Video denoising using fuzzy-connectedness principles

Fuzzy-connectedness principles are effective for image segmentation. In this paper, such a principle is applied to video denoising. Assume a video signal suffers from both additive white Gaussian noise and impulsive noise. The corrupted signal is filtered by a fuzzy system, which fuzzily connects a Wiener filter and a median filter together. The simulation results show that the fuzzy-connectedness approach produces desirable outputs

Multivalued Discrete Tomography Using Dynamical System That Describes Competition

Multivalued discrete tomography involves reconstructing images composed of three or more gray levels from projections. We propose a method based on the continuous-time optimization approach with a nonlinear dynamical system that effectively utilizes competition dynamics to solve the problem of multivalued discrete tomography. We perform theoretical analysis to understand how the system obtains the desired multivalued reconstructed image. Numerical experiments illustrate that the proposed method also works well when the number of pixels is comparatively high even if the exact labels are unknown

Regularizers for Vector-Valued Data and Labeling Problems in Image Processing

Дан обзор последних результатов в области регуляризаторов, основанных на полных вариациях, применительно к векторным данным. Результаты оказались полезными для хранения или улучшения мультимодальных данных и задач разметки на непрерывной области определения. Возможные регуляризаторы и их свойства рассматриваются в рамках единой модели.The review of recent developments on total variation-based regularizers is given with the emphasis on vector-valued data. These have been proven to be useful for restoring or enhancing data with multiple channels, and find particular use in relaxation techniques for labeling problems on continuous domains. The possible regularizers and their properties are considered in a unified framework.Наведено огляд останніх результатів у галузі регуляризаторів, що базуються на повних варіаціях, стосовно векторних даних. Результати виявилися корисними для зберігання та покращення мультимодальних даних і задач розмітки на неперервній області визначення. Можливі регуляризатори та їх властивості розглядаються в рамках єдиної моделі

A Second Order TV-type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data

In this paper we consider denoising and inpainting problems for higher dimensional combined cyclic and linear space valued data. These kind of data appear when dealing with nonlinear color spaces such as HSV, and they can be obtained by changing the space domain of, e.g., an optical flow field to polar coordinates. For such nonlinear data spaces, we develop algorithms for the solution of the corresponding second order total variation (TV) type problems for denoising, inpainting as well as the combination of both. We provide a convergence analysis and we apply the algorithms to concrete problems.Comment: revised submitted versio

A non-invasive technique for burn area measurement

The need for a reliable and accurate method for assessing the surface area of burn wounds currently exists in the branch of medicine involved with burn care and treatment. The percentage of the surface area is of critical importance in evaluating fluid replacement amounts and nutritional support during the 24 hours of postburn therapy. A noninvasive technique has been developed which facilitates the measurement of burn area. The method we shall describe is an inexpensive technique to measure the burn areas accurately. Our imaging system is based on a technique known as structured light. Most structured light computer imaging systems, including ours, use triangulation to determine the location of points in three dimensions as the intersection of two lines: a ray of light originating from the structured light projector and the line of sight determined by the location of the image point in the camera plane. The geometry used to determine 3D location by triangulation is identical to the geometry of other stereo-based vision system, including the human vision system. Our system projects a square grid pattern from 35mm slide onto the patient. The grid on the slide is composed of uniformly spaced orthogonal stripes which may be indexed by row and column. Each slide also has square markers placed in between time lines of the grid in both the horizontal and vertical directions in the center of the slide. Our system locates intersections of the projected grid stripes in the camera image and determines the 3D location of the corresponding points on the body by triangulation. Four steps are necessary in order to reconstruct 3D locations of points on the surface of the skin: camera and projector calibration; image processing to locate the grid intersections in the camera image; grid labeling to establish the correspondence between projected and imaged intersections; and triangulation to determine three-dimensional position. Three steps are required to segment burned portion in image: edge detection to get the strongest edges of the region; edge following to form a closed boundary; and region filling to identify the burn region. After combining the reconstructed 3D locations and segmented image, numerical analysis and geometric modeling techniques are used to calculate the burn area. We use cubic spline interpolation, bicubic surface patches and Gaussian quadrature double integration to calculate the burn wound area. The accuracy of this technique is demonstrated The benefits and advantages of this technique are, first, that we don’t have to make any assumptions about the shape of the human body and second, there is no need for either the Rule-of-Nines, or the weight and height of the patient. This technique can be used for human body shape, regardless of weight proportion, size, sex or skin pigmentation. The low cost, intuitive method, and demonstrated efficiency of this computer imaging technique makes it a desirable alternative to current methods and provides the burn care specialist with a sterile, safe, and effective diagnostic tool in assessing and investigating burn areas

Neutro-Connectedness Theory, Algorithms and Applications

Connectedness is an important topological property and has been widely studied in digital topology. However, three main challenges exist in applying connectedness to solve real world problems: (1) the definitions of connectedness based on the classic and fuzzy logic cannot model the “hidden factors” that could influence our decision-making; (2) these definitions are too general to be applied to solve complex problem; and (4) many measurements of connectedness are heavily dependent on the shape (spatial distribution of vertices) of the graph and violate the intuitive idea of connectedness. This research focused on solving these challenges by redesigning the connectedness theory, developing fast algorithms for connectedness computation, and applying the newly proposed theory and algorithms to solve challenges in real problems. The newly proposed Neutro-Connectedness (NC) generalizes the conventional definitions of connectedness and can model uncertainty and describe the part and the whole relationship. By applying the dynamic programming strategy, a fast algorithm was proposed to calculate NC for general dataset. It is not just calculating NC map, and the output NC forest can discover a dataset’s topological structure regarding connectedness. In the first application, interactive image segmentation, two approaches were proposed to solve the two most difficult challenges: user interaction-dependence and intense interaction. The first approach, named NC-Cut, models global topologic property among image regions and reduces the dependence of segmentation performance on the appearance models generated by user interactions. It is less sensitive to the initial region of interest (ROI) than four state-of-the-art ROI-based methods. The second approach, named EISeg, provides user with visual clues to guide the interacting process based on NC. It reduces user interaction greatly by guiding user to where interacting can produce the best segmentation results. In the second application, NC was utilized to solve the challenge of weak boundary problem in breast ultrasound image segmentation. The approach can model the indeterminacy resulted from weak boundaries better than fuzzy connectedness, and achieved more accurate and robust result on our dataset with 131 breast tumor cases

Contrastive Deep Encoding Enables Uncertainty-aware Machine-learning-assisted Histopathology

Deep neural network models can learn clinically relevant features from millions of histopathology images. However generating high-quality annotations to train such models for each hospital, each cancer type, and each diagnostic task is prohibitively laborious. On the other hand, terabytes of training data -- while lacking reliable annotations -- are readily available in the public domain in some cases. In this work, we explore how these large datasets can be consciously utilized to pre-train deep networks to encode informative representations. We then fine-tune our pre-trained models on a fraction of annotated training data to perform specific downstream tasks. We show that our approach can reach the state-of-the-art (SOTA) for patch-level classification with only 1-10% randomly selected annotations compared to other SOTA approaches. Moreover, we propose an uncertainty-aware loss function, to quantify the model confidence during inference. Quantified uncertainty helps experts select the best instances to label for further training. Our uncertainty-aware labeling reaches the SOTA with significantly fewer annotations compared to random labeling. Last, we demonstrate how our pre-trained encoders can surpass current SOTA for whole-slide image classification with weak supervision. Our work lays the foundation for data and task-agnostic pre-trained deep networks with quantified uncertainty.Comment: 18 pages, 8 figure

A Second Order Non-Smooth Variational Model for Restoring Manifold-Valued Images

We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce the second order difference and the corresponding variational models for manifold data, which up to now only existed for cyclic data. The approach requires a combination of techniques from numerical analysis, convex optimization and differential geometry. First, we establish a suitable definition of absolute second order differences for signals and images with values in a manifold. Employing this definition, we introduce a variational denoising model based on first and second order differences in the manifold setup. In order to minimize the corresponding functional, we develop an algorithm using an inexact cyclic proximal point algorithm. We propose an efficient strategy for the computation of the corresponding proximal mappings in symmetric spaces utilizing the machinery of Jacobi fields. For the n-sphere and the manifold of symmetric positive definite matrices, we demonstrate the performance of our algorithm in practice. We prove the convergence of the proposed exact and inexact variant of the cyclic proximal point algorithm in Hadamard spaces. These results which are of interest on its own include, e.g., the manifold of symmetric positive definite matrices