Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
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Polygon-shaped Filters in Frequency Domain for Practical Filtering of Images

현실적 영상 필터링 방법을 위한 주파수 영역에서의 다각형 형태 필터의 모델링

  • Kim, Ju-O (Department of Computer Engineering, Keimyung University) ;
  • Kim, Ji-Su (Department of Computer Engineering, Keimyung University) ;
  • Park, Cheol-Hyeong (Department of Computer Engineering, Keimyung University) ;
  • Lee, Deok-Woo (Department of Computer Engineering, Keimyung University)
  • 김주오 (계명대학교 공과대학 컴퓨터공학전공) ;
  • 김지수 (계명대학교 공과대학 컴퓨터공학전공) ;
  • 박철형 (계명대학교 공과대학 컴퓨터공학전공) ;
  • 이덕우 (계명대학교 공과대학 컴퓨터공학전공)
  • Received : 2019.02.08
  • Accepted : 2019.03.08
  • Published : 2019.03.31
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Abstract

In this paper, we propose an approach to design a practical filter and a mathematical modeling for images. In the areas of signal processing, including high-dimensional image processing, the filtering process has been fundamental and crucial in diverse practical applications such as image processing, computer vision, and pattern recognition. In general, the ideal filter is modeled as circular-shaped in the 2D frequency domain as the rectangular shape is ideal for the 1D frequency domain. This paper proposes an approach to modeling practical and efficient image filter in the 2D frequency domain. Instead of employing a circular-shaped filter, this study proposes a polygon-shaped filter inspired by the concept of a hexagon cellular system for frequency reuse in wireless communication systems. By employing the concept of frequency reuse, bandwidth efficiency is also achieved in the frequency domain. To substantiate the proposed approach, quantitative evaluation is performed using PSNR.

본 논문에서는 영상신호를 필터링 하기 위해 필요한 현실적인 수학적 모델을 제시한다. 1차원 신호 뿐 아니라 2차원 또는 다차원 신호처리 및 분석에서 필터는 영상처리, 컴퓨터 비전, 패턴 인식 등의 다양한 분야에서 근본적이고 중요한 과정을 수행한다. 일반적인 신호처리에서 신호를 주파수 영역에서 해석할 경우 1차원 신호 영역에서의 이상적인 (저역통과) 필터는 직사각형 형태를 가지고 있듯이, 2차원 신호의 이상적인 필터는 원 형태를 가지고 있다. 본 논문에서는 주파수 영역에서 활용할 수 있는 실용적이고 효율적인 다각형 형태의 영상 필터 모델을 제안한다. 본 논문은 2차원 영상을 필터링 하기 위해 원형 필터를 사용하는 대신 육각형 형태의 필터를 모델링하여 적용한다. 이것은 무선 통신 시스템에서의 주파수 재사용 개념을 도입함으로서, 영상 필터링에서도 주파수 대역을 효율적으로 사용하기 위함이다. 본 논문에서 제시한 육각형태의 필터를 활용한 영상 필터링의 시뮬레이션 결과를 제시하고, 성능을 PSNR로 계산한 결과 제안한 방법이 이상적인 필터의 대안으로서 가능함을 보인다.

Keywords

SHGSCZ_2019_v20n3_1_f0001.png 이미지

Fig. 1. Ideal circular shaped image filter in 2D domain

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Fig. 2. Example of using an ideal circular filter

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Fig. 3. Hexagon-shaped filter for multiple frequency selection

SHGSCZ_2019_v20n3_1_f0004.png 이미지

Fig. 4. The proposed N-polygon shaped ideal filter for 2D image. N = 6 in this work.

SHGSCZ_2019_v20n3_1_f0005.png 이미지

Fig. 5. Sample results of filtered image (high-pass filter) using both circle and polygon shaped filters

SHGSCZ_2019_v20n3_1_f0006.png 이미지

Fig. 6. Results of filtered image using circle and hexagon shaped filters

SHGSCZ_2019_v20n3_1_f0007.png 이미지

Fig. 7. Results of filtered image using circle and hexagon shaped filters

Table 1. Comparison of PSNR using circular and hexagon shaped filters

SHGSCZ_2019_v20n3_1_t0001.png 이미지

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