Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Imputation of Multiple Missing Values by Normal Mixture Model under Markov Random Field: Application to Imputation of Pixel Values of Color Image

마코프 랜덤 필드 하에서 정규혼합모형에 의한 다중 결측값 대체기법: 색조영상 결측 화소값 대체에 응용

  • Kim, Seung-Gu (Department of Data & Information, Sangji University)
  • 김승구 (상지대학교 컴퓨터데이터정보학)
  • Received : 20091000
  • Accepted : 20091000
  • Published : 2009.11.30
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Abstract

There very many approaches to impute missing values in the iid. case. However, it is hardly found the imputation techniques in the Markov random field(MRF) case. In this paper, we show that the imputation under MRF is just to impute by fitting the normal mixture model(NMM) under several practical assumptions. Our multivariate normal mixture model based approaches under MRF is applied to impute the missing pixel values of 3-variate (R, G, B) color image, providing a technique to smooth the imputed values.

자료의 독립성 가청 하에서 EM 알고리즘에 의한 경측치 대체 (imputation of missing values) 기법은 잘 알려져 있다. 그러나 공간자료를 다루는 응용문제에서는 독립성 가정이 확장된 마코프 랜덤 필드 (Markov random field; MRF) 하에서 다루어져야 할 것이다. 이에 본 논문에서는 마코프 랜덤 필드 모형 궁에서 다변량 자료 중에 다중의 결측치의 대체를 위한 EM 알고리즘을 제공한다. 이 기법은 몇 가지 현실척 가정하에서 결국 혼합모형에 의한 대체 기법 임을 보인다. 그리고 제공된 기법으로 3-변량으로 구성된 색조영상(color image)의 결측화소값 대체문제에 적용하여 그 유용성과 문제점을 밝히며, 문제정의 개선방안에 대해 논의한다.

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