Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version

High-performance compression of visual information - A tutorial review - Part I : Still Pictures

Digital images have become an important source of information in the modern world of communication systems. In their raw form, digital images require a tremendous amount of memory. Many research efforts have been devoted to the problem of image compression in the last two decades. Two different compression categories must be distinguished: lossless and lossy. Lossless compression is achieved if no distortion is introduced in the coded image. Applications requiring this type of compression include medical imaging and satellite photography. For applications such as video telephony or multimedia applications, some loss of information is usually tolerated in exchange for a high compression ratio. In this two-part paper, the major building blocks of image coding schemes are overviewed. Part I covers still image coding, and Part II covers motion picture sequences. In this first part, still image coding schemes have been classified into predictive, block transform, and multiresolution approaches. Predictive methods are suited to lossless and low-compression applications. Transform-based coding schemes achieve higher compression ratios for lossy compression but suffer from blocking artifacts at high-compression ratios. Multiresolution approaches are suited for lossy as well for lossless compression. At lossy high-compression ratios, the typical artifact visible in the reconstructed images is the ringing effect. New applications in a multimedia environment drove the need for new functionalities of the image coding schemes. For that purpose, second-generation coding techniques segment the image into semantically meaningful parts. Therefore, parts of these methods have been adapted to work for arbitrarily shaped regions. In order to add another functionality, such as progressive transmission of the information, specific quantization algorithms must be defined. A final step in the compression scheme is achieved by the codeword assignment. Finally, coding results are presented which compare stateof- the-art techniques for lossy and lossless compression. The different artifacts of each technique are highlighted and discussed. Also, the possibility of progressive transmission is illustrated

Left-invariant Stochastic Evolution Equations on SE(2) and its Applications to Contour Enhancement and Contour Completion via Invertible Orientation Scores

We provide the explicit solutions of linear, left-invariant, (convection)-diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2). These diffusion equations are forward Kolmogorov equations for stochastic processes for contour enhancement and completion. The solutions are group-convolutions with the corresponding Green's function, which we derive in explicit form. We mainly focus on the Kolmogorov equations for contour enhancement processes which, in contrast to the Kolmogorov equations for contour completion, do not include convection. The Green's functions of these left-invariant partial differential equations coincide with the heat-kernels on SE(2), which we explicitly derive. Then we compute completion distributions on SE(2) which are the product of a forward and a backward resolvent evolved from resp. source and sink distribution on SE(2). On the one hand, the modes of Mumford's direction process for contour completion coincide with elastica curves minimizing $\int \kappa^{2} + \epsilon ds$, related to zero-crossings of 2 left-invariant derivatives of the completion distribution. On the other hand, the completion measure for the contour enhancement concentrates on geodesics minimizing $\int \sqrt{\kappa^{2} + \epsilon} ds$. This motivates a comparison between geodesics and elastica, which are quite similar. However, we derive more practical analytic solutions for the geodesics. The theory is motivated by medical image analysis applications where enhancement of elongated structures in noisy images is required. We use left-invariant (non)-linear evolution processes for automated contour enhancement on invertible orientation scores, obtained from an image by means of a special type of unitary wavelet transform

Deep learning-based improvement for the outcomes of glaucoma clinical trials

Glaucoma is the leading cause of irreversible blindness worldwide. It is a progressive optic neuropathy in which retinal ganglion cell (RGC) axon loss, probably as a consequence of damage at the optic disc, causes a loss of vision, predominantly affecting the mid-peripheral visual field (VF). Glaucoma results in a decrease in vision-related quality of life and, therefore, early detection and evaluation of disease progression rates is crucial in order to assess the risk of functional impairment and to establish sound treatment strategies. The aim of my research is to improve glaucoma diagnosis by enhancing state of the art analyses of glaucoma clinical trial outcomes using advanced analytical methods. This knowledge would also help better design and analyse clinical trials, providing evidence for re-evaluating existing medications, facilitating diagnosis and suggesting novel disease management. To facilitate my objective methodology, this thesis provides the following contributions: (i) I developed deep learning-based super-resolution (SR) techniques for optical coherence tomography (OCT) image enhancement and demonstrated that using super-resolved images improves the statistical power of clinical trials, (ii) I developed a deep learning algorithm for segmentation of retinal OCT images, showing that the methodology consistently produces more accurate segmentations than state-of-the-art networks, (iii) I developed a deep learning framework for refining the relationship between structural and functional measurements and demonstrated that the mapping is significantly improved over previous techniques, iv) I developed a probabilistic method and demonstrated that glaucomatous disc haemorrhages are influenced by a possible systemic factor that makes both eyes bleed simultaneously. v) I recalculated VF slopes, using the retinal never fiber layer thickness (RNFLT) from the super-resolved OCT as a Bayesian prior and demonstrated that use of VF rates with the Bayesian prior as the outcome measure leads to a reduction in the sample size required to distinguish treatment arms in a clinical trial

Error Resilient Video Coding Using Bitstream Syntax And Iterative Microscopy Image Segmentation

There has been a dramatic increase in the amount of video traffic over the Internet in past several years. For applications like real-time video streaming and video conferencing, retransmission of lost packets is often not permitted. Popular video coding standards such as H.26x and VPx make use of spatial-temporal correlations for compression, typically making compressed bitstreams vulnerable to errors. We propose several adaptive spatial-temporal error concealment approaches for subsampling-based multiple description video coding. These adaptive methods are based on motion and mode information extracted from the H.26x video bitstreams. We also present an error resilience method using data duplication in VPx video bitstreams. A recent challenge in image processing is the analysis of biomedical images acquired using optical microscopy. Due to the size and complexity of the images, automated segmentation methods are required to obtain quantitative, objective and reproducible measurements of biological entities. In this thesis, we present two techniques for microscopy image analysis. Our first method, “Jelly Filling” is intended to provide 3D segmentation of biological images that contain incompleteness in dye labeling. Intuitively, this method is based on filling disjoint regions of an image with jelly-like fluids to iteratively refine segments that represent separable biological entities. Our second method selectively uses a shape-based function optimization approach and a 2D marked point process simulation, to quantify nuclei by their locations and sizes. Experimental results exhibit that our proposed methods are effective in addressing the aforementioned challenges