of an image, fromwhich corners are identified as local extrema. This method
is sensitive to noise, and suffers from missing junctions
and poor localization. Moravec [5] observed that thedifference between adjacent pixels of an edge or a uniform
part of the image is small and the difference issignificantly high in all directions at the corner. Thismethod also sensitive to quantization noise and suffersfrom a loss in localization accuracy. Most of them aresingle-scaled and suitable for objects having similar size,
but not useful for objects containing multiple-size features.
To solve this problem, Rattarangsi and chin [6] proposed amulti scale algorithm based on Gaussian scale space. Thismethod can detect corners of planar curves. This method iscomputationally intensive as it requires a large number ofscales. Moreover, it detects false corners on circles. On theother hand, the curvature scale space (CSS) technique ismore suitable for recovering invariant geometric featuresof a planar curve at multiple scales. Mokhtarian et. Al.
proposed two CSS corner detectors [7, 8] for gray scale
images. Although multi-scale is used for localization, but
still corner detection is in single scale in both method.
These methods fail to detect true corners when σ is large
and detects false corners when σ is small. Also,
performance of these methods is sensitive to a global
threshold.
Fang and Huang [9] proposed a method which was an
improvement on the gradient magnitude of the gradientangle method by Kitchen and Rosenfeld. Chen andRockett utilized Bayesian labeling of corners using a graylevel corner image model in [10]. Wu and Rosenfeld [11]proposed a technique which examines the slope
discontinuities of the x and y projections of an image tofind the possible corner candidates. Paler et al. [12]proposed a technique based on features extracted from thelocal distribution of gray-level values. Rangarajan et al.
[13] proposed a detector which tries to find an analyticalexpression for an optimal functionn whose convolution
with the windows of an image has significant values atcorner points. Arrebola et al. [14] introduced cornerdetection by local histograms of contour chain code. Shilatet al. [15] worked on ridge’s corner detection andcorrespondence. Nassif et al. [16] considered corner
location measurement. Sohn et al. [17] proposed a mean
field-annealing approach to corner detection.
In this paper, we propose an improved corner detection
method based on the CSS corner detector. Curvature ofeach contour is first computed at a relatively low scale toretain all true corners. After determining the cornercandidates by the local maxima of absolute curvaturefunction, the curvature of corner candidate are comparedwith an adaptive local threshold in instead of a single

global threshold to remove the rounded corners. Then theangles of candidate corners are checked to remove any
false corners. The proposed detector has been evaluatedover a number of images with multiple sizes and comparedwith two CSS methods as well as other popular cornerdetectors. It is found that it performs better than any ofexisting corner detectors for objects with multiple-size,
and is more robust and reliable from image to image.

2. The Curvature Scale Space Technique
The CSS technique is suitable for recovering invariant
geometric features of a planar curve at multiple scales.
Curvature is defined as: u,  X u ,  Yu ,   X u , Y u , 
22 1.5X u ,   Y u , 

Where X u ,    x u   g u ,  X u ,   xu   gu ,  ,Y u,   y u   g u,  ,Yu,    y u   gu ,   and is the convolution operator while g(u,σ) denotes a
Gaussian function with derivation σ, and g u ,   ,gu ,   are the 1st and 2nd derivatives of g(u,σ)
respectively.

Original CSS algorithm has the following six steps:
1. Obtain a binary edge map by applying Cannyedge detection to the gray level image.
2. Find the edge contours, fill the gaps and find theT junctions.

(a)

3.
4.
5.
6.

Compute curvature at a high scale for each edge
contour.
The contours having absolute curvature greaterthan threshold is considered as local maxima andtwice as much as one of the neighboring minima.
Track the corners from the highest scale to thelowest scale to improve localization.
Compare T junction to other corners and remove
one of the two corners which are very close.

3. Proposed Method
This paper changes the steps 3 and 4 of the general CSS
method. In step 3, this method said that compute curvature
at a fixed low scale for each contour to get all true corners.
In step 4, this method says that all of the curvature local
maxima are considered as corner candidates, including thefalse corners. Then using adaptive thresholding and true
angle corner, the true corners are found.
We set the threshold for a candidate according to its
neighborhood region’s curvature. The local maxima whose
absolute curvatures are under its local threshold areeliminated. This adaptive threshold is g given by:T u   C    1.5 u  L11  i L1  L2  1 i  u  L2

Where  is the mean curvature of the resion of support, u
is the position of corner, L1 and L2 are sizes of region ofsupport, and C is a coefficient whose value is between 1and 2. If C is set to 2, no corner is removed and 2 is theboundary value for retaining a corner having standard
curvature function. Here, the value of C was chosen 1.5.

(b)

(c)
(d)
Figure 1. Corner detection over image house. a) Original image, b) Detected corner with CSS c) Detected corners withmodified CSS and d) Detected corner with the proposed method

(a)

(b)

(c)

(d)

Figure 2. Corner detection over image hill. a) Original image, b) Detected corner with CSS c) Detected corners withmodified CSS and d) Detected corner with the proposed method

(a)

(c)

(b)

(d)

Figure 3. Corner detection over image airplane. a) Original image, b) Detected corner with CSS c) Detected corners withmodified CSS and d) Detected corner with the proposed method

4. Experimental Results
The proposed method was applied over different images
and the results of the proposed method were comparedwith original CSS and enhanced CSS method. Figure 1
compares the results of the proposed method with the twoother mentioned methods over image house. It can beobserved from this figure that the proposed method candetermine the existence of corner more exactly than theother two methods.
Figure 2 compares the results of the proposed methodwith the two other mentioned methods over image hill. It
can be observed from this figure that the proposed

method can determine the existence of corner moreexactly than the other two methods.
Figure 3 compares the results of the proposed methodwith the two other mentioned methods over image
airplane. It can be seen from this figure that the proposed
method shows better performance for corner detection
than the other two methods.

5. Conclusion
This paper proposed a new corner detection method
based on the curvature scale-space technique and global
threshold. The edges of a real image were extracted using
the Canny edge detector. The gaps between two close

contours were examined in order to find T-junction
corners or to fill the gap to form a continuous contour.
Curvature maxima were extracted at a high scale and thecorner locations were tracked at multiple lower scales toimprove localization. Then using adaptive thresholding
instead of a unique threshold and true angle corner, thetrue corners are found. The proposed method increases
the number of true corners detected and reduces thenumber of false corners detected. It can be said that theproposed method more suitable than other methods.

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