Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods

Image compression with anisotropic diffusion

Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for removing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widely-used JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec

AUTOMATED COMMUNICATION SYSTEM FOR DETECTION OF LUNG CANCER USING CATASTROPHE FEATURES

Jedan od najvećih izazova s kojima se svijet danas suočava je smrtnost od raka. Jedan od četiri svih dijagnosticiranih karcinoma uključuje karcinom pluća, gdje je smrtnost visoka, čak i nakon tolikog tehničkog i medicinskog napretka. Većina slučajeva raka pluća dijagnosticira se u trećem ili četvrtom stadiju, kada se bolest ne može liječiti. Glavni razlog najveće smrtnosti zbog karcinoma pluća je nedostupnost sustava za „preskrining“ koji može detektirati stanice raka u ranim fazama. Stoga je potrebno razviti sustav za predklinički pregled koji pomaže liječnicima da pronađu i otkriju rak pluća u ranim fazama. Od svih vrsta karcinoma pluća, adenokarcinom se povećava alarmantnom brzinom. Razlog se uglavnom pripisuje povećanoj stopi pušenja - i aktivnom i pasivnom. U ovom radu razvijen je sustav za klasifikaciju plućnih žljezdanih stanica za rano otkrivanje raka korištenjem više prostora u boji. Za segmentaciju koriste se razne tehnike klasteriranja na različitim prostorima boja kao što su HSV, CIELAB, CIEXYy i CIELUV. Značajke se izdvajaju i klasificiraju pomoću Support Vector Machine (SVM).One of the biggest challenges the world face today is the mortality due to Cancer. One in four of all diagnosed cancers involve the lung cancer, where the mortality rate is high, even after so much of technical and medical advances. Most lung cancer cases are diagnosed either in the third or fourth stage, when the disease is not treatable. The main reason for the highest mortality, due to lung cancer is because of non availability of prescreening system which can analyze the cancer cells at early stages. So it is necessary to develop a prescreening system which helps doctors to find and detect lung cancer at early stages. Out of all various types of lung cancers, adenocarcinoma is increasing at an alarming rate. The reason is mainly attributed to the increased rate of smoking - both active and passive. In the present work, a system for the classification of lung glandular cells for early detection of Cancer using multiple color spaces is developed. For segmentation, various clustering techniques like K-Means clustering and Fuzzy C-Means clustering on various Color spaces such as HSV, CIELAB, CIEXYy and CIELUV are used. Features are Extracted and classified using Support Vector Machine (SVM)

Locating landmarks using templates

Abstract: This thesis is devoted to automatic location of landmarks (mouth and eyes) in images of faces using templates. There is an unsatisfactory experience with existing software because of its high sensitivity to small rotations of the face. The weighted correlation coeficient as a similarity measure between the template and the image turns out to outperform the classical correlation. It is presented how to choose the weights to increase the discrimination of the parts of the face which correspond to the template from those which do not. Optimization without constraints tends to degenerate and to obtain a robust version we bound the in uence of single pixels. In a similar way the template can be optimized to improve the discrimination further. The results are compared for different initial choices of weights and their robustness to different size or rotation of the face is examined. The method does not use any special properties of the mouth or eyes and can be classified as a robust nonparametric disrimination technique

Subset selection using nonlinear optimization

A common problem in computer science is how to represent a large dataset in a smaller more compact form. This thesis describes a generalized framework for selecting canonical subsets of data points that are highly representative of the original larger dataset. The contributions of the work are formulation of the subset selection problem as an optimization problem, an analysis of the complexity of the problem, the development of approximation algorithms to compute canonical subsets, and a demonstration of the utility of the algorithms in several problem domains.Ph.D., Computer Science -- Drexel University, 200

PDE-based image compression based on edges and optimal data

This thesis investigates image compression with partial differential equations (PDEs) based on edges and optimal data. It first presents a lossy compression method for cartoon-like images. Edges together with some adjacent pixel values are extracted and encoded. During decoding, information not covered by this data is reconstructed by PDE-based inpainting with homogeneous diffusion. The result is a compression codec based on perceptual meaningful image features which is able to outperform JPEG and JPEG2000. In contrast, the second part of the thesis focuses on the optimal selection of inpainting data. The proposed methods allow to recover a general image from only 4% of all pixels almost perfectly, even with homogeneous diffusion inpainting. A simple conceptual encoding shows the potential of an optimal data selection for image compression: The results beat the quality of JPEG2000 when anisotropic diffusion is used for inpainting. Finally, the thesis shows that the combination of the concepts allows for further improvements.Die vorliegende Arbeit untersucht die Bildkompression mit partiellen Differentialgleichungen (PDEs), basierend auf Kanten und optimalen Daten. Sie stellt zunächst ein verlustbehaftetes Kompressionsverfahren für cartoonartige Bilder vor. Dazu werden Kanten zusammen mit einigen benachbarten Pixelwerten extrahiert und anschließend kodiert. Während der Dekodierung, werden Informationen, die durch die gespeicherten Daten nicht abgedeckt sind, mittels PDE-basiertem Inpainting mit homogenener Diffusion rekonstruiert. Das Ergebnis ist ein Kompressionscodec, der auf visuell bedeutsamen Bildmerkmalen basiert und in der Lage ist, die Qualität von JPEG und JPEG2000 zu übertreffen. Im Gegensatz dazu konzentriert sich der zweite Teil der Arbeit auf die optimale Auswahl von Inpaintingdaten. Die vorgeschlagenen Methoden ermöglichen es, ein gewöhnliches Bild aus nur 4% aller Pixel nahezu perfekt wiederherzustellen, selbst mit homogenem Diffusionsinpainting. Eine einfache konzeptuelle Kodierung zeigt das Potential einer optimierten Datenauswahl auf: Die Ergebnisse übersteigen die Qualität von JPEG2000, sofern das Inpainting mit einem anisotropen Diffusionsprozess erfolgt. Schließlich zeigt die Arbeit, dass weitere Verbesserungen durch die Kombination der Konzepte erreicht werden können

Denoising and enhancement of digital images : variational methods, integrodifferential equations, and wavelets

The topics of this thesis are methods for denoising, enhancement, and simplification of digital image data. Special emphasis lies on the relations and structural similarities between several classes of methods which are motivated from different contexts. In particular, one can distinguish the methods treated in this thesis in three classes: For variational approaches and partial differential equations, the notion of the derivative is the tool of choice to model regularity of the data and the desired result. A general framework for such approaches is proposed that involve all partial derivatives of a prescribed order and experimentally are capable of leading to piecewise polynomial approximations of the given data. The second class of methods uses wavelets to represent the data which makes it possible to understand the filtering as very simple pointwise application of a nonlinear function. To view these wavelets as derivatives of smoothing kernels is the basis for relating these methods to integrodifferential equations which are investigated here. In the third case, values of the image in a neighbourhood are averaged where the weights of this averaging can be adapted respecting different criteria. By refinement of the pixel grid and transfer to scaling limits, connections to partial differential equations become visible here, too. They are described in the framework explained before. Numerical aspects of the simplification of images are presented with respect to the NDS energy function, a unifying approach that allows to model many of the aforementioned methods. The behaviour of the filtering methods is documented with numerical examples.Gegenstand der vorliegenden Arbeit sind Verfahren zum Entrauschen, qualitativen Verbessern und Vereinfachen digitaler Bilddaten. Besonderes Augenmerk liegt dabei auf den Beziehungen und der strukturellen Ähnlichkeit zwischen unterschiedlich motivierten Verfahrensklassen. Insbesondere lassen sich die hier behandelten Methoden in drei Klassen einordnen: Bei den Variationsansätzen und partiellen Differentialgleichungen steht der Begriff der Ableitung im Mittelpunkt, um Regularität der Daten und des gewünschten Resultats zu modellieren. Hier wird ein einheitlicher Rahmen für solche Ansätze angegeben, die alle partiellen Ableitungen einer vorgegebenen Ordnung involvieren und experimentell auf stückweise polynomielle Approximationen der gegebenen Daten führen können. Die zweite Klasse von Methoden nutzt Wavelets zur Repräsentation von Daten, mit deren Hilfe sich Filterung als sehr einfache punktweise Anwendung einer nichtlinearen Funktion verstehen lässt. Diese Wavelets als Ableitungen von Glättungskernen aufzufassen bildet die Grundlage für die hier untersuchte Verbindung dieser Verfahren zu Integrodifferentialgleichungen. Im dritten Fall werden Werte des Bildes in einer Nachbarschaft gemittelt, wobei die Gewichtung bei dieser Mittelung adaptiv nach verschiedenen Kriterien angepasst werden kann. Durch Verfeinern des Pixelgitters und Übergang zu Skalierungslimites werden auch hier Verbindungen zu partiellen Differentialgleichungen sichtbar, die in den vorher dargestellten Rahmen eingeordnet werden. Numerische Aspekte beim Vereinfachen von Bildern werden anhand der NDS-Energiefunktion dargestellt, eines einheitlichen Ansatzes, mit dessen Hilfe sich viele der vorgenannten Methoden realisieren lassen. Das Verhalten der einzelnen Filtermethoden wird dabei jeweils durch numerische Beispiele dokumentiert

Understanding and advancing PDE-based image compression

This thesis is dedicated to image compression with partial differential equations (PDEs). PDE-based codecs store only a small amount of image points and propagate their information into the unknown image areas during the decompression step. For certain classes of images, PDE-based compression can already outperform the current quasi-standard, JPEG2000. However, the reasons for this success are not yet fully understood, and PDE-based compression is still in a proof-of-concept stage. With a probabilistic justification for anisotropic diffusion, we contribute to a deeper insight into design principles for PDE-based codecs. Moreover, by analysing the interaction between efficient storage methods and image reconstruction with diffusion, we can rank PDEs according to their practical value in compression. Based on these observations, we advance PDE-based compression towards practical viability: First, we present a new hybrid codec that combines PDE- and patch-based interpolation to deal with highly textured images. Furthermore, a new video player demonstrates the real-time capacities of PDE-based image interpolation and a new region of interest coding algorithm represents important image areas with high accuracy. Finally, we propose a new framework for diffusion-based image colourisation that we use to build an efficient codec for colour images. Experiments on real world image databases show that our new method is qualitatively competitive to current state-of-the-art codecs.Diese Dissertation ist der Bildkompression mit partiellen Differentialgleichungen (PDEs, partial differential equations) gewidmet. PDE-Codecs speichern nur einen geringen Anteil aller Bildpunkte und transportieren deren Information in fehlende Bildregionen. In einigen Fällen kann PDE-basierte Kompression den aktuellen Quasi-Standard, JPEG2000, bereits schlagen. Allerdings sind die Gründe für diesen Erfolg noch nicht vollständig erforscht, und PDE-basierte Kompression befindet sich derzeit noch im Anfangsstadium. Wir tragen durch eine probabilistische Rechtfertigung anisotroper Diffusion zu einem tieferen Verständnis PDE-basierten Codec-Designs bei. Eine Analyse der Interaktion zwischen effizienten Speicherverfahren und Bildrekonstruktion erlaubt es uns, PDEs nach ihrem Nutzen für die Kompression zu beurteilen. Anhand dieser Einsichten entwickeln wir PDE-basierte Kompression hinsichtlich ihrer praktischen Nutzbarkeit weiter: Wir stellen einen Hybrid-Codec für hochtexturierte Bilder vor, der umgebungsbasierte Interpolation mit PDEs kombiniert. Ein neuer Video-Dekodierer demonstriert die Echtzeitfähigkeit PDE-basierter Interpolation und eine Region-of-Interest-Methode erlaubt es, wichtige Bildbereiche mit hoher Genauigkeit zu speichern. Schlussendlich stellen wir ein neues diffusionsbasiertes Kolorierungsverfahren vor, welches uns effiziente Kompression von Farbbildern ermöglicht. Experimente auf Realwelt-Bilddatenbanken zeigen die Konkurrenzfähigkeit dieses Verfahrens auf

Understanding and advancing PDE-based image compression

This thesis is dedicated to image compression with partial differential equations (PDEs). PDE-based codecs store only a small amount of image points and propagate their information into the unknown image areas during the decompression step. For certain classes of images, PDE-based compression can already outperform the current quasi-standard, JPEG2000. However, the reasons for this success are not yet fully understood, and PDE-based compression is still in a proof-of-concept stage. With a probabilistic justification for anisotropic diffusion, we contribute to a deeper insight into design principles for PDE-based codecs. Moreover, by analysing the interaction between efficient storage methods and image reconstruction with diffusion, we can rank PDEs according to their practical value in compression. Based on these observations, we advance PDE-based compression towards practical viability: First, we present a new hybrid codec that combines PDE- and patch-based interpolation to deal with highly textured images. Furthermore, a new video player demonstrates the real-time capacities of PDE-based image interpolation and a new region of interest coding algorithm represents important image areas with high accuracy. Finally, we propose a new framework for diffusion-based image colourisation that we use to build an efficient codec for colour images. Experiments on real world image databases show that our new method is qualitatively competitive to current state-of-the-art codecs.Diese Dissertation ist der Bildkompression mit partiellen Differentialgleichungen (PDEs, partial differential equations) gewidmet. PDE-Codecs speichern nur einen geringen Anteil aller Bildpunkte und transportieren deren Information in fehlende Bildregionen. In einigen Fällen kann PDE-basierte Kompression den aktuellen Quasi-Standard, JPEG2000, bereits schlagen. Allerdings sind die Gründe für diesen Erfolg noch nicht vollständig erforscht, und PDE-basierte Kompression befindet sich derzeit noch im Anfangsstadium. Wir tragen durch eine probabilistische Rechtfertigung anisotroper Diffusion zu einem tieferen Verständnis PDE-basierten Codec-Designs bei. Eine Analyse der Interaktion zwischen effizienten Speicherverfahren und Bildrekonstruktion erlaubt es uns, PDEs nach ihrem Nutzen für die Kompression zu beurteilen. Anhand dieser Einsichten entwickeln wir PDE-basierte Kompression hinsichtlich ihrer praktischen Nutzbarkeit weiter: Wir stellen einen Hybrid-Codec für hochtexturierte Bilder vor, der umgebungsbasierte Interpolation mit PDEs kombiniert. Ein neuer Video-Dekodierer demonstriert die Echtzeitfähigkeit PDE-basierter Interpolation und eine Region-of-Interest-Methode erlaubt es, wichtige Bildbereiche mit hoher Genauigkeit zu speichern. Schlussendlich stellen wir ein neues diffusionsbasiertes Kolorierungsverfahren vor, welches uns effiziente Kompression von Farbbildern ermöglicht. Experimente auf Realwelt-Bilddatenbanken zeigen die Konkurrenzfähigkeit dieses Verfahrens auf