Soumya Ranjan Nayak

Analysing Fractal Dimension of Color Images

Fractal Dimension (FD) is an important feature of fractal geometry that finds the significant application in different fields including texture segmentation, shape classification and image analysis. Various methods were proposed to estimate the fractal dimension of gray scale images. In this paper we found out a uniform fractal dimension for both Color and Grey Scale images using differential box counting (DBC) method.

An improved algorithm to estimate the fractal dimension of gray scale images

Fractal dimension is a very useful technique to estimate surface roughness of digital images; for this estimation many approaches have been implemented. Among them differential box counting mechanism are most popular and commonly used technique for computation of FD of gray scale images. This article presents an improved version of differential box counting method for improvement of accuracy in terms of less fit error and simultaneously provides wider range of FD in terms of least regression line as well as FD at each corresponding box size. Improvement version can achieve by adopting proper box height selection and exact box number calculation. The experimental work done through two sets of images and shows that our proposed methods able to capture accurate roughness and consistently give more satisfactory results as compared to other traditional method like DBC, RDBC and IDBC.

Ground truth study on fractal dimension of color images of similar texture

Abstract Fractal dimension (FD) estimation has become most popular in the field of image analysis and applications; especially estimating the roughness and smoothness of complex objects. In this present investigation, we are considering three most popular methods in the controlled images acquisition experimental setup for eight colored fabrics of the same texture, material property, and illumination. The concept of previous work and the results obtained by this ground truth experiment were discussed to indicate whether FD might be a worth useful metric for the study of color images with self-similarity, such as textures! Interestingly, we found ambiguous FD results here and tried to explain such phenomenon in relation to the development of CIE-based human perception model as texture perception are well associated with the viewing parameters and observer that perceives the image in terms of spatial distribution of color intensity.

A New Extended Differential Box-Counting Method by Adopting Unequal Partitioning of Grid for Estimation of Fractal Dimension of Grayscale Images

Fractal dimension (FD) is most useful research topic in the field of fractal geometry to evaluate surface roughness of digital images by using the concept of self-similarity, and the FD value should lie between 2 and 3 for surfaces of digital images. In this regard, many researchers have contributed their efforts to estimate FD in the digital domain as reported in many kinds of the literature. The differential box-counting (DBC) method is a well-recognized and commonly used technique in this domain. However, based on the DBC approach, several modified versions of DBC have been presented like relative DBC (RDBC), improved box counting (IBC), improved DBC (IDBC). However, the accuracy of an algorithm for FD estimation is still a great challenge. This article presents an improved version of DBC algorithm by partitioning the box of grid into two asymmetric patterns for more precision box count and provides accurate estimation of FD with less fit error as well as less computational time as compared to existing method like DBC, relative DBC (RDBC), improved box counting (IBC), and improved DBC (IDBC).

Fractal Dimension of GrayScale Images

Fractal dimension (FD) is a necessary aspect for characterizing the surface roughness and self-similarity of complex objects. However, fractal dimension gradually established its importance in the area of image processing. A number of algorithms for estimating fractal dimension of digital images have been reported in many literatures. However, different techniques lead to different results. Among them, the differential box-counting (DBC) was most popular and well-liked technique in digital domain. In this paper, we have presented an efficient differential box-counting mechanism for accurate estimation of FD with less fitting error as compared to existing methods like original DBC, relative DBC (RDBC), and improved box-counting (IBC) and improved DBC (IDBC). The experimental work is carried out by one set of fourteen Brodatz images. From this experimental result, we found that the proposed method performs best among the existing methods in terms of less fitting error.