Implementation and complexity of the watershed-from-markers algorithm computed as a minimal cost forest

The watershed algorithm belongs to classical algorithms in mathematical morphology. Lotufo et al. published a principle of the watershed computation by means of an Image Foresting Transform (IFT), which computes a shortest path forest from given markers. The algorithm itself was described for a 2D case (image) without a detailed discussion of its computation and memory demands for real datasets. As IFT cleverly solves the problem of plateaus and as it gives precise results when thin objects have to be segmented, it is obvious to use this algorithm for 3D datasets taking in mind the minimizing of a higher memory consumption for the 3D case without loosing low asymptotical time complexity of O(m+C) (and also the real computation speed). The main goal of this paper is an implementation of the IFT algorithm with a priority queue with buckets and careful tuning of this implementation to reach as minimal memory consumption as possible. The paper presents five possible modifications and methods of implementation of the IFT algorithm. All presented implementations keep the time complexity of the standard priority queue with buckets but the best one minimizes the costly memory allocation and needs only 19-45% of memory for typical 3D medical imaging datasets. Memory saving was reached by an IFT algorithm simplification, which stores more elements in temporary structures but these elements are simpler and thus need less memory. The best presented modification allows segmentation of large 3D medical datasets (up to 512x512x680 voxels) with 12-or 16-bits per voxel on currently available PC based workstations.Comment: v1: 10 pages, 6 figures, 7 tables EUROGRAPHICS conference, Manchester, UK, 2001. v2: 12 pages, reformated for letter, corrected IFT to "Image Foresting Tranform

Analyses of the Watershed Transform

International audienceIn the framework of mathematical morphology, watershed transform (WT) represents a key step in image segmentation procedure. In this paper, we present a thorough analysis of some existing watershed approaches in the discrete case: WT based on flooding, WT based on path-cost minimization, watershed based on topology preservation, WT based on local condition and WT based on minimum spanning forest. For each approach, we present detailed description of processing procedure followed by mathematical foundations and algorithm of reference. Recent publications based on some approaches are also presented and discussed. Our study concludes with a classification of different watershed transform algorithms according to solution uniqueness, topology preservation, prerequisites minima computing and linearity

Tie-zone : the bridge between watershed transforms and fuzzy connectedness

Orientador: Roberto de Alencar LotufoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Esta tese introduz o novo conceito de transformada de zona de empate que unifica as múltiplas soluções de uma transformada de watershed, conservando apenas as partes comuns em todas estas, tal que as partes que diferem constituem a zona de empate. A zona de empate aplicada ao watershed via transformada imagem-floresta (TZ-IFT-WT) se revela um elo inédito entre transformadas de watershed baseadas em paradigmas muito diferentes: gota d'água, inundação, caminhos ótimos e floresta de peso mínimo. Para todos esses paradigmas e os algoritmos derivados, é um desafio se ter uma solução única, fina, e que seja consistente com uma definição. Por isso, propõe-se um afinamento da zona de empate, único e consistente. Além disso, demonstra-se que a TZ-IFT-WT também é o dual de métodos de segmentação baseados em conexidade nebulosa. Assim, a ponte criada entre as abordagens morfológica e nebulosa permite aproveitar avanços de ambas. Em conseqüência disso, o conceito de núcleo de robustez para as sementes é explorado no caso do watershed.Abstract: This thesis introduces the new concept of tie-zone transform that unifies the multiple solutions of a watershed transform, by conserving only the common parts among them such that the differing parts constitute the tie zone. The tie zone applied to the watershed via image-foresting transform (TZ-IFTWT) proves to be a link between watershed transforms based on very different paradigms: drop of water, flooding, optimal paths and forest of minimum weight. For all these paradigms and the derived algorithms, it is a challenge to get a unique and thin solution which is consistent with a definition. That is why we propose a unique and consistent thinning of the tie zone. In addition, we demonstrate that the TZ-IFT-WT is also the dual of segmentation methods based on fuzzy connectedness. Thus, the bridge between the morphological and the fuzzy approaches allows to take benefit from the advance of both. As a consequence, the concept of cores of robustness for the seeds is exploited in the case of watersheds.DoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétric

Preoperative Volume Determination for Pituitary Adenoma

The most common sellar lesion is the pituitary adenoma, and sellar tumors are approximately 10-15% of all intracranial neoplasms. Manual slice-by-slice segmentation takes quite some time that can be reduced by using the appropriate algorithms. In this contribution, we present a segmentation method for pituitary adenoma. The method is based on an algorithm that we have applied recently to segmenting glioblastoma multiforme. A modification of this scheme is used for adenoma segmentation that is much harder to perform, due to lack of contrast-enhanced boundaries. In our experimental evaluation, neurosurgeons performed manual slice-by-slice segmentation of ten magnetic resonance imaging (MRI) cases. The segmentations were compared to the segmentation results of the proposed method using the Dice Similarity Coefficient (DSC). The average DSC for all datasets was 75.92% +/- 7.24%. A manual segmentation took about four minutes and our algorithm required about one second.Comment: 7 pages, 6 figures, 1 table, 16 references in Proc. SPIE 7963, Medical Imaging 2011: Computer-Aided Diagnosis, 79632T (9 March 2011). arXiv admin note: text overlap with arXiv:1103.177

Automatic Detection of Critical Dermoscopy Features for Malignant Melanoma Diagnosis

Improved methods for computer-aided analysis of identifying features of skin lesions from digital images of the lesions are provided. Improved preprocessing of the image that 1) eliminates artifacts that occlude or distort skin lesion features and 2) identifies groups of pixels within the skin lesion that represent features and/or facilitate the quantification of features are provided including improved digital hair removal algorithms. Improved methods for analyzing lesion features are also provided

Interactive Learning for the Analysis of Biomedical and Industrial Imagery

In der vorliegenden Dissertation werden Methoden des überwachten Lernens untersucht und auf die Analyse und die Segmentierung digitaler Bilddaten angewendet, die aus diversen Forschungsgebieten stammen. Die Segmentierung und die Klassifikation spielen eine wichtige Rolle in der biomedizinischen und industriellen Bildverarbeitung, häufig basiert darauf weitere Erkennung und Quantifikation. Viele problemspezifische Ansätze existieren für die unterschiedlichsten Fragestellungen und nutzen meist spezifisches Vorwissen aus den jeweiligen Bilddaten aus. In dieser Arbeit wird ein überwachtes Lernverfahren vorgestellt, das mehrere Objekte und deren Klassen gleichzeitig segmentieren und unterscheiden kann. Die Methode ist generell genug um einen wichtigen Bereich von Anwendungen abzudecken, für deren Lösung lokale Merkmale eine Rolle spielen. Segmentierungsergebnisse dieses Ansatzes werden auf verschiedenen Datensätzen mit unterschiedlichen Problemstellungen gezeigt. Die Resultate unterstreichen die Anwendbarkeit der Lernmethode für viele biomedizinische und industrielle Anwendungen, ohne dass explizite Kenntnisse der Bildverarbeitung und Programmierung vorausgesetzt werden müssen. Der Ansatz basiert auf generellen Merkmalsklassen, die es erlauben lokal Strukturen wie Farbe, Textur und Kanten zu beschreiben. Zu diesem Zweck wurde eine interaktive Software implementiert, welche, für gewöhnliche Bildgrößen, in Echtzeit arbeitet und es somit einem Domänenexperten erlaubt Segmentierungs- und Klassifikationsaufgaben interaktiv zu bearbeiten. Dafür sind keine Kenntnisse in der Bildverarbeitung nötig, da sich die Benutzerinteraktion auf intuitives Markieren mit einem Pinselwerkzeug beschränkt. Das interaktiv trainierte System kann dann ohne weitere Benutzerinteraktion auf viele neue Bilder angewendet werden. Der Ansatz ist auf Segmentierungsprobleme beschränkt, für deren Lösung lokale diskriminative Merkmale ausreichen. Innerhalb dieser Einschränkung zeigt der Algorithmus jedoch erstaunlich gute Resultate, die in einer applikationsspezifischen Prozedur weiter verbessert werden können. Das Verfahren unterstützt bis zu vierdimensionale, multispektrale Bilddaten in vereinheitlichter Weise. Um die Anwendbar- und Übertragbarkeit der Methode weiter zu illustrieren wurden mehrere echte Anwendungsfälle, kommend aus verschiedenen bildgebenden Bereichen, untersucht. Darunter sind u. A. die Segmentierung von Tumorgewebe, aufgenommen mittelsWeitfeldmikroskopie, die Quantifikation von Zellwanderungen in konfokalmikroskopischen Aufnahmen für die Untersuchung der adulten Neurogenese, die Segmentierung von Blutgefäßen in der Retina des Auges, das Verfolgen von Kupferdrähten in einer Anwendung zur Produktauthentifikation und die Qualitätskontrolle von Mikroskopiebildern im Kontext von Hochdurchsatz-Experimenten. Desweiteren wurde eine neue Klassifikationsmethode basierend auf globalen Frequenzschätzungen für die Prozesskontrolle des Papieranlegers an Druckmaschinen entwickelt

Watershed Delineation in the Field: A New Approach for Mobile Applications Using LiDAR Elevation Data

With the advancement of mobile devices, opportunities to take watershed management tasks out of the office and into the field can be realized. In turn, field workers can utilize these technologies to expedite the decision-making process so that they may focus on meeting with clients and addressing agricultural watershed management issues. High-resolution (∼1.5 m postspacing) elevation data gathered by light detection and ranging (LiDAR) provides the topographic detail necessary to model hydrology at the field-scale (∼1 km2). Non-artifactual surface depressions lead to erroneous surface flow patterns when using existing algorithms. So a sequential depression-filling algorithm (SDFA) has been developed to address topographies that contain these types of features. Given a rainfall amount, water distributed across the landscape accumulates and fills only those depressions as necessary, halting the filling process when the only depressions that remain require additional rainfall. After the filling process is completed, the watershed contributing area draining to any particular point of interest may be identified and in the future this may be used as input to hydrologic models. Methods have also been developed to implement subsurface drainage features such as culverts and tile-inlets as well as soil infiltration such that the dynamics of how water is shed from a given landscape can be better represented. Tile inlets and drainage features may be identified via user input and assigned a drainage rate while infiltration may be implemented by assigning a drainage rate to each grid cell in the DEM based on their soil-type. The combination of the sequential depression-filling algorithm and this drainage feature implementation provides the tools to model localized drainage patterns that will match user\u27s field observations at the scale of hundreds of hectares. The flow routing, depression identification, and filling procedures of the SDFA were compared to similar functions in the ArcGIS Hydrology Toolset under conditions where all depressions were filled in order to validate that those components of the algorithm are identical as intended. Furthermore, several digital elevation models (DEMs) were analyzed to determine the variability in hydrologic connectivity across these landscapes as a function of rainfall and as a function of DEM size. In addition to depression storage, the impacts of infiltration on hydrologic connectivity over these landscapes were also analyzed using the SCS Curve Number Method. The assumptions made by existing algorithms that require complete hydrologic connectivity do not hold up in all landscapes, even more so when considering the effects of infiltration. In these landscapes, surface hydrologic connectivity varies noticeably with rainfall excess and it is inaccurate to assume that the watershed should be modeled as a monotonically descending 14 surface. In an applicability study of DEM size, depression features began to be captured around the 1 km 2 scale while it is recommended to use DEMs larger than 2 km 2 to ensure that the depressional features and their contributing areas are completely captured within the DEM extent so that the SDFA may account for those features correctly. The SDFA algorithm was ported from Matlab to an Android application for mobile phones and tablets. The Watershed Delineation app is free and publicly available through the Google Play Store. Users may view DEMs on a Google Map, use the sequential depression-filling algorithm to fill depressions, and delineate watersheds. It was found that the performance of this algorithm is a function of the number of depressions in the DEM which increases with DEM resolution (due to signal-noise effects). At a 3-meter resolution, the ideal DEM dimensions suitable for use of the SDFA on a Google Nexus 4 phone are about 500 x 500 (225 hectares), which took 68 seconds to run. At DEM sizes much greater than this, performance is drastically reduced. As DEM resolution increases, noise effects in the data (which vary based on the raw LiDAR data) result in a high amount of depression features causing an excessive number of iterations of the filling procedure within the algorithm