Filtering is a fundamental operation in image science in general and in medical image science in particular. The most central applications are image enhancement, registration, segmentation and feature extraction. Even though these applications involve non-linear processing a majority of the methodologies available rely on initial estimates using linear filters. Linear filtering is a well established cornerstone of signal processing, which is reflected by the overwhelming amount of literature on finite impulse response filters and their design. Standard techniques for multidimensional filtering are computationally intense. This leads to either a long computation time or a performance loss caused by approximations made in order to increase the computational efficiency. This dissertation presents a framework for realization of efficient multidimensional filters. A weighted least squares design criterion ensures preservation of the performance and the two techniques called filter networks and sub-filter sequences significantly reduce the computational demand. A filter network is a realization of a set of filters, which are decomposed into a structure of sparse sub-filters each with a low number of coefficients. Sparsity is here a key property to reduce the number of floating point operations required for filtering. Also, the network structure is important for efficiency, since it determines how the sub-filters contribute to several output nodes, allowing reduction or elimination of redundant computations. Filter networks, which is the main contribution of this dissertation, has many potential applications. The primary target of the research presented here has been local structure analysis and image enhancement. A filter network realization for local structure analysis in 3D shows a computational gain, in terms of multiplications required, which can exceed a factor 70 compared to standard convolution. For comparison, this filter network requires approximately the same amount of multiplications per signal sample as a single 2D filter. These results are purely algorithmic and are not in conflict with the use of hardware acceleration techniques such as parallel processing or graphics processing units (GPU). To get a flavor of the computation time required, a prototype implementation which makes use of filter networks carries out image enhancement in 3D, involving the computation of 16 filter responses, at an approximate speed of 1MVoxel/s on a standard PC.

In this thesis we address the problem of digitizing the motion of three-dimensional shapes that move and deform in time. These shapes are observed from several points of view with cameras that record the scene's evolution as videos. Using available reconstruction methods, these videos can be converted into a sequence of three-dimensional snapshots that capture the appearance and shape of the objects in the scene. The focus of this thesis is to complement appearance and shape with information on the motion and deformation of objects. In other words, we want to measure the trajectory of every point on the observed surfaces. This is a challenging problem because the captured videos are only sequences of images, and the reconstructed shapes are built independently from each other. While the human brain excels at recreating the illusion of motion from these snapshots, using them to automatically measure motion is still largely an open problem. The majority of prior works on the subject has focused on tracking the performance of one human actor, and used the strong prior knowledge on the articulated nature of human motion to handle the ambiguity and noise inherent to visual data. In contrast, the presented developments consist of generic methods that allow to digitize scenes involving several humans and deformable objects of arbitrary nature. To perform surface tracking as generically as possible, we formulate the problem as the geometric registration of surfaces and deform a reference mesh to fit a sequence of independently reconstructed meshes. We introduce a set of algorithms and numerical tools that integrate into a pipeline whose output is an animated mesh. Our first contribution consists of a generic mesh deformation model and numerical optimization framework that divides the tracked surface into a collection of patches, organizes these patches in a deformation graph and emulates elastic behavior with respect to the reference pose. As a second contribution, we present a probabilistic formulation of deformable surface registration that embeds the inference in an Expectation-Maximization framework that explicitly accounts for the noise and in the acquisition. As a third contribution, we look at how prior knowledge can be used when tracking articulated objects, and compare different deformation model with skeletal-based tracking. The studies reported by this thesis are supported by extensive experiments on various 4D datasets. They show that in spite of weaker assumption on the nature of the tracked objects, the presented ideas allow to process complex scenes involving several arbitrary objects, while robustly handling missing data and relatively large reconstruction artifacts.

The main objective with this study was to investigate so called odd purposes acceptable when registrating property along with how social development affects these purposes, furthermore to investigate how the cadastral surveyors estimates a foreseeable time. Tradition and praxis is used for several obvious purposes such as housing, farming, forests, offices and industry. Praxis is yet to be defined regarding more unique purposes. There is no mention in the law about which purposes are found acceptable to assure the demands on suitability are met. Cadastral authorities are responsible for making sure the division into property units is uniform and rule of law-accordingly. This study illustrates the issue of how the cadastral operation applies the rules to support a uniform application of the rule. A legal method, a survey analysis, an interview analysis and a case study were methods used in the study to answer the purpose and research questions. The legal method was used to learn more about the legal position. The survey was performed in order to gather data and information about which purposes previously have been regarded as odd by the cadastral surveyors. To obtain an understanding about and background to the selected odd purposes, an interview study was conducted with the cadastral surveyors. The intent of the case study was to form a base and insight in how the odd purposes are valued. The result of the legal method showed proof of how to interpret the prerequisite in the law. The survey provided information about which odd purposes are used in dividing of property. The interview study was based on the results from the survey and the information gathered from it. Answers regarding the background to the cadastral procedures were given, as well as the concept purpose, its origin and the evaluation of the time concept foreseeable time. The case study provided a background to the decision making and history about the debate as well as how purpose has been a question when making assessments. The most important conclusion made was that the prerequisite, intended function, current circumstances and requirements determine an acceptable purpose. The same factors determine the assessment of foreseeable time and as a result the concept varies from case to case. Social development causes the conditions for dividing into property units to be interchangeable, as a result the possible purposes changes with them. A more uniform application of the rule, considering the prerequisites, intended function, current circumstances and requirements should so be applied. / Huvudsyftet med studien var att undersöka vilka ”udda” ändamål som kan godtas vid fastighetsbildning med delsyften om hur samhällsutvecklingen påverkar ändamålen och att undersöka hur förrättningslantmätarna bedömer ”överskådlig tid”. Tradition och praxis finns för ett flertal ändamål som kan anses vara självklara, till exempel bostad, jordbruk, skog, kontor och industri. För mer udda ändamål är praxis oklar. Lagen talar inte om vilka ändamål som kan anses vara godtagbara för att kraven om lämplighet ska anses uppfyllda. Lantmäterimyndigheterna har till uppgift att ansvara för en enhetlig och rättssäker fastighetsindelning. Studien belyser frågan om hur lantmäteriverksamheten tillämpar reglerna idag för att ge stöd åt en enhetlig rättstillämpning. Metoder som använts i studien för att besvara syfte och forskningsfrågor var en juridisk metod, en enkätstudie, en intervjustudie och en rättsfallsstudie. Den juridiska metoden användes för att få kunskap om rättsläget. Enkätstudien genomfördes för att samla data och information om ändamål som förrättningslantmätarna ansett vara ”udda”. För att få förståelse och en bakgrund till förrättningarna av de utvalda ”udda” ändamålen genomfördes en intervjustudie med förrättningslantmätarna. Rättsfallsstudien syftade till att få en grund och inblick i hur ”udda” ändamål bedömts. Resultatet av den juridiska metoden visade på hur rekvisiten i lagen ska tolkas. Enkätstudien gav information för vilka ”udda” ändamål det fastighetsbildats. Intervjustudien grundade sig på enkätstudiens resultat och den information som lämnats. Den gav svar på förrättningarnas bakgrund, begreppet ändamålet och dess tillkomst och bedömningen av tidsbegreppet ”överskådlig tid”. Rättsfallsstudien gav en bakgrund till besluten och om hur diskussionerna förts samt huruvida ändamålet varit föremål för bedömning. Den viktigaste slutsatsen var att det är rekvisiten, den tilltänkta funktion, den rådande situation och behoven som avgör vilket ändamål som är godtagbart. Samma faktorer avgör bedömningen av överskådlig tid som i och med det varierar från fall till fall. Samhällsutvecklingen medför att förutsättningarna för fastighetsbildning är föränderliga och därmed förändras också möjliga ändamål. En enhetlig rättstillämpning bör därmed ske utifrån rekvisiten, den tilltänkta funktion, den rådande situation och behoven.

Image segmentation is important with applications to several problems in biology and medicine. While extensively researched, generally, current segmentation methods perform adequately in the applications for which they were designed, but often require extensive modifications or calibrations before used in a different application. We describe a system that, with few modifications, can be used in a variety of image segmentation problems. The system is based on a supervised learning strategy that utilizes intensity neighborhoods to assign each pixel in a test image its correct class based on training data. In summary, we have several innovations: (1) A general framework for such a system is proposed, where rotations and variations of intensity neighborhoods in scales are modeled, and a multi-scale classification framework is utilized to segment unknown images; (2) A fast algorithm for training data selection and pixel classification is presented, where a majority voting based criterion is proposed for selecting a small subset from raw training set. When combined with 1-nearest neighbor (1-NN) classifier, such an algorithm is able to provide descent classification accuracy within reasonable computational complexity. (3) A general deformable model for optimization of segmented regions is proposed, which takes the decision values from previous pixel classification process as input, and optimize the segmented regions in a partial differential equation (PDE) framework. We show that the performance of this system in several different biomedical applications, such as tissue segmentation tasks in magnetic resonance and histopathology microscopy images, as well as nuclei segmentation from fluorescence microscopy images, is similar or better than several algorithms specifically designed for each of these applications. In addition, we describe another general segmentation system for biomedical applications where a strong prior on shape is available (e.g. cells, nuclei). The idea is based on template matching and supervised learning, and we show the examples of segmenting cells and nuclei from microscopy images. The method uses examples selected by a user for building a statistical model which captures the texture and shape variations of the nuclear structures from a given data set to be segmented. Segmentation of subsequent, unlabeled, images is then performed by finding the model instance that best matches (in the normalized cross correlation sense) local neighborhood in the input image. We demonstrate the application of our method to segmenting cells and nuclei from a variety of imaging modalities, and quantitatively compare our results to several other methods. Quantitative results using both simulated and real image data show that, while certain methods may work well for certain imaging modalities, our software is able to obtain high accuracy across several imaging modalities studied. Results also demonstrate that, relative to several existing methods, the template based method we propose presents increased robustness in the sense of better handling variations in illumination, variations in texture from different imaging modalities, providing more smooth and accurate segmentation borders, as well as handling better cluttered cells and nuclei.

The objects of the South African Pharmacy Council in terms of the Pharmacy Act, 1974 (5311974) as amended are, inter alia, "to uphold and safeguard the rights of the general public to universally acceptable standards of pharmacy practice in both the private and the public sector" as well as "to establish, develop, maintain and control universally acceptable standards of practice of the various categories of persons required to be registered.. ." One of the major difficulties health care providers worldwide are faced with is how to maintain a proper balance between the trio goals of health care, namely adequate access, high quality and acceptable costs (Li, 2003:192-193). Relatively little is known about such problems as do exist for patients regarding access to pharmaceutical services (Doucette et al., 1999:1268). Two main objectives were identified for this study, namely to investigate the demographic profile of community and institutional pharmacies registered with the South African Pharmacy Council; and to determine the standard of pharmaceutical services provided by these pharmacies. Inspection results of community and institutional pharmacies were obtained from the South African Pharmacy Council and extracted for the time period 1 January 2004 to 31 May 2005. To determine the demographic and geographic profile of these pharmacies, data of the Register of Pharmacies of the South African Pharmacy Council for August 2003, 2004 and 2005 were merged with the Census data of South Africa of 2001. It was found that the total number of pharmacies in both the public and private sectors increased with 2.1% (n=68) from August 2003 to August 2005. Public and private pharmacies that provided services directly to patients increased with 6.3% (n=33) and 1.3% (n=35) from August 2003 to 2005. It was found that the Gauteng province was the best provided with registered pharmacies in South Africa, as only 0.06% (n=5 783) of the population did not have any registered pharmacy available on municipality level. It was also revealed that the majority of inspections were carried out in Gauteng, whilst this province accounts for only 19.7% of the total population of South Africa. During the study period a total of 1178 community pharmacy inspections were carried out in 1103 community pharmacies (one or more inspections per pharmacy) representing 43% (n=2 550) of the total number of community pharmacies registered with the South African Pharmacy Council during May 2005. Nationally community pharmacies achieved a score of 92.27 (+ 6.65 per cent) for compliance with Good Pharmacy Practice guidelines. The lowest compliance score (73.34 + 27.49 per cent) was obtained for the availability of written standard operating procedures and the highest was for the promotion of public health (99.02 + 6.30 per cent). No practical significant differences (dc0.8) were found between the overall compliance scores obtained by community pharmacies of the different provinces. The highest compliance score was obtained by community pharmacies in the Free State (93.09 + 4.90 per cent), followed by Western Cape, Eastern Cape, Kwazulu Natal, Limpopo, Northern Cape, Gauteng, Mpumalanga and the North West. A total of 343 institutional pharmacy inspections (one or more inspections per pharmacy) were carried out in public and state subsidised institutions (n=245), private institutions (n=90) and mine hospitals (n=5). These pharmacies represented 46% of the total number of institutional pharmacies registered with the South African Pharmacy Council during May 2005. Nationally all institutional pharmacies (both private and public) achieved a score of 92.49 + 8.33 per cent for compliance with Good Pharmacy Practice guidelines for all above-mentioned aspects. Nationally public and state subsidised institutional pharmacies obtained a lower compliance score (91.02 + 9.08 per cent) than private institutional pharmacies (96.39 + 3.91 per cent). Lastly, a grading system was developed that was based on the results obtained through this study, in order to quantify the standard of pharmaceutical services provided by pharmacies in South Africa. / Thesis (M.Pharm. (Pharmacy Practice))--North-West University, Potchefstroom Campus, 2007.

Even though the prospect of fusing images issued by different medical imagery systems is highly contemplated, the practical instantiation of it is subject to a theoretical hurdle: the definition of a similarity between images. Efforts in this field have proved successful for select pairs of images; however defining a suitable similarity between images regardless of their origin is one of the biggest challenges in deformable registration. In this thesis, we chose to develop generic approaches that allow the comparison of any two given modality. The recent advances in Machine Learning permitted us to provide innovative solutions to this very challenging problem. To tackle the problem of comparing incommensurable data we chose to view it as a data embedding problem where one embeds all the data in a common space in which comparison is possible. To this end, we explored the projection of one image space onto the image space of the other as well as the projection of both image spaces onto a common image space in which the comparison calculations are conducted. This was done by the study of the correspondences between image features in a pre-aligned dataset. In the pursuit of these goals, new methods for image regression as well as multi-modal metric learning methods were developed. The resulting learned similarities are then incorporated into a discrete optimization framework that mitigates the need for a differentiable criterion. Lastly we investigate on a new method that discards the constraint of a database of images that are pre-aligned, only requiring data annotated (segmented) by a physician. Experiments are conducted on two challenging medical images data-sets (Pre-Aligned MRI images and PET/CT images) to justify the benefits of our approach.

The ability of humans to perceive significant pattern and structure of an image is something which humans take for granted. We can recognize objects and patterns independent of changes in image contrast and illumination. In the past decades, it has been widely recognized in both biology and computer vision that phase contains critical information in characterizing the structures in images. Despite the importance of local phase information and its significant success in many computer vision and image processing applications, the coherence behavior of local phases at scale-space is not well understood. This thesis concentrates on developing an invariant image representation method based on local phase information. In particular, considerable effort is devoted to study the coherence relationship between local phases at different scales in the vicinity of image features and to develop robust methods to measure the strength of this relationship. A computational framework that computes local phase coherence (LPC) intensity with arbitrary selections in the number of coefficients, scales, as well as the scale ratios between them has been developed. Particularly, we formulate local phase prediction as an optimization problem, where the objective function computes the closeness between true local phase and the predicted phase by LPC. The proposed framework not only facilitates flexible and reliable computation of LPC, but also broadens the potentials of LPC in many applications. We demonstrate the potentials of LPC in a number of image processing applications. Firstly, we have developed a novel sharpness assessment algorithm, identified as LPC-Sharpness Index (LPC-SI), without referencing the original image. LPC-SI is tested using four subject-rated publicly-available image databases, which demonstrates competitive performance when compared with state-of-the-art algorithms. Secondly, a new fusion quality assessment algorithm has been developed to objectively assess the performance of existing fusion algorithms. Validations over our subject-rated multi-exposure multi-focus image database show good correlations between subjective ranking score and the proposed image fusion quality index. Thirdly, the invariant properties of LPC measure have been employed to solve image registration problem where inconsistency in intensity or contrast patterns are the major challenges. LPC map has been utilized to estimate image plane transformation by maximizing weighted mutual information objective function over a range of possible transformations. Finally, the disruption of phase coherence due to blurring process is employed in a multi-focus image fusion algorithm. The algorithm utilizes two activity measures, LPC as sharpness activity measure along with local energy as contrast activity measure. We show that combining these two activity measures result in notable performance improvement in achieving both maximal contrast and maximal sharpness simultaneously at each spatial location.

The ability of humans to perceive significant pattern and structure of an image is something which humans take for granted. We can recognize objects and patterns independent of changes in image contrast and illumination. In the past decades, it has been widely recognized in both biology and computer vision that phase contains critical information in characterizing the structures in images. Despite the importance of local phase information and its significant success in many computer vision and image processing applications, the coherence behavior of local phases at scale-space is not well understood. This thesis concentrates on developing an invariant image representation method based on local phase information. In particular, considerable effort is devoted to study the coherence relationship between local phases at different scales in the vicinity of image features and to develop robust methods to measure the strength of this relationship. A computational framework that computes local phase coherence (LPC) intensity with arbitrary selections in the number of coefficients, scales, as well as the scale ratios between them has been developed. Particularly, we formulate local phase prediction as an optimization problem, where the objective function computes the closeness between true local phase and the predicted phase by LPC. The proposed framework not only facilitates flexible and reliable computation of LPC, but also broadens the potentials of LPC in many applications. We demonstrate the potentials of LPC in a number of image processing applications. Firstly, we have developed a novel sharpness assessment algorithm, identified as LPC-Sharpness Index (LPC-SI), without referencing the original image. LPC-SI is tested using four subject-rated publicly-available image databases, which demonstrates competitive performance when compared with state-of-the-art algorithms. Secondly, a new fusion quality assessment algorithm has been developed to objectively assess the performance of existing fusion algorithms. Validations over our subject-rated multi-exposure multi-focus image database show good correlations between subjective ranking score and the proposed image fusion quality index. Thirdly, the invariant properties of LPC measure have been employed to solve image registration problem where inconsistency in intensity or contrast patterns are the major challenges. LPC map has been utilized to estimate image plane transformation by maximizing weighted mutual information objective function over a range of possible transformations. Finally, the disruption of phase coherence due to blurring process is employed in a multi-focus image fusion algorithm. The algorithm utilizes two activity measures, LPC as sharpness activity measure along with local energy as contrast activity measure. We show that combining these two activity measures result in notable performance improvement in achieving both maximal contrast and maximal sharpness simultaneously at each spatial location.

Nous proposons de construire un atlas numérique 3D contenant les caractéristiques moyennes et les variabilités de la morphologie d’un organe. Nos travaux seront appliqués particulièrement à la construction d'un atlas numérique 3D de la totalité de la cornée humaine incluant la surface antérieure et postérieure à partir des cartes topographiques fournies par le topographe Orbscan II. Nous procédons tout d'abord par normalisation de toute une population de cornées. Dans cette étape, nous nous sommes basés sur l'algorithme de recalage ICP (iterative closest point) pour aligner simultanément les surfaces antérieures et postérieures d'une population de cornée vers les surfaces antérieure et postérieure d'une cornée de référence. En effet, nous avons élaboré une variante de l'algorithme ICP adapté aux images (cartes) de cornées qui tient compte de changement d'échelle pendant le recalage et qui se base sur la recherche par voisinage via la distance euclidienne pour établir la correspondance entre les points. Après, nous avons procédé pour la construction de l'atlas cornéen par le calcul des moyennes des élévations de surfaces antérieures et postérieures recalées et leurs écarts-types associés. Une population de 100 cornées saines a été utilisée pour construire l'atlas cornéen normal. Pour visualiser l’atlas, on a eu recours à des cartes topographiques couleurs similairement à ce qu’offrent déjà les systèmes topographiques actuels. Enfin, des observations ont été réalisées sur l'atlas cornéen reflétant sa précision et permettant de développer une meilleure connaissance de l’anatomie cornéenne. / We propose to build a 3D digital atlas which contains the average characteristics and variability of the morphology of an organ. In particular our work consists in the construction of a 3D digital atlas of the entire human cornea including anterior and posterior surfaces. The atlas was built using topographies provided by the Orbscan II system. First, we normalized the given population of corneas using a variant of the ICP (iterative closest point) algorithm for shape registration to fit simultaneously the anterior and posterior surfaces with the anterior and posterior surfaces of a reference cornea. Indeed, we developed a specific algorithm for corneas topographies that considers scaling during registration and which is based on neighborhood search via the Euclidean distance to find the correspondence between points. After that, we built the corneal atlas by averaging elevations of anterior and posterior surfaces and by calculating their associated standard deviations. A population of 100 healthy corneas was used to construct the normal corneal atlas. To illustrate the atlas, we used topographic color maps like those already offered by existing topographic systems. Finally, observations were made on the corneal atlas that reflects its precision and allows to develop a better understanding of corneal anatomy.

函數型資料分析的是一組曲線資料，通常定義域為一段時間範圍。常見的如某一個地區人口在成長期的身高紀錄表或是氣候統計資料。函數型資料主要特色曲線間常有共同趨勢，而且個別曲線反應共同趨勢時也有時間和強度上的差異。本文研究主要是使用Kneip 和 Ramsay提出，結合對齊程序和主成分分析的想法作為模型架構，來分析函數型資料的特性。首先在對齊過程中，使用時間轉換函數(warping function)，解決觀測資料上時間的差異；並使用主成分分析方法，幫助研究者探討資料的主要特性。基於函數型資料被預期的共同趨勢性，我們可以利用此一特色作為各種類型資料分類上的依據。此外本研究會對幾種選取主成分個數的方法，進行綜合討論與比較。 / In this thesis, a procedure combining curve alignment and functional principal component analysis is studied. The procedure is proposed by Kneip and Ramsay .In functional principal component analysis, if the data curves are roughly linear combinations of k basis curves, then the data curves are expected to be explained well by principle component curves. The goal of this study is to examine whether this property still holds when curves need to be aligned. It is found that, if the aligned data curves can be approximated well by k basis curves, then applying Kneip and Ramsay's procedure to the unaligned curves gives k principal components that can explain the aligned curves well. Several approaches for selecting the number of principal components are proposed and compared.