On Invariance, Equivariance, Correlation and Convolution of Spherical Harmonic Representations for Scalar and Vectorial Data

The mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation and practical implementation of SH representations, summarizing works on rotation invariant and equivariant features, as well as convolutions and exact correlations of signals on spheres. In extension, these methods are then generalized from scalar SH representations to Vectorial Harmonics (VH), providing the same capabilities for 3d vector fields on spheresComment: 106 pages, tech repor

Novel Approaches to the Representation and Analysis of 3D Segmented Anatomical Districts

Nowadays, image processing and 3D shape analysis are an integral part of clinical practice and have the potentiality to support clinicians with advanced analysis and visualization techniques. Both approaches provide visual and quantitative information to medical practitioners, even if from different points of view. Indeed, shape analysis is aimed at studying the morphology of anatomical structures, while image processing is focused more on the tissue or functional information provided by the pixels/voxels intensities levels. Despite the progress obtained by research in both fields, a junction between these two complementary worlds is missing. When working with 3D models analyzing shape features, the information of the volume surrounding the structure is lost, since a segmentation process is needed to obtain the 3D shape model; however, the 3D nature of the anatomical structure is represented explicitly. With volume images, instead, the tissue information related to the imaged volume is the core of the analysis, while the shape and morphology of the structure are just implicitly represented, thus not clear enough. The aim of this Thesis work is the integration of these two approaches in order to increase the amount of information available for physicians, allowing a more accurate analysis of each patient. An augmented visualization tool able to provide information on both the anatomical structure shape and the surrounding volume through a hybrid representation, could reduce the gap between the two approaches and provide a more complete anatomical rendering of the subject. To this end, given a segmented anatomical district, we propose a novel mapping of volumetric data onto the segmented surface. The grey-levels of the image voxels are mapped through a volume-surface correspondence map, which defines a grey-level texture on the segmented surface. The resulting texture mapping is coherent to the local morphology of the segmented anatomical structure and provides an enhanced visual representation of the anatomical district. The integration of volume-based and surface-based information in a unique 3D representation also supports the identification and characterization of morphological landmarks and pathology evaluations. The main research contributions of the Ph.D. activities and Thesis are: \u2022 the development of a novel integration algorithm that combines surface-based (segmented 3D anatomical structure meshes) and volume-based (MRI volumes) information. The integration supports different criteria for the grey-levels mapping onto the segmented surface; \u2022 the development of methodological approaches for using the grey-levels mapping together with morphological analysis. The final goal is to solve problems in real clinical tasks, such as the identification of (patient-specific) ligament insertion sites on bones from segmented MR images, the characterization of the local morphology of bones/tissues, the early diagnosis, classification, and monitoring of muscle-skeletal pathologies; \u2022 the analysis of segmentation procedures, with a focus on the tissue classification process, in order to reduce operator dependency and to overcome the absence of a real gold standard for the evaluation of automatic segmentations; \u2022 the evaluation and comparison of (unsupervised) segmentation methods, finalized to define a novel segmentation method for low-field MR images, and for the local correction/improvement of a given segmentation. The proposed method is simple but effectively integrates information derived from medical image analysis and 3D shape analysis. Moreover, the algorithm is general enough to be applied to different anatomical districts independently of the segmentation method, imaging techniques (such as CT), or image resolution. The volume information can be integrated easily in different shape analysis applications, taking into consideration not only the morphology of the input shape but also the real context in which it is inserted, to solve clinical tasks. The results obtained by this combined analysis have been evaluated through statistical analysis

Variable illumination and invariant features for detecting and classifying varnish defects

This work presents a method to detect and classify varnish defects on wood surfaces. Since these defects are only partially visible under certain illumination directions, one image doesn\u27t provide enough information for a recognition task. A classification requires inspecting the surface under different illumination directions, which results in image series. The information is distributed along this series and can be extracted by merging the knowledge about the defect shape and light direction

The Role of Transient Vibration of the Skull on Concussion

Concussion is a traumatic brain injury usually caused by a direct or indirect blow to the head that affects brain function. The maximum mechanical impedance of the brain tissue occurs at 450±50 Hz and may be affected by the skull resonant frequencies. After an impact to the head, vibration resonance of the skull damages the underlying cortex. The skull deforms and vibrates, like a bell for 3 to 5 milliseconds, bruising the cortex. Furthermore, the deceleration forces the frontal and temporal cortex against the skull, eliminating a layer of cerebrospinal fluid. When the skull vibrates, the force spreads directly to the cortex, with no layer of cerebrospinal fluid to reflect the wave or cushion its force. To date, there is few researches investigating the effect of transient vibration of the skull. Therefore, the overall goal of the proposed research is to gain better understanding of the role of transient vibration of the skull on concussion. This goal will be achieved by addressing three research objectives. First, a MRI skull and brain segmentation automatic technique is developed. Due to bones’ weak magnetic resonance signal, MRI scans struggle with differentiating bone tissue from other structures. One of the most important components for a successful segmentation is high-quality ground truth labels. Therefore, we introduce a deep learning framework for skull segmentation purpose where the ground truth labels are created from CT imaging using the standard tessellation language (STL). Furthermore, the brain region will be important for a future work, thus, we explore a new initialization concept of the convolutional neural network (CNN) by orthogonal moments to improve brain segmentation in MRI. Second, the creation of a novel 2D and 3D Automatic Method to Align the Facial Skeleton is introduced. An important aspect for further impact analysis is the ability to precisely simulate the same point of impact on multiple bone models. To perform this task, the skull must be precisely aligned in all anatomical planes. Therefore, we introduce a 2D/3D technique to align the facial skeleton that was initially developed for automatically calculating the craniofacial symmetry midline. In the 2D version, the entire concept of using cephalometric landmarks and manual image grid alignment to construct the training dataset was introduced. Then, this concept was extended to a 3D version where coronal and transverse planes are aligned using CNN approach. As the alignment in the sagittal plane is still undefined, a new alignment based on these techniques will be created to align the sagittal plane using Frankfort plane as a framework. Finally, the resonant frequencies of multiple skulls are assessed to determine how the skull resonant frequency vibrations propagate into the brain tissue. After applying material properties and mesh to the skull, modal analysis is performed to assess the skull natural frequencies. Finally, theories will be raised regarding the relation between the skull geometry, such as shape and thickness, and vibration with brain tissue injury, which may result in concussive injury

Optical flow estimation via steered-L1 norm

Global variational methods for estimating optical flow are among the best performing methods due to the subpixel accuracy and the ‘fill-in’ effect they provide. The fill-in effect allows optical flow displacements to be estimated even in low and untextured areas of the image. The estimation of such displacements are induced by the smoothness term. The L1 norm provides a robust regularisation term for the optical flow energy function with a very good performance for edge-preserving. However this norm suffers from several issues, among these is the isotropic nature of this norm which reduces the fill-in effect and eventually the accuracy of estimation in areas near motion boundaries. In this paper we propose an enhancement to the L1 norm that improves the fill-in effect for this smoothness term. In order to do this we analyse the structure tensor matrix and use its eigenvectors to steer the smoothness term into components that are ‘orthogonal to’ and ‘aligned with’ image structures. This is done in primal-dual formulation. Results show a reduced end-point error and improved accuracy compared to the conventional L1 norm

Optical flow estimation via steered-L1 norm

Global variational methods for estimating optical flow are among the best performing methods due to the subpixel accuracy and the ‘fill-in’ effect they provide. The fill-in effect allows optical flow displacements to be estimated even in low and untextured areas of the image. The estimation of such displacements are induced by the smoothness term. The L1 norm provides a robust regularisation term for the optical flow energy function with a very good performance for edge-preserving. However this norm suffers from several issues, among these is the isotropic nature of this norm which reduces the fill-in effect and eventually the accuracy of estimation in areas near motion boundaries. In this paper we propose an enhancement to the L1 norm that improves the fill-in effect for this smoothness term. In order to do this we analyse the structure tensor matrix and use its eigenvectors to steer the smoothness term into components that are ‘orthogonal to’ and ‘aligned with’ image structures. This is done in primal-dual formulation. Results show a reduced end-point error and improved accuracy compared to the conventional L1 norm

Variable illumination and invariant features for detecting and classifying varnish defects

This work presents a method to detect and classify varnish defects on wood surfaces. Since these defects are only partially visible under certain illumination directions, one image doesn't provide enough information for a recognition task. A classification requires inspecting the surface under different illumination directions, which results in image series. The information is distributed along this series and can be extracted by merging the knowledge about the defect shape and light direction

Segmentation of whole cells and cell nuclei from 3-D optical microscope images using dynamic programming

金沢大学医薬保健研究域医学系Communications between cells in large part drive tissue development and function, as well as disease-related processes such as tumorigenesis. Understanding the mechanistic bases of these processes necessitates quantifying specific molecules in adjacent cells or cell nuclei of intact tissue. However, a major restriction on such analyses is the lack of an efficient method that correctly segments each object (cell or nucleus) from 3-D images of an intact tissue specimen. We report a highly reliable and accurate semi-automatic algorithmic method for segmenting fluorescence-labeled cells or nuclei from 3-D tissue images. Segmentation begins with semi-automatic, 2-D object delineation in a user-selected plane, using dynamic programming (DP) to locate the border with an accumulated intensity per unit length greater that any other possible border around the same object. Then the two surfaces of the object in planes above and below the selected plane are found using an algorithm that combines DP and combinatorial searching. Following segmentation, any perceived errors can be interactively corrected. Segmentation accuracy is not significantly affected by intermittent labeling of object surfaces, diffuse surfaces, or spurious signals away from surfaces. The unique strength of the segmentation method was demonstrated on a variety of biological tissue samples where all cells, including irregularly shaped cells, were accurately segmented based on visual inspection. © 2006 IEEE