Hello Sheema,

Here i am giving you a brief recent work has been taken on Rough entropy,

please go through this this may helpful to you i think so.

An application of rough sets and granular computing for object extraction from gray scale image. In gray scale images boundaries between object regions are often ill-defined. This uncertainty can be handled by describing the different objects as rough sets with upper (outer) and lower (inner) approximations. The set approximation capability of rough sets is exploited in the present investigation to formulate an entropy measure, called rough entropy, quantifying the uncertainty in an object-background image. This has been done by defining an image as a collection of pixels and the equivalence relation induced partition as pixels lying within each non-overlapping window over the image. With this definition the roughness of various transforms (or partitions) of the image can be computed using image granules, i.e., windows, of different sizes.

Maximization of the said rough entropy measure minimizes the uncertainty arising from vagueness of the boundary region of the object. Therefore, for a given granule size, the threshold for object-background classification can be obtained through its maximization with respect to different image partitions. A guideline for selecting the appropriate granule size from gray level distribution is given, as well as a way of computing the rough entropy efficiently only in one pass (or scan) of the image. Effectiveness of the method is demonstrated on different kinds of images.

Rough entropy measure of an image

Rough set

Let A=〈U,A〉 be an information system, and let B ⊆ A and X ⊆ U . We can approximate the set X using only the information contained in B by constructing the lower and upper approximations of X . If X ⊆ U , the sets {x ∈ U : [x]B ⊆ X } and {x ∈ U : [x]B ∩ X ≠ ∅}, where [x]B denotes the equivalence class of the object x ∈ U relative to I B (the equivalence relation), are called the B-lower and B-upper approximations of X in U . They are denoted by BX and , respectively. The objects in BX can be certainly classified as members of X on the basis of knowledge in B , while objects in can only be classified as possible members of X on the basis of B. These are illustrated in Fig. where the sets of dark-gray granules represent lower approximation, while those of both dark-gray and light-gray granules together denote upper approximation. Therefore, a rough set is nothing but a crisp set with rough representation.

Fig. Rough representation of a set with upper and lower approximations.

The roughness of a set X with respect to B can be characterized numerically as . This means if roughness of the set X is 0 then X is crisp with respect to B, and if Rα > 0 thenX is rough (i.e., X is vague with respect to B).

Hello Sheema,

Here i am giving you a brief recent work has been taken on Rough entropy,

please go through this this may helpful to you i think so.

An application of rough sets and granular computing for object extraction from gray scale image. In gray scale images boundaries between object regions are often ill-defined. This uncertainty can be handled by describing the different objects as rough sets with upper (outer) and lower (inner) approximations. The set approximation capability of rough sets is exploited in the present investigation to formulate an entropy measure, called rough entropy, quantifying the uncertainty in an object-background image. This has been done by defining an image as a collection of pixels and the equivalence relation induced partition as pixels lying within each non-overlapping window over the image. With this definition the roughness of various transforms (or partitions) of the image can be computed using image granules, i.e., windows, of different sizes.

Maximization of the said rough entropy measure minimizes the uncertainty arising from vagueness of the boundary region of the object. Therefore, for a given granule size, the threshold for object-background classification can be obtained through its maximization with respect to different image partitions. A guideline for selecting the appropriate granule size from gray level distribution is given, as well as a way of computing the rough entropy efficiently only in one pass (or scan) of the image. Effectiveness of the method is demonstrated on different kinds of images.

Rough entropy measure of an image

Rough set

Let A=〈U,A〉 be an information system, and let B ⊆ A and X ⊆ U . We can approximate the set X using only the information contained in B by constructing the lower and upper approximations of X . If X ⊆ U , the sets {x ∈ U : [x]B ⊆ X } and {x ∈ U : [x]B ∩ X ≠ ∅}, where [x]B denotes the equivalence class of the object x ∈ U relative to I B (the equivalence relation), are called the B-lower and B-upper approximations of X in U . They are denoted by BX and , respectively. The objects in BX can be certainly classified as members of X on the basis of knowledge in B , while objects in can only be classified as possible members of X on the basis of B. These are illustrated in Fig. where the sets of dark-gray granules represent lower approximation, while those of both dark-gray and light-gray granules together denote upper approximation. Therefore, a rough set is nothing but a crisp set with rough representation.

Fig. Rough representation of a set with upper and lower approximations.

The roughness of a set X with respect to B can be characterized numerically as . This means if roughness of the set X is 0 then X is crisp with respect to B, and if Rα > 0 thenX is rough (i.e., X is vague with respect to B).

Here is the figure

What about Renyi,Tsallis and shanon entropy trends in image processing?

Tsallis entropy based mutli -level thresolding have been attempted for different images...

Hello Sheema,

i agree with the Kavitha's answer

Thank you all, Kavitha can you please give detail explanation?

1. Characterization of optic disc in human retinal images using tsallis entropy based method... this is one paper that we have attempted....u can see our references.

2. Tsallis entropy based optimal multilevel thresholding using cuckoo search algorithm ....this is another latest reference that might help u to work in tsallis+optimization techniques.... also

3. Optimum Multilevel Image Thresholding Based on Tsallis

Entropy Method with Bacterial Foraging Algorithm

Thank you both of you.Can you guys help me regarding rough entropy implementation in matlab .How to compute R for background n R for object then use in formula.

Can you people please guide me how to calculate lower approx. and upper apprx and/or object rough set background rough set practically in matlab?

What is the procedure to calculate Renyi, Tsallis , shannon and permutation entropy in case of a gray scale image in matlab. Please can any one help me.