Fiji is a distribution of the popular open-source software ImageJ focused on biological-image analysis. Fiji uses modern software engineering practices to combine powerful software libraries with a broad range of scripting languages to enable rapid prototyping of image-processing algorithms. Fiji facilitates the transformation of new algorithms into ImageJ plugins that can be shared with end users through an integrated update system. We propose Fiji as a platform for productive collaboration between computer science and biology research communities.

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Fiji: an open-source platform for biological-image analysis

There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A snake is an energy-minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges. Snakes are active contour models: they lock onto nearby edges, localizing them accurately. Scale-space continuation can be used to enlarge the capture region surrounding a feature. Snakes provide a unified account of a number of visual problems, including detection of edges, lines, and subjective contours; motion tracking; and stereo matching. We have used snakes successfully for interactive interpretation, in which user-imposed constraint forces guide the snake near features of interest.

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Snakes : Active Contour Models

The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of 'shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces. >

A method for registration of 3-D shapes

We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by the gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We give a numerical algorithm using finite differences. Finally, we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.

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Active contours without edges

https://www.cs.ucla.edu/~dt/papers/mia96/mia96.pdf

Deformable models in medical image analysis: a survey

The theory of elasticity describes deformable materials such as rubber, cloth, paper, and flexible metals. We employ elasticity theory to construct differential equations that model the behavior of non-rigid curves, surfaces, and solids as a function of time. Elastically deformable models are active: they respond in a natural way to applied forces, constraints, ambient media, and impenetrable obstacles. The models are fundamentally dynamic and realistic animation is created by numerically solving their underlying differential equations. Thus, the description of shape and the description of motion are unified.

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Elastically deformable models

Natural images are the composite consequence of multiple factors related to scene structure, illumination, and imaging. Multilinear algebra, the algebra of higher-order tensors, offers a potent mathematical framework for analyzing the multifactor structure of image ensembles and for addressing the difficult problem of disentangling the constituent factors or modes. Our multilinear modeling technique employs a tensor extension of the conventional matrix singular value decomposition (SVD), known as the N-mode SVD. As a concrete example, we consider the multilinear analysis of ensembles of facial images that combine several modes, including different facial geometries (people), expressions, head poses, and lighting conditions. Our resulting "TensorFaces" representation has several advantages over conventional eigenfaces. More generally, multilinear analysis shows promise as a unifying framework for a variety of computer vision problems.

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Multilinear Analysis of Image Ensembles: TensorFaces

Image segmentation is a key topic in image processing and computer vision with applications such as scene understanding, medical image analysis, robotic perception, video surveillance, augmented reality, and image compression, among many others. Various algorithms for image segmentation have been developed in the literature. Recently, due to the success of deep learning models in a wide range of vision applications, there has been a substantial amount of works aimed at developing image segmentation approaches using deep learning models. In this survey, we provide a comprehensive review of the literature at the time of this writing, covering a broad spectrum of pioneering works for semantic and instance-level segmentation, including fully convolutional pixel-labeling networks, encoder-decoder architectures, multi-scale and pyramid based approaches, recurrent networks, visual attention models, and generative models in adversarial settings. We investigate the similarity, strengths and challenges of these deep learning models, examine the most widely used datasets, report performances, and discuss promising future research directions in this area.

Demetri Terzopoulos

Papers

Snakes : Active Contour Models

Deformable models in medical image analysis: a survey

Elastically deformable models

Multilinear Analysis of Image Ensembles: TensorFaces

Image Segmentation Using Deep Learning: A Survey