Novel convolution kernels for computer vision and shape analysis based on electromagnetism

Computer vision is a growing field with a lot of new applications in automation and robotics, since it allows the analysis of images and shapes for the generation of numerical or analytical information. One of the most used method of information extraction is image filtering through convolution kernels, with each kernel specialized for specific applications. The objective of this paper is to present a novel convolution kernels, based on principles of electromagnetic potentials and fields, for a general use in computer vision and to demonstrate its usage for shape and stroke analysis. Such filtering possesses unique geometrical properties that can be interpreted using well understood physics theorems. Therefore, this paper focuses on the development of the electromagnetic kernels and on their application on images for shape and stroke analysis. It also presents several interesting features of electromagnetic kernels, such as resolution, size and orientation independence, robustness to noise and deformation, long distance stroke interaction and ability to work with 3D images

Model and Appearance Based Analysis of Neuronal Morphology from Different Microscopy Imaging Modalities

The neuronal morphology analysis is key for understanding how a brain works. This process requires the neuron imaging system with single-cell resolution; however, there is no feasible system for the human brain. Fortunately, the knowledge can be inferred from the model organism, Drosophila melanogaster, to the human system. This dissertation explores the morphology analysis of Drosophila larvae at single-cell resolution in static images and image sequences, as well as multiple microscopy imaging modalities. Our contributions are on both computational methods for morphology quantification and analysis of the influence of the anatomical aspect. We develop novel model-and-appearance-based methods for morphology quantification and illustrate their significance in three neuroscience studies. Modeling of the structure and dynamics of neuronal circuits creates understanding about how connectivity patterns are formed within a motor circuit and determining whether the connectivity map of neurons can be deduced by estimations of neuronal morphology. To address this problem, we study both boundary-based and centerline-based approaches for neuron reconstruction in static volumes. Neuronal mechanisms are related to the morphology dynamics; so the patterns of neuronal morphology changes are analyzed along with other aspects. In this case, the relationship between neuronal activity and morphology dynamics is explored to analyze locomotion procedures. Our tracking method models the morphology dynamics in the calcium image sequence designed for detecting neuronal activity. It follows the local-to-global design to handle calcium imaging issues and neuronal movement characteristics. Lastly, modeling the link between structural and functional development depicts the correlation between neuron growth and protein interactions. This requires the morphology analysis of different imaging modalities. It can be solved using the part-wise volume segmentation with artificial templates, the standardized representation of neurons. Our method follows the global-to-local approach to solve both part-wise segmentation and registration across modalities. Our methods address common issues in automated morphology analysis from extracting morphological features to tracking neurons, as well as mapping neurons across imaging modalities. The quantitative analysis delivered by our techniques enables a number of new applications and visualizations for advancing the investigation of phenomena in the nervous system

Green Function and Electromagnetic Potential for Computer Vision and Convolutional Neural Network Applications

RÉSUMÉ Pour les problèmes de vision machine (CV) avancées, tels que la classification, la segmentation de scènes et la détection d’objets salients, il est nécessaire d’extraire le plus de caractéristiques possibles des images. Un des outils les plus utilisés pour l’extraction de caractéristiques est l’utilisation d’un noyau de convolution, où chacun des noyaux est spécialisé pour l’extraction d’une caractéristique donnée. Ceci a mené au développement récent des réseaux de neurones convolutionnels (CNN) qui permet d’optimiser des milliers de noyaux à la fois, faisant du CNN la norme pour l’analyse d’images. Toutefois, une limitation importante du CNN est que les noyaux sont petits (généralement de taille 3x3 à 7x7), ce qui limite l’interaction longue-distance des caractéristiques. Une autre limitation est que la fusion des caractéristiques se fait par des additions pondérées et des opérations de mise en commun (moyennes et maximums locaux). En effet, ces opérations ne permettent pas de fusionner des caractéristiques du domaine spatial avec des caractéristiques puisque ces caractéristiques occupent des positions éloignées sur l’image. L’objectif de cette thèse est de développer des nouveaux noyaux de convolutions basés sur l’électromagnétisme (EM) et les fonctions de Green (GF) pour être utilisés dans des applications de vision machine (CV) et dans des réseaux de neurones convolutionnels (CNN). Ces nouveaux noyaux sont au moins aussi grands que l’image. Ils évitent donc plusieurs des limitations des CNN standards puisqu’ils permettent l’interaction longue-distance entre les pixels de limages. De plus, ils permettent de fusionner les caractéristiques du domaine spatial avec les caractéristiques du domaine du gradient. Aussi, étant donné tout champ vectoriel, les nouveaux noyaux permettent de trouver le champ vectoriel conservatif le plus rapproché du champ initial, ce qui signifie que le nouveau champ devient lisse, irrotationnel et conservatif (intégrable par intégrale curviligne). Pour répondre à cet objectif, nous avons d’abord développé des noyaux convolutionnels symétriques et asymétriques basés sur les propriétés des EM et des GF et résultant en des noyaux qui sont invariants en résolution et en rotation. Ensuite, nous avons développé la première méthode qui permet de déterminer la probabilité d’inclusion dans des contours partiels, permettant donc d’extrapoler des contours fins en des régions continues couvrant l’espace 2D. De plus, la présente thèse démontre que les noyaux basés sur les GF sont les solveurs optimaux du gradient et du Laplacien.----------ABSTRACT For advanced computer vision (CV) tasks such as classification, scene segmentation, and salient object detection, extracting features from images is mandatory. One of the most used tools for feature extraction is the convolutional kernel, with each kernel being specialized for specific feature detection. In recent years, the convolutional neural network (CNN) became the standard method of feature detection since it allowed to optimize thousands of kernels at the same time. However, a limitation of the CNN is that all the kernels are small (usually between 3x3 and 7x7), which limits the receptive field. Another limitation is that feature merging is done via weighted additions and pooling, which cannot be used to merge spatial-domain features with gradient-domain features since they are not located at the same pixel coordinate. The objective of this thesis is to develop electromagnetic (EM) convolutions and Green’s functions (GF) convolutions to be used in Computer Vision and convolutional neural networks (CNN). These new kernels do not have the limitations of the standard CNN kernels since they allow an unlimited receptive field and interaction between any pixel in the image by using kernels bigger than the image. They allow merging spatial domain features with gradient domain features by integrating any vector field. Additionally, they can transform any vector field of features into its least-error conservative field, meaning that the field of features becomes smooth, irrotational and conservative (line-integrable). At first, we developed different symmetrical and asymmetrical convolutional kernel based on EM and GF that are both resolution and rotation invariant. Then we developed the first method of determining the probability of being inside partial edges, which allow extrapolating thin edge features into the full 2D space. Furthermore, the current thesis proves that GF kernels are the least-error gradient and Laplacian solvers, and they are empirically demonstrated to be faster than the fastest competing method and easier to implement. Consequently, using the fast gradient solver, we developed the first method that directly combines edges with saliency maps in the gradient domain, then solves the gradient to go back to the saliency domain. The improvement of the saliency maps over the F-measure is on average 6.6 times better than the nearest competing algorithm on a selected dataset. Then, to improve the saliency maps further, we developed the DSS-GIS model which combines edges with salient regions deep inside the network