RAPPORT Algebraic Framework for Linear and Morphological Scale - Spaces
نویسنده
چکیده
This paper proposes a general algebraic construction technique for image scale-spaces. The basic idea is to rst downscale the image by some factor using an invertible scaling, then apply an image operator (linear or morphological) at a unit scale, and nally resize the image to its original scale. It is then required that the resulting one-parameter family of image operators satis es the semigroup property. Such an approach encompasses linear as well as nonlinear (morphological) operators. Furthermore, there exists some freedom as to which semigroup operation on the scale(or time-) axis is being chosen. Particular attention is given to additive and supremal semigroups. A large part of the paper is devoted to morphological scale-spaces, in particular to scale-spaces associated with an erosion or an opening. In these cases, classical tools from convex analysis, such as the (Young-Fenchel) conjugate, play an important role. 1991 Mathematics Subject Classi cation: 68U10, 52A41.
منابع مشابه
Algebraic distance in algebraic cone metric spaces and its properties
In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.
متن کاملAlgebraic Framework for Linear and Morphological Scale-Spaces
This paper proposes a general algebraic construction technique for image scale-spaces. The basic idea is to rst downscale the image by some factor using an invertible scaling, then apply an image operator (linear or morphological) at a unit scale, and nally resize the image to its original scale. It is then required that the resulting one-parameter family of image operators satisses the semigro...
متن کاملFamilies of Generalised Morphological Scale Spaces
Morphological and linear scale spaces are well-established instruments in image analysis. They display interesting analogies which make a deeper insight into their mutual relation desirable. A contribution to the understanding of this relation is presented here. We embed morphological dilation and erosion scale spaces with paraboloid structure functions into families of scale spaces which are f...
متن کاملIncreasing the Robustness of Heteroassociative Morphological Memories for Practical Applications
Associative Morphological Memories are a recently proposed neural networks architecture based on the shift of the basic algebraic framework. They possess some robustness to specific noise models (erosive and dilative noise). Combining the Associative Morphological Memories with erosion/dilation scale-spaces, we achieved an increased robustness against noise. Here we report ongoing work on their...
متن کاملFisher’s Linear Discriminant Analysis for Weather Data by reproducing kernel Hilbert spaces framework
Recently with science and technology development, data with functional nature are easy to collect. Hence, statistical analysis of such data is of great importance. Similar to multivariate analysis, linear combinations of random variables have a key role in functional analysis. The role of Theory of Reproducing Kernel Hilbert Spaces is very important in this content. In this paper we study a gen...
متن کامل