Mathematical Morphology

Diabetes is one of the most rapidly increasing health threats worldwide. One of the further abnormalities is on retina (diabetic retinopathy). Early treatment can be conduct from detection of microaneurysms. The main concentration of this paper is the algorithm to detect microaneurysm with mathematical morphology. The mathematical morphology is choosen because microaneurysms tend to have typical shape. Generally, the algorithm is consist of three stages. The first is preprocessing, the second is detecting candidate microaneurysms, and the third is postprocessing handling the process of removing unused features. The performances is evaluated using the database from DIARETDB1 which provides ground truth collected from several experts and a strict evaluation protocol. The optimal performance will be satified when considering green channel obtaining, PAL size image processing, adaptive histogram equalization threshold at 0.03, canny edge detection threshold at 0.16, MAs and optimum microaneurysms size at 5 to 16 pixels.

This paper concerns the application of mathematical morphology for object-oriented classification of satellite images. The example of distinguishing different bodies of water using the author-made algorithm will be presented. Different types of water bodies like lakes and rivers are easy to differentiate when visually interpreted. However, it is much more difficult to differentiate using a traditional, pixel-based classification process. Mathematical morphology operations, which take into account such important
features of objects like shape and size, allow these two types of water bodies to be distinguished in object classification. The proposed algorithm allows one practically error-free classification. The results show, that mathematical morphology is a potent tool for object-oriented classification.

A MATHEMATICAL MODEL is presented to define new inclusions, intersections and unions as alternatives to the usual ones between crisp and fuzzy subsets. In particular, the concept of “the non-trivial content of the empty set ∅” is analyzed.
This proposed model is based on the interconnection of two consolidated mathematical concepts in specialized literature:
One of them, (which belongs to the field of image processing using Mathematical Morphology techniques), is that of activity  ordering and that we use here in the general context of lattices (L, ≤) and in particular in that of Boolean Algebras.
The other consists of a version in distributive lattices (L, ≤) of the symmetric difference operator Δ, a classic concept in Set Theory.
The utility of the model is illustrated in the following fields: analysis of risk maps, (areas of avalanches, risk of fires, landslides, earthquakes, ...), as well as maps with contour lines: (isochrons, isotherms, salinity , rainfall, intensity of earthquakes, ...). Also in data pre-processing for “Data Mining” tasks and in “Data Analysis with Uncertainty”.
A special section is dedicated to the application of the model in Digital Image Processing using Mathematical Morphology techniques.
Finally, it is justified that the model can be useful in other fields such as Analysis of Formal Concepts, Probability and in theoretical contexts such as Topology.

Rubble detection is a key element in post disaster crisis assessment and response procedures. In this paper we present an automated method for rapid detection and quantification of rubble from very high resolution (VHR) aerial imagery of urban regions. It is a two step procedure in which the input image is projected onto a hierarchical representation structure for efficient mining and
decomposition. Image features matching the geometric and
chromatic properties of rubble are fused into a rubble layer that can be re-adjusted interactively. The targeted objects are evaluated based on a density metric given by spatial aggregation. The method is tested on a small-scale exercise on the publicly available aerial imagery of Port-au-Prince, Haiti. Performance and preliminary results are discussed.

Detection of external defects on potatoes is the most important technology in the realization of automatic potato sorting stations. This paper presents a hierarchical grading method applied to the potatoes. In this work a potato defect detection combining with size sorting system using the machine vision will be proposed. This work also will focus on the mathematics methods used in automation with a particular emphasis on the issues associated with designing, implementing and using classification algorithms to solve equations. In the first step, a simple size sorting based on mathematical binarization is described, and the second step is to segment the defects; to do this, color based classifiers are used. All the detection standards for this work are referenced from the United States Agriculture Department, and Canadian Food Industries. Results show that we have a high accuracy in both size sorting and classification. Experimental results show that support vector machines have very high accuracy and speed between classifiers for defect detection.