FCM(fuzzy c-means)은 일반적으로 영상 분할에서 좋은 성능을 보인다. 하지만 공간 정보를 사용하지 않는 일반적인 FCM 알고리즘은 낮은 대비의 영상, 경계선이 뚜렷하지 않은 영상, 잡음이 포함된 영상의 분할에는 좋지 않은 성능을 보인다. 이와 같은 문제를 해결하기 위해 본 논문에서는 3x3 크기의 윈도우를 이용하여 윈도우 내의 중심 픽셀과 주변 픽셀간의 거리 정보를 소속 함수에 추가한 개선된 공간적 퍼지 클러스터링알고리즘을 제안한다. 본 논문에서는 분할 계수, 분할 엔트로피, Xie-Bdni 함수와 같은 클러스터링 검증 함수를 이용하여 FCM 기반의 다양한 클러스터링 알고리즘과 제안한 알고리즘과의 성능을 비교하였다. 성능 평가 결과 제안한 알고리즘이 기존의 FCM기반의 클러스터링 알고리즘보다 클러스터링 검증 함수에서 성능이 우수함을 확인 할 수 있었다.
FCM(fuzzy c-means)은 일반적으로 영상 분할에서 좋은 성능을 보인다. 하지만 공간 정보를 사용하지 않는 일반적인 FCM 알고리즘은 낮은 대비의 영상, 경계선이 뚜렷하지 않은 영상, 잡음이 포함된 영상의 분할에는 좋지 않은 성능을 보인다. 이와 같은 문제를 해결하기 위해 본 논문에서는 3x3 크기의 윈도우를 이용하여 윈도우 내의 중심 픽셀과 주변 픽셀간의 거리 정보를 소속 함수에 추가한 개선된 공간적 퍼지 클러스터링 알고리즘을 제안한다. 본 논문에서는 분할 계수, 분할 엔트로피, Xie-Bdni 함수와 같은 클러스터링 검증 함수를 이용하여 FCM 기반의 다양한 클러스터링 알고리즘과 제안한 알고리즘과의 성능을 비교하였다. 성능 평가 결과 제안한 알고리즘이 기존의 FCM기반의 클러스터링 알고리즘보다 클러스터링 검증 함수에서 성능이 우수함을 확인 할 수 있었다.
Conventional fuzzy c-means (FCM) algorithms have achieved a good clustering performance. However, they do not fully utilize the spatial information in the image and this results in lower clustering performance for images that have low contrast, vague boundaries, and noises. To overcome this issue, w...
Conventional fuzzy c-means (FCM) algorithms have achieved a good clustering performance. However, they do not fully utilize the spatial information in the image and this results in lower clustering performance for images that have low contrast, vague boundaries, and noises. To overcome this issue, we propose an enhanced spatial fuzzy c-means (ESFCM) algorithm that takes into account the influence of neighboring pixels on the center pixel by assigning weights to the neighbors in a $3{\times}3$ square window. To evaluate between the proposed ESFCM and various FCM based segmentation algorithms, we utilized clustering validity functions such as partition coefficient ($V_{pc}$), partition entropy ($V_{pe}$), and Xie-Bdni function ($V_{xb}$). Experimental results show that the proposed ESFCM outperforms other FCM based algorithms in terms of clustering validity functions.
Conventional fuzzy c-means (FCM) algorithms have achieved a good clustering performance. However, they do not fully utilize the spatial information in the image and this results in lower clustering performance for images that have low contrast, vague boundaries, and noises. To overcome this issue, we propose an enhanced spatial fuzzy c-means (ESFCM) algorithm that takes into account the influence of neighboring pixels on the center pixel by assigning weights to the neighbors in a $3{\times}3$ square window. To evaluate between the proposed ESFCM and various FCM based segmentation algorithms, we utilized clustering validity functions such as partition coefficient ($V_{pc}$), partition entropy ($V_{pe}$), and Xie-Bdni function ($V_{xb}$). Experimental results show that the proposed ESFCM outperforms other FCM based algorithms in terms of clustering validity functions.
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제안 방법
Therefore, many validity functions have been proposed for image segmentation [16]. In this paper, we utilize the following three validity functions to evaluate the performance of the proposed algorithm and conventional FCM algorithms. The representative validity functions based on the fuzzy partitions are the partition coefficient Vpc [17] and partition entropy Vpe [18], which are defined as follows:
Firstly, image smoothing techniques are included in clustering algorithms based on FCM to improve the clustering performance [6-8]. The main idea of these techniques is that they use a spatial filter to smooth the image before applying the standard FCM. Szilagyi et al.
Consequently, we propose an enhanced spatial FCM (ESFCM) algorithm in order to improve the clustering performance. The proposed algorithm exploits the influence of neighboring pixels on the center pixel by calculating new membership values that incorporate both the given pixel attributes and the spatial information of the neighboring pixels.
이론/모형
presented a spatial fuzzy clustering algorithm that exploits the spatial contextual information in image data, where the influence of the neighboring pixels is suppressed in non-homogeneous regions of the image [12]. This method utilizes the difference between the pixel intensity and the centroid of a cluster, called the dissimilarity index, to take into account the influence of the neighboring pixels on the center pixel. Mohamed et al.
성능/효과
This factor is then incorporated into the membership function of the conventional FCM. Experimental results indicate that the proposed ESFCM provides better clustering performance than other FCM algorithms (FCM [3], EnFCM [6], FGFCM [8], SFCM [12], MFCM [13], and FCMSI [14]).
The algorithm assigns the neighboring pixels weights based on their intensity and location distance to the center pixel in order to indicate the importance of their memberships. Experimental results, as evaluated by three validity functions, indicated that the proposed ESFCM significantly outperforms other FCM based algorithms.
2(a)-(c), respectively. The ESFCM clearly outperformed FCM, SFCM, MFCM, EnFCM, FCMSI, and FGFCM with good interpretation and partitioning for all cases in which the samples in one cluster were compact and the samples in different clusters were separated. This is because ESFCM optimizes the membership and centroid functions by incorporating a weighting coefficient that can be calculated from the pixel intensities and locations within a 3x3 window to the membership function.
The proposed ESFCM algorithm outperformed the FCM, SFCM, MFCM, EnFCM, FCMSI, and FGFCM algorithms in all of the cluster validity functions (Vpc, Vpe, and Vxb), where the maximum Vpc, the minimum Vpe, or the minimum Vxb led to a good interpretation and partitioning of the samples.
그림 2. c=4를 가지고 제안한 ESFCM 알고리즘과 기존의 FCM 기반 알고리즘의 클러스터링 성능. (a) Vpc, (b) Vpe, and (c) Vxb
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