Schneider, M. Fieguth , W. Karl, and A. Wang, L. Clausi , A. Carrington, A. Fieguth , and H. Shafiee, M. Karimi, A-H. Shafiee, C. Scharfenberger, I. Haider , N. Scharfenberger , I B. Kasiri, K. Siva, P. Scharfenberger , I. Lui , F. Wong , and M. Kumar, D. Gawish, A. Marschall, and K. Khalvati, F. Wong , G. Bjarnason, and M. Cameron, A. Modhafar, F. Barshan, E. Leigh, S. Scharfenberger , D D. Carvalho, J. Fieguth , G. Zhao, and M.

Carter, K. Sorbara, and K. Fieguth , Z. Yang, and Y. Amelard, R.

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Kumar, A. Mishra, D. Clausi, and P. Fieguth , and G. Kuang, and H. Hariri, A. Moayed, K. Gangeh, M. Shabani , and M. Kamel, " Nonlinear scale-space theory in texture classification using multiple classifier systems ", International Conference on Image Analysis and Recognition, June, Zaboli, S. Yang, X. Fieguth , and K. Babadi, M. Clausi , N. Dunk, and J. Fieguth , and E. Maillard, P. Wesolkowski, S. Ramunas, J. Clausi, D. Sabri, M. The same approach that is taken with one frame can be applied to multiple, and after the results are merged, peaks and valleys that were previously difficult to identify are more likely to be distinguishable.

The histogram can also be applied on a per-pixel basis where the resulting information is used to determine the most frequent color for the pixel location. This approach segments based on active objects and a static environment, resulting in a different type of segmentation useful in video tracking. Edge detection is a well-developed field on its own within image processing. Region boundaries and edges are closely related, since there is often a sharp adjustment in intensity at the region boundaries.

Edge detection techniques have therefore been used as the base of another segmentation technique. The edges identified by edge detection are often disconnected. To segment an object from an image however, one needs closed region boundaries. The desired edges are the boundaries between such objects or spatial-taxons.

Spatial-taxons [20] are information granules, [21] consisting of a crisp pixel region, stationed at abstraction levels within a hierarchical nested scene architecture. They are similar to the Gestalt psychological designation of figure-ground, but are extended to include foreground, object groups, objects and salient object parts. Edge detection methods can be applied to the spatial-taxon region, in the same manner they would be applied to a silhouette.

This method is particularly useful when the disconnected edge is part of an illusory contour [22] [23]. Segmentation methods can also be applied to edges obtained from edge detectors. Lindeberg and Li [24] developed an integrated method that segments edges into straight and curved edge segments for parts-based object recognition, based on a minimum description length M DL criterion that was optimized by a split-and-merge-like method with candidate breakpoints obtained from complementary junction cues to obtain more likely points at which to consider partitions into different segments.

This method is a combination of three characteristics of the image: partition of the image based on histogram analysis is checked by high compactness of the clusters objects , and high gradients of their borders. The first space allows to measure how compactly the brightness of the image is distributed by calculating a minimal clustering kmin. The bitmap b is an object in dual space.

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On that bitmap a measure has to be defined reflecting how compact distributed black or white pixels are. So, the goal is to find objects with good borders. Maximum of MDC defines the segmentation. Region-growing methods rely mainly on the assumption that the neighboring pixels within one region have similar values.

The common procedure is to compare one pixel with its neighbors. If a similarity criterion is satisfied, the pixel can be set to belong to the same cluster as one or more of its neighbors. The selection of the similarity criterion is significant and the results are influenced by noise in all instances. The method of Statistical Region Merging [26] SRM starts by building the graph of pixels using 4-connectedness with edges weighted by the absolute value of the intensity difference.

Initially each pixel forms a single pixel region. SRM then sorts those edges in a priority queue and decides whether or not to merge the current regions belonging to the edge pixels using a statistical predicate.

## Handbook Of Biomedical Image Analysis Vol2 Segmentation Models Part B

One region-growing method is the seeded region growing method. This method takes a set of seeds as input along with the image. The seeds mark each of the objects to be segmented. The regions are iteratively grown by comparison of all unallocated neighboring pixels to the regions. The pixel with the smallest difference measured in this way is assigned to the respective region. This process continues until all pixels are assigned to a region.

Because seeded region growing requires seeds as additional input, the segmentation results are dependent on the choice of seeds, and noise in the image can cause the seeds to be poorly placed. Another region-growing method is the unseeded region growing method. It is a modified algorithm that does not require explicit seeds. At each iteration it considers the neighboring pixels in the same way as seeded region growing. One variant of this technique, proposed by Haralick and Shapiro , [1] is based on pixel intensities.

The mean and scatter of the region and the intensity of the candidate pixel are used to compute a test statistic. Otherwise, the pixel is rejected, and is used to form a new region. It is based on pixel intensities and neighborhood-linking paths. A degree of connectivity connectedness is calculated based on a path that is formed by pixels. Split-and-merge segmentation is based on a quadtree partition of an image. It is sometimes called quadtree segmentation. This method starts at the root of the tree that represents the whole image.

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If it is found non-uniform not homogeneous , then it is split into four child squares the splitting process , and so on. If, in contrast, four child squares are homogeneous, they are merged as several connected components the merging process. The node in the tree is a segmented node. This process continues recursively until no further splits or merges are possible.

Using a partial differential equation PDE -based method and solving the PDE equation by a numerical scheme, one can segment the image. The central idea is to evolve an initial curve towards the lowest potential of a cost function, where its definition reflects the task to be addressed. As for most inverse problems , the minimization of the cost functional is non-trivial and imposes certain smoothness constraints on the solution, which in the present case can be expressed as geometrical constraints on the evolving curve.

Lagrangian techniques are based on parameterizing the contour according to some sampling strategy and then evolving each element according to image and internal terms. Such techniques are fast and efficient, however the original "purely parametric" formulation due to Kass, Witkin and Terzopoulos in and known as " snakes " , is generally criticized for its limitations regarding the choice of sampling strategy, the internal geometric properties of the curve, topology changes curve splitting and merging , addressing problems in higher dimensions, etc..

Nowadays, efficient "discretized" formulations have been developed to address these limitations while maintaining high efficiency. In both cases, energy minimization is generally conducted using a steepest-gradient descent, whereby derivatives are computed using, e. The level-set method was initially proposed to track moving interfaces by Dervieux and Thomasset [32] [33] in and and was later reinvented by Osher and Sethian in The central idea is to represent the evolving contour using a signed function whose zero corresponds to the actual contour.

Then, according to the motion equation of the contour, one can easily derive a similar flow for the implicit surface that when applied to the zero level will reflect the propagation of the contour. The level-set method affords numerous advantages: it is implicit, is parameter-free, provides a direct way to estimate the geometric properties of the evolving structure, allows for change of topology, and is intrinsic.

It can be used to define an optimization framework, as proposed by Zhao, Merriman and Osher in One can conclude that it is a very convenient framework for addressing numerous applications of computer vision and medical image analysis. The fast marching method has been used in image segmentation, [36] and this model has been improved permitting a both positive and negative speed propagation speed in an approach called the generalized fast marching method.

The goal of variational methods is to find a segmentation which is optimal with respect to a specific energy functional. The functionals consist of a data fitting term and a regularizing terms.

## Handbook Of Biomedical Image Analysis Vol2 Segmentation Models Part B

The binary variant of the Potts model, i. The optimization problems are known to be NP-hard in general but near-minimizing strategies work well in practice. Classical algorithms are graduated non-convexity and Ambrosio-Tortorelli approximation. Graph partitioning methods are an effective tools for image segmentation since they model the impact of pixel neighborhoods on a given cluster of pixels or pixel, under the assumption of homogeneity in images. In these methods, the image is modeled as a weighted, undirected graph. Usually a pixel or a group of pixels are associated with nodes and edge weights define the dis similarity between the neighborhood pixels.

The graph image is then partitioned according to a criterion designed to model "good" clusters. Each partition of the nodes pixels output from these algorithms are considered an object segment in the image. Some popular algorithms of this category are normalized cuts, [40] random walker , [41] minimum cut, [42] isoperimetric partitioning, [43] minimum spanning tree-based segmentation , [44] and segmentation-based object categorization.

MRFs are completely characterized by their prior probability distributions, marginal probability distributions, cliques , smoothing constraint as well as criterion for updating values. The criterion for image segmentation using MRFs is restated as finding the labelling scheme which has maximum probability for a given set of features. The broad categories of image segmentation using MRFs are supervised and unsupervised segmentation.

In terms of image segmentation, the function that MRFs seek to maximize is the probability of identifying a labelling scheme given a particular set of features are detected in the image. This is a restatement of the Maximum a posteriori estimation method. Each optimization algorithm is an adaptation of models from a variety of fields and they are set apart by their unique cost functions. The common trait of cost functions is to penalize change in pixel value as well as difference in pixel label when compared to labels of neighboring pixels.

The ICM algorithm tries to reconstruct the ideal labeling scheme by changing the values of each pixel over each iteration and evaluating the energy of the new labeling scheme using the cost function given below,. A major issue with ICM is that, similar to gradient descent, it has a tendency to rest over local maxima and thus not obtain a globally optimal labeling scheme. Derived as an analogue of annealing in metallurgy, SA uses change in pixel label over iterations and estimates the difference in energy of each newly formed graph to the initial data.

If the newly formed graph is more profitable, in terms of low energy cost, given by:. Simulated annealing requires the input of temperature schedules which directly affects the speed of convergence of the system, as well as energy threshold for minimization to occur.

A range of other methods exist for solving simple as well as higher order MRFs. Apart from likelihood estimates, graph-cut using maximum flow [48] and other highly constrained graph based methods [49] [50] exist for solving MRFs. A subset of unsupervised machine learning, the Expectation—maximization algorithm is utilized to iteratively estimate the a posterior probabilities and distributions of labeling when no training data is available and no estimate of segmentation model can be formed.

A general approach is to use histograms to represent the features of an image and proceed as outlined briefly in the 3-step algorithm mentioned below,.

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E-Step: Estimate class statistics based on the random segmentation model defined. Using these, compute the conditional probability of belonging to a label given the feature set is calculated using naive Bayes' theorem. M-Step: The established relevance of a given feature set to a labeling scheme is now used to compute the a priori estimate of a given label in the second part of the algorithm.

Since the actual number of total labels is unknown from a training data set , a hidden estimate of the number of labels given by the user is utilized in computations. Segmentation of optic nerve head for glaucoma detection using fundus images. Biomedical and Pharmacology Journal ;7 2 Research in Ophthalmology ;2 1 Chanwimaluang T, Fan G.

An efficient blood vessel detection algorithm for retinal images using local entropy thresholding. Hecth-Nelsen R. Forecasting with artificial neural networks: The state of the art. International Journal of Forecasting ; The connection between regularization operators and support vector kernels. Neural Networks ;11 4 Glaucoma diagnosis of morphological processing in optical coherence tomography.

In: Proceedings of international conference Computer Engineering and Applications. A new wavelet based edge detection technique for Iris imagery. Papamarkos N, Gatos B.

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## Handbook Of Biomedical Image Analysis Vol2 Segmentation Models Part B

Graphical Models and Image Processing ;56 5 Kuragano T, Yamaguchi A. A Method to generate freeform curves from a hand drawn sketch. JSCI ;5 2 Automatic detection of Glaucoma in OCT image.