New characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones

We study three representations of hierarchies of partitions: dendrograms (direct representations), saliency maps, and minimum spanning trees. We provide a new bijection between saliency maps and hierarchies based on quasi-flat zones as used in image processing and characterize saliency maps and minimum spanning trees as solutions to constrained minimization problems where the constraint is quasi-flat zones preservation. In practice, these results form a toolkit for new hierarchical methods where one can choose the most convenient representation. They also invite us to process non-image data with morphological hierarchies

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

Contains and Inside relationships within combinatorial Pyramids

Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions. The different graph models used within the irregular pyramid framework encode different types of relationships between regions. This paper compares different graph models used within the irregular pyramid framework according to a set of relationships between regions. We also define a new algorithm based on a pyramid of combinatorial maps which allows to determine if one region contains the other using only local calculus.Comment: 35 page

Optimal topological simplification of discrete functions on surfaces

We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse theory and persistent homology. Our method completely removes homological noise with persistence less than 2{\delta}, constructively proving the tightness of a lower bound on the number of critical points given by the stability theorem of persistent homology in dimension two for any input function. We also show that an optimal solution can be computed in linear time after persistence pairs have been computed.Comment: 27 pages, 8 figure

Rapid Segmentation Techniques for Cardiac and Neuroimage Analysis

Recent technological advances in medical imaging have allowed for the quick acquisition of highly resolved data to aid in diagnosis and characterization of diseases or to guide interventions. In order to to be integrated into a clinical work flow, accurate and robust methods of analysis must be developed which manage this increase in data. Recent improvements in in- expensive commercially available graphics hardware and General-Purpose Programming on Graphics Processing Units (GPGPU) have allowed for many large scale data analysis problems to be addressed in meaningful time and will continue to as parallel computing technology improves. In this thesis we propose methods to tackle two clinically relevant image segmentation problems: a user-guided segmentation of myocardial scar from Late-Enhancement Magnetic Resonance Images (LE-MRI) and a multi-atlas segmentation pipeline to automatically segment and partition brain tissue from multi-channel MRI. Both methods are based on recent advances in computer vision, in particular max-flow optimization that aims at solving the segmentation problem in continuous space. This allows for (approximately) globally optimal solvers to be employed in multi-region segmentation problems, without the particular drawbacks of their discrete counterparts, graph cuts, which typically present with metrication artefacts. Max-flow solvers are generally able to produce robust results, but are known for being computationally expensive, especially with large datasets, such as volume images. Additionally, we propose two new deformable registration methods based on Gauss-Newton optimization and smooth the resulting deformation fields via total-variation regularization to guarantee the problem is mathematically well-posed. We compare the performance of these two methods against four highly ranked and well-known deformable registration methods on four publicly available databases and are able to demonstrate a highly accurate performance with low run times. The best performing variant is subsequently used in a multi-atlas segmentation pipeline for the segmentation of brain tissue and facilitates fast run times for this computationally expensive approach. All proposed methods are implemented using GPGPU for a substantial increase in computational performance and so facilitate deployment into clinical work flows. We evaluate all proposed algorithms in terms of run times, accuracy, repeatability and errors arising from user interactions and we demonstrate that these methods are able to outperform established methods. The presented approaches demonstrate high performance in comparison with established methods in terms of accuracy and repeatability while largely reducing run times due to the employment of GPU hardware

Doctor of Philosophy in Computing

dissertationImage segmentation is the problem of partitioning an image into disjoint segments that are perceptually or semantically homogeneous. As one of the most fundamental computer vision problems, image segmentation is used as a primary step for high-level vision tasks, such as object recognition and image understanding, and has even wider applications in interdisciplinary areas, such as longitudinal brain image analysis. Hierarchical models have gained popularity as a key component in image segmentation frameworks. By imposing structures, a hierarchical model can efficiently utilize features from larger image regions and make optimal inference for final segmentation feasible. We develop a hierarchical merge tree (HMT) model for image segmentation. Motivated by the application in large-scale segmentation of neuronal structures in electron microscopy (EM) images, our model provides a compact representation of region merging hypotheses and utilizes higher order information for efficient segmentation inference. Taking advantage of supervised learning, our model is free from parameter tuning and outperforms previous state-of-the-art methods on both two-dimensional (2D) and three-dimensional EM image data sets without any change. We also extend HMT to the hierarchical merge forest (HMF) model. By identifying region correspondences, HMF utilizes inter-section information to correct intra-section errors and improves 2D EM segmentation accuracy. HMT is a generic segmentation model. We demonstrate this by applying it to natural image segmentation problems. We propose a constrained conditional model formulation with a globally optimal inference algorithm for HMT and an iterative merge tree sampling algorithm that significantly improves its performance. Experimental results show our approach achieves state-of-the-art accuracy for object-independent image segmentation. Finally, we propose a semi-supervised HMT (SSHMT) model to reduce the high demand for labeled data by supervised learning. We introduce a differentiable unsupervised loss term that enforces consistent boundary predictions and develop a Bayesian learning model that combines supervised and unsupervised information. We show that with a very small amount of labeled data, SSHMT consistently performs close to the supervised HMT with full labeled data sets and significantly outperforms HMT trained with the same labeled subsets

CAD, BIM, GIS and other tricks of the computer science in the education of the Building Engineer

Revisione internazionale- relazione a invito- chair sessione S8T The paper aims to develop some thoughts on the upgrade implemented in the disciplines of drawing from the latest forms of digital representation, commenting on the experiences under way in some university courses included in the learning curriculum provided to engineering students with regard to the course of study in Ingegneria Edile (Building Engineering, also known as Architectural or Construction Engineering) at the Politecnico di Torino. It's a matter of reasoning on what and how to suggest knowledge and practises in the experience of teaching that result as an improvement of skills and abilities appropriate for future commitments required by the job world. Method: Methodological reasons, subject contents and experiences positively carried out during the activities of the course of Representation Techniques and Data Management (in the post graduate "Laurea Magistrale") are treated, focusing on all the resources needed to conduct profitable operations training and first clarifying the specific skills and experience required for the teaching staff, essential qualities to ensure good results: all the activities organized to achieve the training objectives are based on the belief that early training is needed to trigger virtuous review processes for engineering practice and that opportunities to practice through simulations in the academic curriculum for future engineers can produce effects of greater permanence and enable an enhancement of learning outcomes. Result: The analysis, which is addressed primarily to illustrate the result of some of the outcomes of exercise activities leaded by students, brings attention to a solicitation that seems to be constraining and that concerns the system of relations required between operators of the design and construction process, which are requested to enter into shared aims while operating in the specificity of the various technical fields; in this sense, the tricks of the CAD, which is at the service of a geometric knowledge, measured and fulfilled by its attributes, the attention demanded by BIM, which builds a widespread and open network of relationship, the cunnings of the GIS, which has to gather dynamic information and alternative choices, appear to address areas of operational testing following a single purpose directed towards a better characterization of the process of conceptual development and a more advantageous control of the working method. Discussion & Conclusion: So, with the design and over the usual representations, we speak of computer tricks to say that to be understood as the necessary infrastructure to solicit and investigate the reasons of doing and how to solve the complexity of operating on the field, upon which students must impractical themselves to identify qualities and limits, whether they are exploring the reasons of the survey or the reasons bound with the design; certainly a renewal for the most usual ways of designing useful to produce different levels of knowledge and a new shared place for the exchange and discussion of the hypotheses, with what results

Summer Research Fellowship Project Descriptions 2019

A summary of research done by Smith College’s 2019 Summer Research Fellowship (SURF) Program participants. Ever since its 1967 start, SURF has been a cornerstone of Smith’s science education. Supervised by faculty mentor-advisors drawn from the Clark Science Center and connected to its eighteen science, mathematics, and engineering departments and programs and associated centers and units. At summer’s end, SURF participants were asked to summarize their research experiences for this publication.https://scholarworks.smith.edu/clark_womeninscience/1008/thumbnail.jp

CAD, BIM, GIS and other tricks of the computer science in the education of the Building Engineer

Revisione internazionale- relazione a invito- chair sessione S8T The paper aims to develop some thoughts on the upgrade implemented in the disciplines of drawing from the latest forms of digital representation, commenting on the experiences under way in some university courses included in the learning curriculum provided to engineering students with regard to the course of study in Ingegneria Edile (Building Engineering, also known as Architectural or Construction Engineering) at the Politecnico di Torino. It’s a matter of reasoning on what and how to suggest knowledge and practises in the experience of teaching that result as an improvement of skills and abilities appropriate for future commitments required by the job world. Method: Methodological reasons, subject contents and experiences positively carried out during the activities of the course of Representation Techniques and Data Management (in the post graduate “Laurea Magistrale”) are treated, focusing on all the resources needed to conduct profitable operations training and first clarifying the specific skills and experience required for the teaching staff, essential qualities to ensure good results: all the activities organized to achieve the training objectives are based on the belief that early training is needed to trigger virtuous review processes for engineering practice and that opportunities to practice through simulations in the academic curriculum for future engineers can produce effects of greater permanence and enable an enhancement of learning outcomes. Result: The analysis, which is addressed primarily to illustrate the result of some of the outcomes of exercise activities leaded by students, brings attention to a solicitation that seems to be constraining and that concerns the system of relations required between operators of the design and construction process, which are requested to enter into shared aims while operating in the specificity of the various technical fields; in this sense, the tricks of the CAD, which is at the service of a geometric knowledge, measured and fulfilled by its attributes, the attention demanded by BIM, which builds a widespread and open network of relationship, the cunnings of the GIS, which has to gather dynamic information and alternative choices, appear to address areas of operational testing following a single purpose directed towards a better characterization of the process of conceptual development and a more advantageous control of the working method. Discussion & Conclusion: So, with the design and over the usual representations, we speak of computer tricks to say that to be understood as the necessary infrastructure to solicit and investigate the reasons of doing and how to solve the complexity of operating on the field, upon which students must impractical themselves to identify qualities and limits, whether they are exploring the reasons of the survey or the reasons bound with the design; certainly a renewal for the most usual ways of designing useful to produce different levels of knowledge and a new shared place for the exchange and discussion of the hypotheses, with what results

Un arbre des formes pour les images multivariées

Nowadays, the demand for multi-scale and region-based analysis in many computer vision and pattern recognition applications is obvious. No one would consider a pixel-based approach as a good candidate to solve such problems. To meet this need, the Mathematical Morphology (MM) framework has supplied region-based hierarchical representations of images such as the Tree of Shapes (ToS). The ToS represents the image in terms of a tree of the inclusion of its level-lines. The ToS is thus self-dual and contrast-change invariant which make it well-adapted for high-level image processing. Yet, it is only defined on grayscale images and most attempts to extend it on multivariate images - e.g. by imposing an “arbitrary” total ordering - are not satisfactory. In this dissertation, we present the Multivariate Tree of Shapes (MToS) as a novel approach to extend the grayscale ToS on multivariate images. This representation is a mix of the ToS's computed marginally on each channel of the image; it aims at merging the marginal shapes in a “sensible” way by preserving the maximum number of inclusion. The method proposed has theoretical foundations expressing the ToS in terms of a topographic map of the curvilinear total variation computed from the image border; which has allowed its extension on multivariate data. In addition, the MToS features similar properties as the grayscale ToS, the most important one being its invariance to any marginal change of contrast and any marginal inversion of contrast (a somewhat “self-duality” in the multidimensional case). As the need for efficient image processing techniques is obvious regarding the larger and larger amount of data to process, we propose an efficient algorithm that can be build the MToS in quasi-linear time w.r.t. the number of pixels and quadraticw.r.t. the number of channels. We also propose tree-based processing algorithms to demonstrate in practice, that the MToS is a versatile, easy-to-use, and efficient structure. Eventually, to validate the soundness of our approach, we propose some experiments testing the robustness of the structure to non-relevant components (e.g. with noise or with low dynamics) and we show that such defaults do not affect the overall structure of the MToS. In addition, we propose many real-case applications using the MToS. Many of them are just a slight modification of methods employing the “regular” ToS and adapted to our new structure. For example, we successfully use the MToS for image filtering, image simplification, image segmentation, image classification and object detection. From these applications, we show that the MToS generally outperforms its ToS-based counterpart, demonstrating the potential of our approachDe nombreuses applications issues de la vision par ordinateur et de la reconnaissance des formes requièrent une analyse de l'image multi-échelle basée sur ses régions. De nos jours, personne ne considérerait une approche orientée « pixel » comme une solution viable pour traiter ce genre de problèmes. Pour répondre à cette demande, la Morphologie Mathématique a fourni des représentations hiérarchiques des régions de l'image telles que l'Arbre des Formes (AdF). L'AdF représente l'image par un arbre d'inclusion de ses lignes de niveaux. L'AdF est ainsi auto-dual et invariant au changement de contraste, ce qui fait de lui une structure bien adaptée aux traitements d'images de haut niveau. Néanmoins, il est seulement défini aux images en niveaux de gris et la plupart des tentatives d'extension aux images multivariées (e.g. en imposant un ordre total «arbitraire ») ne sont pas satisfaisantes. Dans ce manuscrit, nous présentons une nouvelle approche pour étendre l'AdF scalaire aux images multivariées : l'Arbre des Formes Multivarié (AdFM). Cette représentation est une « fusion » des AdFs calculés marginalement sur chaque composante de l'image. On vise à fusionner les formes marginales de manière « sensée » en préservant un nombre maximal d'inclusion. La méthode proposée a des fondements théoriques qui consistent en l'expression de l'AdF par une carte topographique de la variation totale curvilinéaire depuis la bordure de l'image. C'est cette reformulation qui a permis l'extension de l'AdF aux données multivariées. De plus, l'AdFM partage des propriétés similaires avec l'AdF scalaire ; la plus importante étant son invariance à tout changement ou inversion de contraste marginal (une sorte d'auto-dualité dans le cas multidimensionnel). Puisqu'il est évident que, vis-à-vis du nombre sans cesse croissant de données à traiter, nous ayons besoin de techniques rapides de traitement d'images, nous proposons un algorithme efficace qui permet de construire l'AdF en temps quasi-linéaire vis-à-vis du nombre de pixels et quadratique vis-à-vis du nombre de composantes. Nous proposons également des algorithmes permettant de manipuler l'arbre, montrant ainsi que, en pratique, l'AdFM est une structure facile à manipuler, polyvalente, et efficace. Finalement, pour valider la pertinence de notre approche, nous proposons quelques expériences testant la robustesse de notre structure aux composantes non-pertinentes (e.g. avec du bruit ou à faible dynamique) et nous montrons que ces défauts n'affectent pas la structure globale de l'AdFM. De plus, nous proposons des applications concrètes utilisant l'AdFM. Certaines sont juste des modifications mineures aux méthodes employant d'ores et déjà l'AdF scalaire mais adaptées à notre nouvelle structure. Par exemple, nous utilisons l'AdFM à des fins de filtrage, segmentation, classification et de détection d'objet. De ces applications, nous montrons ainsi que les méthodes basées sur l'AdFM surpassent généralement leur analogue basé sur l'AdF, démontrant ainsi le potentiel de notre approch