This paper is intended as a rst introduction into mathematical morphology, and does not require any preliminary knowledge in this eld. The paper discusses the basic morphological operators, such as dilations, erosions, openings, closings, rank operators, skeletons, and reconstruction operators. Furthermore, it introduces the complete lattice framework for morphology. The paper concludes with an...

We present an unsupervised, language agnostic approach for exploiting morphological regularities present in high dimensional vector spaces. We propose a novel method for generating embeddings of words from their morphological variants using morphological transformation operators. We evaluate this approach on MSR word analogy test set (Mikolov et al., 2013d) with an accuracy of 85% which is 12% ...

The purpose of this paper is to define and to analyze three new sets of logarithmic morphological operators and it is focused on theoretical and practical aspects concerning the enhancement of the transmitted images and the physical absorption/transmission laws expressed within LIP (Logarithmic Image Processing) mathematical framework. Using different logarithmic image representations, an appro...

Mathematical Morphology (MM) is a general framework for studying mappings between complete lattices. In particular, mappings between binary images that are translation invariant and locally defined within a window are of special interest in MM. They are called W-operators. A key aspect of MM is the representation of W-operators in terms of dilations, erosions, intersection, union, complementati...

In classical mathematical morphology for scalar images, the natural ordering of grey levels is used to define the erosion/dilation and the derived operators. Various operators can be sequentially applied to the resulting images always using the same ordering. In this paper we propose to consider the result of a prior transformation to define the imaginary part of a complex image, where the real...

This paper presents a new approach based on morphological operators for application of biometric identification of individuals by segmentation and analysis of the iris. Algorithms based on morphological operators are developed to segment the iris region from the eye image and also to highlight chosen iris patterns. The extracted features are used to represent and characterize the iris. In order...

The operators of greyscale morphology rely on the notions of maximum and minimum which regrettably are not directly available for tensor-valued data since the straightforward component-wise approach fails. This paper aims at the extension of the maximum and minimum operations to the tensor-valued setting by employing the Loewner ordering for symmetric matrices. This prepares the ground for matr...

Potato image segmentation is an important part of image-based potato defect detection. This paper presents a robust potato color image segmentation through a combination of a fuzzy rule based system, an image thresholding based on Genetic Algorithm (GA) optimization and morphological operators. The proposed potato color image segmentation is robust against variation of background, distance and ...