A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Weighted fusion graphs: merging properties and watersheds

International audienc

Discrete region merging and watersheds

incollectionThis paper summarizes some results of the authors concerning watershed divides and their use in region merging schemes.The first aspect deals with properties of watershed divides that can be used in particular for hierarchical region merging schemes. We introduce the mosaic to retrieve the altitude of points along the divide set. A desirable property is that, when two minima are separated by a crest in the original image, they are still separated by a crest of the same altitude in the mosaic. Our main result states that this is the case if and only if the mosaic is obtained through a topological thinning.The second aspect is closely related to the thinness of watershed divides. We present fusion graphs, a class of graphs in which any region can be always merged without any problem. This class is equivalent to the one in which watershed divides are thin. Topological thinnings do not always produce thin divides, even on fusion graphs. We also present the class of perfect fusion graphs, in which any pair of neighbouring regions can be merged through their common neighborhood. An important theorem states that the divides of any ultimate topological thinning are thin on any perfect fusion graph

Making microscopy count: quantitative light microscopy of dynamic processes in living plants

First published: April 2016This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.Cell theory has officially reached 350 years of age as the first use of the word ‘cell’ in a biological context can be traced to a description of plant material by Robert Hooke in his historic publication “Micrographia: or some physiological definitions of minute bodies”. The 2015 Royal Microscopical Society Botanical Microscopy meeting was a celebration of the streams of investigation initiated by Hooke to understand at the sub-cellular scale how plant cell function and form arises. Much of the work presented, and Honorary Fellowships awarded, reflected the advanced application of bioimaging informatics to extract quantitative data from micrographs that reveal dynamic molecular processes driving cell growth and physiology. The field has progressed from collecting many pixels in multiple modes to associating these measurements with objects or features that are meaningful biologically. The additional complexity involves object identification that draws on a different type of expertise from computer science and statistics that is often impenetrable to biologists. There are many useful tools and approaches being developed, but we now need more inter-disciplinary exchange to use them effectively. In this review we show how this quiet revolution has provided tools available to any personal computer user. We also discuss the oft-neglected issue of quantifying algorithm robustness and the exciting possibilities offered through the integration of physiological information generated by biosensors with object detection and tracking

Watersheds on edge or node weighted graphs

The literature on the watershed is separated in two families: the watersheds on node weighted graphs and the watersheds on edge weighted graphs. The simplest node weighted graphs are images, where the nodes are the pixels ; neighboring pixels being linked by unweighted pixels. The edge weights on an edge weighted graph express dissimilarities between the unweighted nodes. Distinct definitions of minima and catchment basins have been given for both types of graphs from which different algorithms have been derived. This paper aims at showing that watersheds on edge or node weighted graphs are strictly equivalent. Moreover, all algorithms developed for edge weighted graphs may be applied on node weighted graphs and vice versa. From any node or edge weighted graph it is possible to derive a flooding graph with node and edge weights. Its regional minima and catchment basins are identical whether one considers the node weights alone or the edge weights alone. A lexicographic order relation permits to compare non ascending paths with the same origin according to their steepness. Overlapping zones between neighboring catchment basins are reduced or even suppressed by pruning edges in the flooding graph through which does not pass a steepest path and reduces, without arbitrary choices the overlapping zones between adjacent catchment basins. We propose several ways to break the remaining ties, the simplest being to assign slightly distinct weights to regional minima with the same weight. Like that each node is linked with only one regional minimum by a path of maximal steepness

Enhancing Rock Image Segmentation in Digital Rock Physics: A Fusion of Generative AI and State-of-the-Art Neural Networks

In digital rock physics, analysing microstructures from CT and SEM scans is crucial for estimating properties like porosity and pore connectivity. Traditional segmentation methods like thresholding and CNNs often fall short in accurately detailing rock microstructures and are prone to noise. U-Net improved segmentation accuracy but required many expert-annotated samples, a laborious and error-prone process due to complex pore shapes. Our study employed an advanced generative AI model, the diffusion model, to overcome these limitations. This model generated a vast dataset of CT/SEM and binary segmentation pairs from a small initial dataset. We assessed the efficacy of three neural networks: U-Net, Attention-U-net, and TransUNet, for segmenting these enhanced images. The diffusion model proved to be an effective data augmentation technique, improving the generalization and robustness of deep learning models. TransU-Net, incorporating Transformer structures, demonstrated superior segmentation accuracy and IoU metrics, outperforming both U-Net and Attention-U-net. Our research advances rock image segmentation by combining the diffusion model with cutting-edge neural networks, reducing dependency on extensive expert data and boosting segmentation accuracy and robustness. TransU-Net sets a new standard in digital rock physics, paving the way for future geoscience and engineering breakthroughs

Automatic Detection and Segmentation of Lentil Breeding Plots from Images Captured by Multi-spectral UAV-Mounted Camera

Automatic Detection and Segmentation of Lentil Breeding Plots from Images Captured by Multi-spectral UAV-Mounted Camer

Automatic Detection and Segmentation of Lentil Breeding Plots from Images Captured by Multi-spectral UAV-Mounted Camera

Automatic Detection and Segmentation of Lentil Breeding Plots from Images Captured by Multi-spectral UAV-Mounted Camer

An interdisciplinary analysis of Colorado Rocky Mountain environments using ADP techniques

The author has identified the following significant results. Good ecological, classification accuracy (90-95%) can be achieved in areas of rugged relief on a regional basis for Level 1 cover types (coniferous forest, deciduous forest, grassland, cropland, bare rock and soil, and water) using computer-aided analysis techniques on ERTS/MSS data. Cost comparisons showed that a Level 1 cover type map and a table of areal estimates could be obtained for the 443,000 hectare San Juan Mt. test site for less than 0.1 cent per acre, whereas photointerpretation techniques would cost more than 0.4 cent per acre. Results of snow cover mapping have conclusively proven that the areal extent of snow in mountainous terrain can be rapidly and economically mapped by using ERTS/MSS data and computer-aided analysis techniques. A distinct relationship between elevation and time of freeze or thaw was observed, during mountain lake mapping. Basic lithologic units such as igneous, sedimentary, and unconsolidated rock materials were successfully identified. Geomorphic form, which is exhibited through spatial and textual data, can only be inferred from ERTS data. Data collection platform systems can be utilized to produce satisfactory data from extremely inaccessible locations that encounter very adverse weather conditions, as indicated by results obtained from a DCP located at 3,536 meters elevation that encountered minimum temperatures of -25.5 C and wind speeds of up to 40.9m/sec (91 mph), but which still performed very reliably

Fast unsupervised multiresolution color image segmentation using adaptive gradient thresholding and progressive region growing

In this thesis, we propose a fast unsupervised multiresolution color image segmentation algorithm which takes advantage of gradient information in an adaptive and progressive framework. This gradient-based segmentation method is initialized by a vector gradient calculation on the full resolution input image in the CIE L*a*b* color space. The resultant edge map is used to adaptively generate thresholds for classifying regions of varying gradient densities at different levels of the input image pyramid, obtained through a dyadic wavelet decomposition scheme. At each level, the classification obtained by a progressively thresholded growth procedure is combined with an entropy-based texture model in a statistical merging procedure to obtain an interim segmentation. Utilizing an association of a gradient quantized confidence map and non-linear spatial filtering techniques, regions of high confidence are passed from one level to another until the full resolution segmentation is achieved. Evaluation of our results on several hundred images using the Normalized Probabilistic Rand (NPR) Index shows that our algorithm outperforms state-of the art segmentation techniques and is much more computationally efficient than its single scale counterpart, with comparable segmentation quality