On Estimation of Fractal Dimension of Noisy Images

Objectives: This paper studies the noise effect on the estimation of Fractal Dimension (FD) of gray scale images and finds out which filter is best for estimating FD accurately for noised images. Methods/Statistical Analysis: Noise can lead to inaccurate estimation of FD, for this experimental analysis we have taken various types of noise factors to generate noisy images. The FD of original and noisy images has been estimated by using improved differential box-counting (IDBC) and compared. Further, three standard noise filtering techniques are used to remove the noise, and then it estimate the variation in fractal dimension of the original and de-noised image. Findings: As roughness of image is concerned, it will increase the addition of noise so FD also increased accordingly. In order to accurately estimate the FD of noised images, we have taken various standard filters to remove noise and to finding out which filter is best for estimating FD accurately for noised images. So in this regard, we have taken average FD variation for each image with each filter and found the nontexture images, mean filter has minimum FD variation even if it has a slightly more mean square error than other filters. Application/Improvements: it is easier to estimate the accurate fractal dimension of noisy textured images as compared to non-textured images. Further, other techniques are to be explored for estimating the accurate fractal dimension of noisy images.