range | ||||||
Lena1 | 21.9715 | 22.1662 | 21.5974 | 21.9076 | 21.1507 | 21.6422 |
Lena2 | 22.8407 | 23.1224 | 22.5366 | 22.8503 | 22.3337 | 22.6582 |
Pepper | 20.9797 | 21.4961 | 20.4562 | 20.8171 | 20.1147 | 20.4185 |
As a generalization of the fuzzy set and intuitionistic fuzzy set, the neutrosophic set (NS) have been developed to represent uncertain, imprecise, incomplete and inconsistent information existing in the real world. Now the interval neutrosophic set (INS) which is an expansion of the neutrosophic set have been proposed exactly to address issues with a set of numbers in the real unit interval, not just one specific number. After definition of concepts and operations, INS is applied to image segmentation. Images are converted to the INS domain, which is described using three membership interval sets: T, I and F. Then, in order to increase the contrast between membership and evaluate the indeterminacy, a fuzzy intensification for each element in the interval set is made and a score function in the INS is defined. Finally, the proposed method is employed to perform image segmentation using the traditional k-means clustering. The experimental results on a variety of images demonstrate that the proposed approach can segment different sorts of images. Especially, it can segment "clean" images and images with various levels of noise.
Citation: |
Figure 6. For Lena image, the first part is the original image, the middle part is the segmentation by the approach in [9], and the third part is the segmentation by interval neutrosophic set method
Table 1.
The value of PSNR in different ranges for the three images (
range | ||||||
Lena1 | 21.9715 | 22.1662 | 21.5974 | 21.9076 | 21.1507 | 21.6422 |
Lena2 | 22.8407 | 23.1224 | 22.5366 | 22.8503 | 22.3337 | 22.6582 |
Pepper | 20.9797 | 21.4961 | 20.4562 | 20.8171 | 20.1147 | 20.4185 |
Table 2. The value of PSNR for the three images with different noises
noise | gaussian noise(1) | gaussian noise(2) | salt noise | speckle noise |
k-means | 19.1443 | 13.8363 | 22.6033 | 19.5381 |
INI | 21.2599 | 18.4293 | 21.1605 | 21.6448 |
k-means | 19.1969 | 13.9415 | 23.3081 | 20.9689 |
INI | 22.1729 | 18.6085 | 22.4192 | 22.6730 |
k-means | 18.6936 | 13.8596 | 21.4768 | 19.4912 |
INI | 20.6764 | 18.0361 | 20.7433 | 20.6611 |
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