• Korean Journal of Computational Design and Engineering
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• v.15 no.2
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• pp.115-123
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• 2010

We present an efficient algorithm for computing the Hausdorff distance between two planar curves. The algorithm is based on an efficient trimming technique that eliminates the curve domains that make no contribution to the final Hausdorff distance. The input curves are first approximated with biarcs within a given error bound in a pre-processing step. Using the biarc approximation, the distance map of an input curve is then approximated and stored into the graphics hardware depth-buffer by rendering the distance maps (represented as circular cones) of the biarcs. We repeat the same procedure for the other input curve. By sampling points on each input curve and reading the distance from the other curve (stored in the hardware depth-buffer), we can easily estimate a lower bound of the Hausdorff distance. Based on the lower bound, the algorithm eliminates redundant curve segments where the exact Hausdorff distance can never be obtained. Finally, we employ a multivariate equation solver to compute the Hausdorff distance efficiently using the remaining curve segments only.

• The Journal of the Korea Contents Association
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• v.6 no.10
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• pp.134-142
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• 2006

In this paper, we investigate a Hausdorff distance, which is used for the measurement of image similarity, to see whether it is also effective for document retrieval. The proposed method uses a local crowdedness and a Hausdorff distance to locate text images by determining whether a pair of images scanned at different time comes from the same text or not. To reduce the processing time, which is one of the disadvantages of a Hausdorff distance algorithm, we adopt a local crowdedness for feature point extraction. We apply the proposed method to 190 pairs of the same class and 190 pairs of the different class collected from postal envelop images. The results show that the modified Hausdorff distance proposed in this paper performed well in locating the tort region and calculating the degree of similarity between two images. An improvement of accuracy by 2.7% and 9.0% has been obtained, compared to a binary correlation method and the original Hausdorff distance method, respectively.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.9
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• pp.916-921
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• 2011

Mobile robot localization is the task of estimating the robot pose in a given environment. This research deals with outdoor localization based on an elevation map. Since outdoor environments are large and contain many complex objects, it is difficult to robustly estimate the robot pose. This paper proposes a Hausdorff distance-based map matching method. The Hausdorff distance is exploited to measure the similarity between extracted features obtained from the robot and elevation map. The experiments and simulations show that the proposed Hausdorff distance-based map matching is useful for robust outdoor localization using an elevation map. Also, it can be easily applied to other probabilistic approaches such as a Markov localization method.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.36S no.11
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• pp.60-67
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• 1999

This paper proposes a robust oriented Hausdorff measure (ROHM) for 20D object matching. The ROHM is introduced by replacing the distance concept of the conventional Hausdorff distance (HD) algorithm by the accumulation scheme of the Hough transform (HT). The proposed algorithm can be considered as the modified directed HT using the distance transform (DT). The orientation information at each pixel is also used for removing incorrect correspondences. Experiments with various test images show that the performance of the proposed algorithm is better than that of conventional HD algorithms considered.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.2
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• pp.56-62
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• 2015

The Hausdorff distance is commonly used as a similarity measure between two-dimensional binary images. Since the document images may be contaminated by a variety of noise sources during transmission, scanning or conversion to digital form, the measure should be robust to the noise. Original Hausdorff distance has been known to be sensitive to outliers. Transforming the given image to grayscale image is one of methods to deal with the noises. In this paper, we propose a Hausdorff distance applied to grayscale images. The proposed method is tested with synthetic images with various levels of noises and compared with other methods to show its robustness.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.641-648
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• 2007

In this paper, we present the exact Hausdorff distance between the offset curve of quadratic $B\'{e}zier$ curve and its quadratic $GC^1$ approximation. To illustrate the formula for the Hausdorff distance, we give an example of the quadratic $GC^1$ approximation of the offset curve of a quadratic $B\'{e}zier$ curve.

• Proceedings of the KIEE Conference
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• 2001.11c
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• pp.438-441
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• 2001

This paper describes a system for tracking a face in a input video sequence using facial convex hull based facial segmentation and a robust hausdorff distance. The algorithm adapts YCbCr color model for classifying face region by [l]. Then, we obtain an initial face model with preprocessing and convex hull. For tracking, a Robust Hausdorff distance is computed and the best possible displacement is selected. Finally, the previous face model is updated using the displacement t. It is robust to some noises and outliers. We provide an example to illustrate the proposed tracking algorithm in video sequences obtained from CCD camera.

• Journal of the Korea Society of Computer and Information
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• v.15 no.11
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• pp.67-73
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• 2010

In this paper, a new face detection method that is more accurate than the conventional methods is proposed. This method utilizes a hybrid of Hausdorff distance based on the geometric similarity between the two sets of points and the LBP distance based on the distribution of local micro texture of an image. The parameters for normalization and the optimal blending factor of the two different metrics were calculated from training sample images. Popularly used face database was used to show that the proposed method is more effective and robust to the variation of the pose, illumination, and back ground than the methods based on the Hausdorff distance or LBP distance. In the particular case, the average error distance between the detected and the true face location was reduced to 47.9% of the result of LBP method, and 22.8% of the result of Hausdorff method.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.643-654
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• 2000

In this paper, we review some class of t-norms on which fuzzy arithmetic operations preserve the shapes of fuzzy numbers and the Hausdorff-distance between fuzzy numbers as the measure of distance between fuzzy numbers. And we suggest the least Hausdorff-distance square method for fuzzy linear regression model using shape preserving fuzzy arithmetic operations.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.2
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• pp.111-123
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• 2009

We present an efficient algorithm for computing the Hausdorff distance between two 2D convex polygons. Two convex polygons are bounded by k-DOPs and the regions of interest are traced using the orientational and hierarchical properties of k-DOP. The algorithm runs in a logarithmic time in the average case, and the worst case time complexity is linear.