• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.11
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• pp.93-101
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• 1997

A Hausdorff distance (HD) is one of commonly used measures for object matching. It calculates the distance between two point sets of edges in two-dimensional binary images without establishing correspondences. This paper proposes three object matching algorithm using robust HD measures based on M-estimation, least trimmed square (LTS), and .alpha.-trimmed mean methods, which are more efficient than the conventional HD measures. By computer simulation with synthetic and real images, the matching performance of the conventional HD smeasures and proposed' robust ones is compared.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.833-850
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• 2013

We present an algorithm for computing the Hausdorff distance between two parametric curves in $\mathbb{R}^n$, or more generally between two sets of parametric curves in $\mathbb{R}^n$. During repeated subdivision of the parameter space, we prune subintervals that cannot contain an optimal point. Typically, our algorithm costs O(logM) operations, compared with O(M) operations for a direct, brute-force method, to achieve an accuracy of $O(M^{-1})$.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.571-592
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• 2022

By established a Banach space with the Hausdorff distance, we introduce the alternative fixed-point theorem to explore the existence and uniqueness of a fixed subset of Y and investigate the stability of set-valued Euler-Lagrange functional equations in this space. Some properties of the Hausdorff distance are furthermore explored by a short and simple way.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.632-635
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• 2003

This paper describes a system fur tracking multiple faces in an input video sequence using facial convex hull based facial segmentation and robust hausdorff distance. The algorithm adapts skin color reference map in YCbCr color space and hair color reference map in RGB color space for classifying face region. Then, we obtain an initial face model with preprocessing and convex hull. For tracking, this algorithm computes displacement of the point set between frames using a robust hausdorff distance and the best possible displacement is selected. Finally, the initial face model is updated using the displacement. We provide an example to illustrate the proposed tracking algorithm, which efficiently tracks rotating and zooming faces as well as existing multiple faces in video sequences obtained from CCD camera.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.1
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• pp.87-92
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• 2003

This paper describes a system for tracking multiple faces in an input video sequence using facial convex hull based facial segmentation and robust hausdorff distance. The algorithm adapts skin color reference map in YCbCr color space and hair color reference map in RGB color space for classifying face region. Then, we obtain an initial face model with preprocessing and convex hull. For tracking, this algorithm computes displacement of the point set between frames using a robust hausdorff distance and the best possible displacement is selected. Finally, the initial face model is updated using the displacement. We provide an example to illustrate the proposed tracking algorithm, which efficiently tracks rotating and zooming faces as well as existing multiple faces in video sequences obtained from CCD camera.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.419-433
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• 2007

Medial axis transform (MAT) is very sensitive to noise, in the sense that, even if a shape is perturbed only slightly, the Hausdorff distance between the MATs of the original shape and the perturbed one may be large. Recently, Choi et al.(2002) showed that MAT is stable for a class of 2D domains called weakly injective, if we view this phenomenon with the one-sided Hausdorff distance, rather than with the two-sided Hausdorff distance. In this paper, we extend this result to general 2D domains with natural boundary regularity. We also present explicit bounds for this general one-sided stability of the 2D MAT.

• Journal of Korea Multimedia Society
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• v.8 no.1
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• pp.34-45
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• 2005

In this paper, a novel implementation of a person verification system based on depth-weighted Hausdorff distance (DWHD) using the surface curvature of the face is proposed. The definition of Hausdorff distance is a measure of the correspondence of two point sets. The approach works by finding the nose tip that has a protrusion shape on the face. In feature recognition of 3D face image, one has to take into consideration the orientated frontal posture to normalize after extracting face area from original image. The binary images are extracted by using the threshold values for the curvature value of surface for the person which has differential depth and surface characteristic information. The proposed DWHD measure for comparing two pixel sets were used, because it is simple and robust. In the experimental results, the minimum curvature which has low pixel distribution achieves recognition rate of 98% among the proposed methods.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.6C
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• pp.624-633
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• 2003

We propose a novel method of selecting key VOPs from MPEG-4 compressed domain without fully decoding the compressed data. Approximated shapes of VOPs are obtained from the shape coding mode and then VOPs are clustered by shape similarity to generate key VOPs. The proposed method reduces the computation time of shape approximation, compared with Erol's method. Nevertheless, the resulting VOPs have a good summarizing capability of a video sequence. NMHD (normalized mean Hausdorff distance) values are 2-means clustered to generate key VOPs. In the video search, the MHD of a query VOP from key VOPs are computed and the VOP with the lowest distance is returned. Tests on standard MPEG-4 test sequences show that the computational complexity is very low. Recursive clustering proved to be very effective for generating suitable key VOPs.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.571-580
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• 2013

In this paper, we extend the familiar limit curve theorem in [2] to a situation where each causal curve lies in a sequence of compact interpolating spacetimes converging to a limit Lorentz space in the sense of Lorentzian Gromov-Hausdorff distance.

• Journal of information and communication convergence engineering
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• v.13 no.2
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• pp.74-80
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• 2015

In cognitive radios, spectrum sensing plays an important role in accurately detecting the presence or absence of a licensed user. However, the intervention of malicious users (MUs) degrades the performance of spectrum sensing. Such users manipulate the local results and send falsified data to the data fusion center; this process is called spectrum sensing data falsification (SSDF). Thus, MUs degrade the spectrum sensing performance and increase uncertainty issues. In this paper, we propose a method based on the Hausdorff distance and a similarity measure matrix to measure the difference between the normal user evidence and the malicious user evidence. In addition, we use the Dempster-Shafer theory to combine the sets of evidence from each normal user evidence. We compare the proposed method with the k-means and Jaccard distance methods for malicious user detection. Simulation results show that the proposed method is effective against an SSDF attack.