Abstract-This article aims to understand the practical features of hierarchies of morphological segmentations, namely the quasi-flat zones hierarchy and watershed hierarchies, and to evaluate their potential in the context of natural image analysis. We propose a novel evaluation framework for hierarchies of partitions designed to capture various aspects of those representations: precision of their regions and contours, possibility to extract high quality horizontal cuts and optimal non-horizontal cuts for image segmentation, and ease of finding a set of regions representing a semantic object. This framework is used to assess and to optimize hierarchies with respect to the possible pre-and post-processing steps. We show that, used in conjunction with a state-of-the-art contour detector, watershed hierarchies are competitive with complex state-of-the-art methods for hierarchy construction. In particular, the proposed framework allows us to identify a watershed hierarchy based on a novel extinction value, the number of parent nodes, that outperforms the other hierarchies of morphological segmentations. This coupled with the fact that watershed hierarchies satisfy clear global optimality properties and can be efficiently computed on large data, make them valuable candidates for various computer vision tasks.Index Terms-mathematical morphology, hierarchy of partitions, watershed segmentation, image analysis.

Combining hierarchical watersheds has proven to be a good alternative method to outperform individual hierarchical watersheds. Consequently, this raises the question of whether the resulting combinations are hierarchical watersheds themselves. Since the naive algorithm to answer this question has a factorial time complexity, we propose a new characterization of hierarchical watersheds which leads to a quasi-linear time algorithm to determine if a hierarchy is a hierarchical watershed.

Human activities in the sea, such as intensive fishing and exploitation of offshore wind farms, may impact negatively on the marine mega fauna. As an attempt to control such impacts, surveying, and tracking of marine animals are often performed on the sites where those activities take place. Nowadays, thank to high resolution cameras and to the development of machine learning techniques, tracking of wild animals can be performed remotely and the analysis of the acquired images can be automatized using state-of-the-art object detection models. However, most state-of-the-art detection methods require lots of annotated data to provide satisfactory results. Since analyzing thousands of images acquired during a flight survey can be a cumbersome and time consuming task, we focus in this article on the weakly supervised detection of marine animals. We propose a modification of the patch distribution modeling method (PaDiM), which is currently one of the state-of-the-art approaches for anomaly detection and localization for visual industrial inspection. In order to show its effectiveness and suitability for marine animal detection, we conduct a comparative evaluation of the proposed method against the original version, as well as other state-of-the-art approaches on two high-resolution marine animal image datasets. On both tested datasets, the proposed method yielded better F1 and recall scores (75% recall/41% precision, and 57% recall/60% precision, respectively) when trained on images known to contain no object of interest. This shows a great potential of the proposed approach to speed up the marine animal discovery in new flight surveys. Additionally, such a method could be adopted for bounding box proposals to perform faster and cheaper annotation within a fully-supervised detection framework.

The mathematical morphology presents a systematic model to extract geometrical characteristics of images using morphological operators, which transforms the original image into another, using a third image called structural element. The fuzzy mathematical morphology extends the morphological operators to grayscale and coloured images using the fuzzy logic, where the definition of the operators are defined using the concepts of implications and fuzzy conjunctions, specifically, the implications and conjunctions of Lukasiewicz. In this paper it was proposed a counting method of mycorrhizal fungi spores which are derived from mycorrhizas, a symbiotic association between a fungus and a plant, using fuzzy morphological operators. The counting of these spores was done manually using corrugated plate and the aid of a stereoscopic microscope.

The fuzzy mathematical morphology extends the binary morphological operators to gray-scale and coloured images using concepts of fuzzy logic. To define the morphological operators of fuzzy erosion and dilatation it is used the implications and conjunctions respectively. This work presents an analysis of some R-implications to verify if the pairs of implications and T-norms (conjunctions) were adjunctions. It was used a fuzzy application developed in the Matlab for implementation and tests with the respectively results.

In this paper we describe our implementation of algorithms for face detection

Watershed is a well established clustering and segmentation method. In this article, we aim to achieve a better theoretical understanding of the hierarchical version of the watershed operator. More precisely, we propose a characterization of hierarchical watersheds in the framework of edge-weighted graphs. The proposed characterization leads to an efficient algorithm to recognize hierarchical watersheds.

The main goal of this paper is to evaluate the potential of some combinations of watershed hierarchies. We also propose a new combination based on merging level sets of hierarchies. Experiments were performed on natural image datasets and were based on evaluating the segmentations extracted from level sets of each hierarchy against the image ground truths. Our experiments show that most of combinations studied here are superior to their individual counterparts, which opens a path for a deeper investigation on combination of hierarchies.