Showing papers by "Prasanna K. Sahoo published in 1997"
TL;DR: This paper presents a general technique for thresholding of digital images based on Renyi's entropy, which includes two of the previously proposed well known global thresholding methods.
414 citations
TL;DR: The proposed gray-level threshold selection method is similar to the maximum entropy method proposed by Kapur et al. (1985), however, the new method provided a good threshold value in many instances where the previous method did not.
Abstract: A new gray-level threshold selection method for image segmentation is presented. It is based on minimizing the difference between entropies of the object and the background distributions of the gray-level histogram. The proposed method is similar to the maximum entropy method proposed by Kapur et al. (1985), however, the new method provided a good threshold value in many instances where the previous method did not. The effectiveness of our method is demonstrated by its performance on videomicroscopic images of the rat lung. Extension of the method to higher order probability density functions is described.
73 citations
TL;DR: A survey of all important characterizations of sum form information measures that depend upon discrete complete probability distributions of lengthn and which satisfy a generalized additivity property is given.
Abstract: The goal of this paper is to give a survey of all important characterizations of sum form information measures that depend uponk discrete complete probability distributions (without zero probabilities) of lengthn and which satisfy a generalized additivity property. It turns out that most of the problems have been solved, but some open problems lead to the very simple looking functional equations
$$f(pq) + f(p(1 - q)) + f((1 - p)q) - f((1 - p)(1 - q)) = 0, p,q \in ]0, 1[^k (FE)$$
and
$$f(pq) + f(p(1 - q)) + f((1 - p)q) - f((1 - p)(1 - q)) = g(p)g(q), p,q \in ]0, 1[^k , (LI)$$
wheref, g: ]0, , 1[
k
→ ℝ andk ∈ ℕ. Moreover new entropies analogous to the Shannon entropy, entropies of degree α, entropies of degree (α, β) are introduced for χ, β ∈ ℕ.
12 citations
TL;DR: In this paper, the general solutions of the functional equations are obtained without any regularity assumptions, where f 1, f 2, g and h are complex-valued functions defined on the open-closed unit interval.
Abstract: In this paper, the general solutions of the functional equations
$$f_1 (pr,qs) + f_2 (ps,qr) = g(p,q) + h(r,s), p,q,r,s \in ]0, 1]$$
, and
$$f(pr,qs) + f(ps,qr) = g(p,q)h(r,s) + g(r,s)h(p,q), p,q,r,s \in ]0, 1]$$
, are obtained without any regularity assumptions. Heref, f 1, f2, g andh are complex-valued functions defined on the open-closed unit interval [0,1]. The last functional equation is a generalization of
$$f(pr,qs) + f(ps,qr) = g(p,q)f(r,s) + g(r,s)f(p,q), p,q,r,s \in ]0, 1]$$
, which arises in the characterizations of the distance measures.
11 citations
TL;DR: In this article, the general solution of the Simpson's rule for definite integrals is determined. But the solution of this functional equation is achieved through the functional equation, and the solution is not known to us.
Abstract: In this paper, we determine the general solution of the functional equation
$$f(x)-g(y)=(x-y)\lbrack h(x+y)+\psi (x)+\phi (y)\rbrack$$
for all real numbers x and y. This equation arises in connection with Simpson’s Rule for the numerical evaluation of definite integrals. The solution of this functional equation is achieved through the functional equation
$$g(x)-g(y)=(x-y)f(x+y)+(x+y)f(x-y).$$
2 citations
TL;DR: In this paper, the authors determined all functions ǫ defined on a field K and taking values in an abelian group, such that the quadratic difference ƒ(x + y) + ǔ(x − y) − 2ǫ(x) −2ǫǔǫ (ǫ) depends only on the product xy for all x, y ∈ K.
Abstract: In this paper, we determine all functions ƒ, defined on a field K (belonging to a certain class) and taking values in an abelian group, such that the quadratic difference ƒ(x + y) + ƒ(x − y) − 2ƒ(x) − 2ƒ(y) depends only on the product xy for all x, y ∈ K. Using this result, we find the general solution of the functional equation ƒ1(x + y) + ƒ2(x − y) = ƒ3(x) + ƒ4(y) + g(xy).
1 citations