Image segmentation - Knowledge (XXG)

4162:. In 1989, Reinhard Eckhorn introduced a neural model to emulate the mechanism of a cat's visual cortex. The Eckhorn model provided a simple and effective tool for studying the visual cortex of small mammals, and was soon recognized as having significant application potential in image processing. In 1994, the Eckhorn model was adapted to be an image processing algorithm by John L. Johnson, who termed this algorithm Pulse-Coupled Neural Network. Over the past decade, PCNNs have been utilized for a variety of image processing applications, including: image segmentation, feature generation, face extraction, motion detection, region growing, noise reduction, and so on. A PCNN is a two-dimensional neural network. Each neuron in the network corresponds to one pixel in an input image, receiving its corresponding pixel's color information (e.g. intensity) as an external stimulus. Each neuron also connects with its neighboring neurons, receiving local stimuli from them. The external and local stimuli are combined in an internal activation system, which accumulates the stimuli until it exceeds a dynamic threshold, resulting in a pulse output. Through iterative computation, PCNN neurons produce temporal series of pulse outputs. The temporal series of pulse outputs contain information of input images and can be utilized for various image processing applications, such as image segmentation and feature generation. Compared with conventional image processing means, PCNNs have several significant merits, including robustness against noise, independence of geometric variations in input patterns, capability of bridging minor intensity variations in input patterns, etc. 2259:

an implicit manner. 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 1996. One can conclude that it is a very convenient framework for addressing numerous applications of computer vision and medical image analysis. Research into various

411: 31: 2246:"), 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.g., finite differences. 4097:

been carried over to clinical use by Dam. Vincken et al. proposed a hyperstack for defining probabilistic relations between image structures at different scales. The use of stable image structures over scales has been furthered by Ahuja and his co-workers into a fully automated system. A fully automatic brain segmentation algorithm based on closely related ideas of multi-scale watersheds has been presented by Undeman and Lindeberg and been extensively tested in brain databases.

425: 3989: 2218:(PDE)-based method and solving the PDE equation by a numerical scheme, one can segment the image. Curve propagation is a popular technique in this category, with numerous applications to object extraction, object tracking, stereo reconstruction, etc. 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 627:

simple agglomerative clustering method. The distortion in the lossy compression determines the coarseness of the segmentation and its optimal value may differ for each image. This parameter can be estimated heuristically from the contrast of textures in an image. For example, when the textures in an image are similar, such as in camouflage images, stronger sensitivity and thus lower quantization is required.

669:

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

2854:(MRF) for images was suggested in early 1984 by Geman and Geman. Their strong mathematical foundation and ability to provide a global optimum even when defined on local features proved to be the foundation for novel research in the domain of image analysis, de-noising and segmentation. MRFs are completely characterized by their prior probability distributions, marginal probability distributions, 126: 3644: 1862:. 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. 1830:(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. 4089:

proposed to study how iso-intensity contours evolve over scales and this approach was investigated in more detail by Lifshitz and Pizer. Unfortunately, however, the intensity of image features changes over scales, which implies that it is hard to trace coarse-scale image features to finer scales using iso-intensity information.

2858:, 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. 4037:

prior. Such a task may involve (i) registration of the training examples to a common pose, (ii) probabilistic representation of the variation of the registered samples, and (iii) statistical inference between the model and the image. Other important methods in the literature for model-based segmentation include

4096:

Gauch and Pizer studied the complementary problem of ridges and valleys at multiple scales and developed a tool for interactive image segmentation based on multi-scale watersheds. The use of multi-scale watershed with application to the gradient map has also been investigated by Olsen and Nielsen and

4092:

Lindeberg studied the problem of linking local extrema and saddle points over scales, and proposed an image representation called the scale-space primal sketch which makes explicit the relations between structures at different scales, and also makes explicit which image features are stable over large

3671:

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 this

1429:

This mathematical expression can be implemented by convolving with an appropriate mask. If we extend this equation to three dimensions (x,y,z), the intensity at each pixel location around a central pixel at (x, y, z) is replaced by their corresponding values. This equation becomes particularly useful

696:

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

589:

Compression based methods postulate that the optimal segmentation is the one that minimizes, over all possible segmentations, the coding length of the data. The connection between these two concepts is that segmentation tries to find patterns in an image and any regularity in the image can be used to

4084:

There have been numerous research works in this area, out of which a few have now reached a state where they can be applied either with interactive manual intervention (usually with application to medical imaging) or fully automatically. The following is a brief overview of some of the main research

3864:

3. 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

2258:

was initially proposed to track moving interfaces by Dervieux and Thomasset in 1979 and 1981 and was later reinvented by Osher and Sethian in 1988. This has spread across various imaging domains in the late 1990s. It can be used to efficiently address the problem of curve/surface/etc. propagation in

668:

Histogram-based approaches can also be quickly adapted to apply to multiple frames, while maintaining their single pass efficiency. The histogram can be done in multiple fashions when multiple frames are considered. The same approach that is taken with one frame can be applied to multiple, and after

621:

whose entropy has a closed form expression. An interesting property of this model is that the estimated entropy bounds the true entropy of the data from above. This is because among all distributions with a given mean and covariance, normal distribution has the largest entropy. Thus, the true coding

390:

New methods suggested the usage of multi-dimensional fuzzy rule-based non-linear thresholds. In these works decision over each pixel's membership to a segment is based on multi-dimensional rules derived from fuzzy logic and evolutionary algorithms based on image lighting environment and application.

4027:

considers the gradient magnitude of an image as a topographic surface. Pixels having the highest gradient magnitude intensities (GMIs) correspond to watershed lines, which represent the region boundaries. Water placed on any pixel enclosed by a common watershed line flows downhill to a common local

2167:

This method starts at the root of the tree that represents the whole image. 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

4176:

architecture, as such it contains two sub-structures. The encoder structure follows the traditional stack of convolutional and max pooling layers to increase the receptive field as it goes through the layers. It is used to capture the context in the image. The decoder structure utilizes transposed

626:

For any given segmentation of an image, this scheme yields the number of bits required to encode that image based on the given segmentation. Thus, among all possible segmentations of an image, the goal is to find the segmentation which produces the shortest coding length. This can be achieved by a

4128:

Most of the aforementioned segmentation methods are based only on color information of pixels in the image. Humans use much more knowledge when performing image segmentation, but implementing this knowledge would cost considerable human engineering and computational time, and would require a huge

4100:

These ideas for multi-scale image segmentation by linking image structures over scales have also been picked up by Florack and Kuijper. Bijaoui and Rué associate structures detected in scale-space above a minimum noise threshold into an object tree which spans multiple scales and corresponds to a

1822:

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

1671:

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. For that purpose two spaces have to be introduced: one space is the one-dimensional

4180:

In addition to pixel-level semantic segmentation tasks which assign a given category to each pixel, modern segmentation applications include instance-level semantic segmentation tasks in which each individual in a given category must be uniquely identified, as well as panoptic segmentation tasks

4036:

The central assumption of model-based approaches is that the structures of interest have a tendency towards a particular shape. Therefore, one can seek a probabilistic model that characterizes the shape and its variation. When segmenting an image, constraints can be imposed using this model as a

3658:

A range of other methods exist for solving simple as well as higher order MRFs. They include Maximization of Posterior Marginal, Multi-scale MAP estimation, Multiple Resolution segmentation and more. Apart from likelihood estimates, graph-cut using maximum flow and other highly constrained graph

4088:

The nesting structure that Witkin described is, however, specific for one-dimensional signals and does not trivially transfer to higher-dimensional images. Nevertheless, this general idea has inspired several other authors to investigate coarse-to-fine schemes for image segmentation. Koenderink

4075:

A key observation is that the zero-crossings of the second derivatives (minima and maxima of the first derivative or slope) of multi-scale-smoothed versions of a signal form a nesting tree, which defines hierarchical relations between segments at different scales. Specifically, slope extrema at

3470: 1837:

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 difference between a pixel's

1662:

The detection of isolated points has significant applications in various fields, including X-ray image processing. For instance, an original X-ray image of a turbine blade can be examined pixel-by-pixel to detect porosity in the upper-right quadrant of the blade. The result of applying an edge

3187:

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.

2042:

of the region and the intensity of the candidate pixel are used to compute a test statistic. If the test statistic is sufficiently small, the pixel is added to the region, and the region's mean and scatter are recomputed. Otherwise, the pixel is rejected, and is used to form a new region.

684:

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.

3830: 2825:

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; see

4120:, Intelligent Scissors or IT-SNAPS are used in this kind of segmentation. In an alternative kind of semi-automatic segmentation, the algorithms return a spatial-taxon (i.e. foreground, object-group, object or object-part) selected by the user or designated via prior probabilities. 348:

combines both semantic and instance segmentation. Like semantic segmentation, panoptic segmentation is an approach that identifies, for every pixel, the belonging class. Moreover, like in instance segmentation, panoptic segmentation distinguishes different instances of the same

4195:

Related images such as a photo album or a sequence of video frames often contain semantically similar objects and scenes, therefore it is often beneficial to exploit such correlations. The task of simultaneously segmenting scenes from related images or video frames is termed

3354: 3152: 2168:(the merging process). The node in the tree is a segmented node. This process continues recursively until no further splits or merges are possible. When a special data structure is involved in the implementation of the algorithm of the method, its time complexity can reach 6266:

C. Undeman and T. Lindeberg (2003) "Fully Automatic Segmentation of MRI Brain Images using Probabilistic Anisotropic Diffusion and Multi-Scale Watersheds", Proc. Scale-Space'03, Isle of Skye, Scotland, Springer Lecture Notes in Computer Science, volume 2695, pages

4177:

convolution layers for upsampling so that the end dimensions are close to that of the input image. Skip connections are placed between convolution and transposed convolution layers of the same shape in order to preserve details that would have been lost otherwise.

2233:

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,

700:

Segmentation methods can also be applied to edges obtained from edge detectors. Lindeberg and Li developed an integrated method that segments edges into straight and curved edge segments for parts-based object recognition, based on a minimum description length

4076:

coarse scales can be traced back to corresponding features at fine scales. When a slope maximum and slope minimum annihilate each other at a larger scale, the three segments that they separated merge into one segment, thus defining the hierarchy of segments.

4093:

ranges of scale including locally appropriate scales for those. Bergholm proposed to detect edges at coarse scales in scale-space and then trace them back to finer scales with manual choice of both the coarse detection scale and the fine localization scale.

2812:

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,

869: 4144:

can process small areas of an image to extract simple features such as edges. Another neural network, or any decision-making mechanism, can then combine these features to label the areas of an image accordingly. A type of network designed this way is the

2676: 1654:. If the response magnitude is greater than or equal to the threshold, the function returns 1, indicating the presence of an isolated point; otherwise, it returns 0. This helps in the effective detection and segmentation of isolated points in the image. 1584: 3960: 6313:

Barghout, Lauren. Visual Taxometric Approach to Image Segmentation using Fuzzy-Spatial Taxon Cut Yields Contextually Relevant Regions. IPMU 2014, Part II. A. Laurent et al (Eds.) CCIS 443, pp 163–173. Springer International Publishing

1700:). The first space allows to measure how compactly the brightness of the image is distributed by calculating a minimal clustering kmin. Threshold brightness T corresponding to kmin defines the binary (black-and-white) image – bitmap 1896:—the pixel chosen here does not markedly influence the final segmentation. At each iteration it considers the neighboring pixels in the same way as seeded region growing. It differs from seeded region growing in that if the minimum 1241: 1094: 2399: 6173:

Dam, E., Johansen, P., Olsen, O. Thomsen,, A. Darvann, T., Dobrzenieck, A., Hermann, N., Kitai, N., Kreiborg, S., Larsen, P., Nielsen, M.: "Interactive multi-scale segmentation in clinical use" in European Congress of Radiology

3649:

the algorithm selects the newly formed graph. 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.

2283:

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. A classical representative is the

341:

is an approach that identifies, for every pixel, the specific belonging instance of the object. It detects each distinct object of interest in the image. For example, when each person in a figure is segmented as an individual

334:

is an approach detecting, for every pixel, the belonging class. For example, in a figure with many people, all the pixels belonging to persons will have the same class id and the pixels in the background will be classified as

3639:{\displaystyle \ell _{i}={\begin{cases}\ell _{i}^{\text{new}},&{\text{if }}\Delta U\leq 0,\\\ell _{i}^{\text{new}},&{\text{if }}\Delta U>0{\text{ and }}\delta <e^{-\Delta U/T},\ell _{i}^{\text{old}}\end{cases}}} 1433:

A sphere mask has been developed for use with three-dimensional datasets. The sphere mask is designed to use only integer arithmetic during calculations, thereby eliminating the need for floating-point hardware or software.

713:

The detection of isolated points in an image is a fundamental part of image segmentation. This process primarily depends on the second derivative, indicating the use of the Laplacian operator. The Laplacian of a function

3412:(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: 1424: 688:

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.

705:) 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. 386:

Recently, methods have been developed for thresholding computed tomography (CT) images. The key idea is that, unlike Otsu's method, the thresholds are derived from the radiographs instead of the (reconstructed) image.

305:

and techniques have been developed for image segmentation. To be useful, these techniques must typically be combined with a domain's specific knowledge in order to effectively solve the domain's segmentation problems.

4718:

Kamalakannan, Sridharan; Gururajan, Arunkumar; Sari-Sarraf, Hamed; Rodney, Long; Antani, Sameer (17 February 2010). "Double-Edge Detection of Radiographic Lumbar Vertebrae Images Using Pressurized Open DGVF Snakes".

2866:

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

3692: 3200:(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, 2222:, 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. 78:). The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Image segmentation is typically used to locate objects and 4659:

Ye, En Zhou; Ye, En Hui; Bouthillier, Maxime; Ye, Run Zhou (2022-02-18). "DeepImageTranslator V2: analysis of multimodal medical images using semantic segmentation maps generated through deep learning".

3206: 661:

apply the histogram-seeking method to clusters in the image in order to divide them into smaller clusters. This operation is repeated with smaller and smaller clusters until no more clusters are formed.

590:

compress it. The method describes each segment by its texture and boundary shape. Each of these components is modeled by a probability distribution function and its coding length is computed as follows:

6119:

Lindeberg, T.: Detecting salient blob-like image structures and their scales with a scale-space primal sketch: A method for focus-of-attention, International Journal of Computer Vision, 11(3), 283–318,

6108:

Lifshitz, L. and Pizer, S.: A multiresolution hierarchical approach to image segmentation based on intensity extrema, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12:6, 529–540, 1990.

5971:

S. Geman and D. Geman (1984): "Stochastic relaxation, Gibbs Distributions and Bayesian Restoration of Images", IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 721–741, Vol. 6, No. 6.

5658: 5124: 2993: 82:(lines, curves, etc.) in images. More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain characteristics. 6150:

Gauch, J. and Pizer, S.: Multiresolution analysis of ridges and valleys in grey-scale images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 15:6 (June 1993), pages: 635–646, 1993.

4072:

Witkin's seminal work in scale space included the notion that a one-dimensional signal could be unambiguously segmented into regions, with one scale parameter controlling the scale of segmentation.

3462: 3400:

is the Kronecker delta function. 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.

1776:

is an object in dual space. 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. For all

2275:

has been used in image segmentation, and this model has been improved (permitting both positive and negative propagation speeds) in an approach called the generalized fast marching method.

371:

The key of this method is to select the threshold value (or values when multiple-levels are selected). Several popular methods are used in industry including the maximum entropy method,

755: 5444:

Barghout, Lauren (2014). Vision. Global Conceptual Context Changes Local Contrast Processing (Ph.D. Dissertation 2003). Updated to include Computer Vision Techniques. Scholars' Press.

4109:

In one kind of segmentation, the user outlines the region of interest with the mouse clicks and algorithms are applied so that the path that best fits the edge of the image is shown.

4064:

Segmentation criteria can be arbitrarily complex and may take into account global as well as local criteria. A common requirement is that each region must be connected in some sense.

438:. Note that a common technique to improve performance for large images is to downsample the image, compute the clusters, and then reassign the values to the larger image if necessary. 692:

Spatial-taxons are information granules, consisting of a crisp pixel region, stationed at abstraction levels within a hierarchical nested scene architecture. They are similar to the

2538: 3859: 4212:, human action localization methods provide finer-grained results, typically per-image segmentation masks delineating the human object of interest and its action category (e.g., 4871: 1478: 6211:

M. Tabb and N. Ahuja, Unsupervised multiscale image segmentation by integrated edge and region detection, IEEE Transactions on Image Processing, Vol. 6, No. 5, 642–655, 1997.

2791: 2502: 548:

number of clusters. This has the advantage of not having to start with an initial guess of such parameter which makes it a better general solution for more diverse cases.

3871: 137:: The anterior thoracic wall, the airways and the pulmonary vessels anterior to the root of the lung have been digitally removed in order to visualize thoracic contents: 5521: 2204: 4172:

which takes as input an image and outputs a label for each pixel. U-Net initially was developed to detect cell boundaries in biomedical images. U-Net follows classical

2765: 2152: 2132: 2112: 2092: 2064: 1632: 3983: 2021: 1914: 1856: 1437:

When applying these concepts to actual images represented as arrays of numbers, we need to consider what happens when we reach an edge or border region. The function

1470: 907: 747: 2476: 2429: 1988: 1961: 1894: 1663:

detector’s response to this X-ray image can be approximated. This demonstrates the segmentation of isolated points in an image with the aid of single-pixel probes.

3394: 4800: 2739: 2719: 2699: 2522: 2449: 2306: 1934: 1652: 947: 927: 5980:

A. Bouman and M. Shapiro (2002): "A multiscale Random field model for Bayesian image segmentation", IEEE Transactions on Image Processing, pp. 162–177, Vol. 3.

5344:, Proceedings of the Asian Conference on Computer Vision (ACCV) 2009, H. Zha, R.-i. Taniguchi, and S. Maybank (Eds.), Part I, LNCS 5994, pp. 135–146, Springer. 5160: 4464:

Forghani, M.; Forouzanfar, M.; Teshnehlab, M. (2010). "Parameter optimization of improved fuzzy c-means clustering algorithm for brain MR image segmentation".

6568: 6494: 1102: 955: 559:

The idea is simple: look at the differences between a pair of images. Assuming the object of interest is moving, the difference will be exactly that object.

2314: 5648:

Dervieux, A. and Thomasset, F. 1979. A finite element method for the simulation of Raleigh-Taylor instability. Springer Lect. Notes in Math., 771:145–158.

4360:

Barghout, Lauren, and Lawrence W. Lee. "Perceptual information processing system." Paravue Inc. U.S. Patent Application 10/618,543, filed July 11, 2003.

2074:

and neighborhood-linking paths. A degree of connectivity (connectedness) is calculated based on a path that is formed by pixels. For a certain value of

5184:

Kashanipour, A.; Milani, N; Kashanipour, A.; Eghrary, H. (May 2008). "Robust Color Classification Using Fuzzy Rule-Based Particle Swarm Optimization".

4612:"DeepImageTranslator: A free, user-friendly graphical interface for image translation using deep-learning and its applications in 3D CT image analysis" 6367:

Johnson, John L. (September 1994). "Pulse-coupled neural nets: translation, rotation, scale, distortion, and intensity signal invariance for images".

6015:

Corso, Z. Tu, and A. Yuille (2008): "MRF Labelling with Graph-Shifts Algorithm", Proceedings of International workshop on combinatorial Image Analysis

4762:

Georgescu, Mariana-Iuliana; Ionescu, Radu Tudor; Miron, Andreea-Iuliana (2022-12-21). "Diversity-Promoting Ensemble for Medical Image Segmentation".

5259: 2839: 2835: 2827: 642:. In this technique, a histogram is computed from all of the pixels in the image, and the peaks and valleys in the histogram are used to locate the 1252: 4548:"Brain tumor detection and segmentation in a CRF (Conditional random fields) framework with pixel-pairwise affinity and superpixel-level features" 3668: 6327:

Vision: How Global Perceptual Context Changes Local Contrast Processing (Ph.D. Dissertation 2003). Updated to include Computer Vision Techniques

5671:

Osher, Stanley; Sethian, James A (1988). "Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations".

5337: 3825:{\displaystyle P(\lambda \mid f_{i})={\frac {P(f_{i}\mid \lambda )P(\lambda )}{\Sigma _{\lambda \in \Lambda }P(f_{i}\mid \lambda )P(\lambda )}}} 2793:. The optimization problems are known to be NP-hard in general but near-minimizing strategies work well in practice. Classical algorithms are 1869:

method is the unseeded region growing method. It is a modified algorithm that does not require explicit seeds. It starts with a single region

6448: 6335: 6250: 5449: 5201: 4304: 4101:

kind of feature in the original signal. Extracted features are accurately reconstructed using an iterative conjugate gradient matrix method.

6277:

Florack, L. and Kuijper, A.: The topological structure of scale-space images, Journal of Mathematical Imaging and Vision, 12:1, 65–79, 2000.

5767:

Forcadel, Nicolas; Le Guyader, Carole; Gout, Christian (July 2008), "Generalized fast marching method: applications to image segmentation",

874:

The Laplacian operator is employed such that the partial derivatives are derived from a specific equation. The second partial derivative of

4113: 6530: 2875: 105:. Adjacent regions are significantly different with respect to the same characteristic(s). When applied to a stack of images, typical in 638:-based methods are very efficient compared to other image segmentation methods because they typically require only one pass through the 38:. It shows the outer surface (red), the surface between compact bone and spongy bone (green) and the surface of the bone marrow (blue). 5934: 3349:{\displaystyle \alpha (1-\delta (\ell _{i}-\ell _{{\text{initial }}i})+\beta \Sigma _{q\in N(i)}(1-\delta (\ell _{i},\ell _{q(i)})).} 665:

One disadvantage of the histogram-seeking method is that it may be difficult to identify significant peaks and valleys in the image.

6138: 5732: 5590: 5568:

S.L. Horowitz and T. Pavlidis, Picture Segmentation by a Directed Split and Merge Procedure, Proc. ICPR, 1974, Denmark, pp. 424–433.

4387: 4349: 3147:{\displaystyle {\frac {1}{\sigma (\ell _{i}){\sqrt {2\pi }}}}e^{-(f_{i}-\mu (\ell _{i}))^{2}/(2\sigma (\ell _{i})^{2})}\,d\ell _{i}} 6559: 6213: 30: 618: 5859: 5406:, chapter in Geometric Level Set Methods in Imaging, Vision and Graphics, (S. Osher, N. Paragios, Eds.), Springer Verlag, 2003. 5435:

Witold Pedrycz (Editor), Andrzej Skowron (Co-Editor), Vladik Kreinovich (Co-Editor). Handbook of Granular Computing. Wiley 2008

4117: 2868: 2831: 372: 365: 359: 5577:

S.L. Horowitz and T. Pavlidis, Picture Segmentation by a Tree Traversal Algorithm, Journal of the ACM, 23 (1976), pp. 368–388.

5519: 4593: 410: 6502: 6410:

Ronneberger, Olaf; Fischer, Philipp; Brox, Thomas (2015). "U-Net: Convolutional Networks for Biomedical Image Segmentation".

6025: 5411: 594:

The boundary encoding leverages the fact that regions in natural images tend to have a smooth contour. This prior is used by

3418: 4610:

Ye, Run Zhou; Noll, Christophe; Richard, Gabriel; Lepage, Martin; Turcotte, Éric E.; Carpentier, André C. (February 2022).

1589:

This above equation is used to determine whether a point in the image is an isolated point based on the response magnitude

2215: 186: 5473:"Segmentation and classification of edges using minimum description length approximation and complementary junction cues" 4370:

Nielsen, Frank; Nock, Richard (2003). "On region merging: The statistical soundness of fast sorting, with applications".

4221: 4169: 2157: 658: 614: 4783: 2798: 2529: 505:

is the squared or absolute difference between a pixel and a cluster center. The difference is typically based on pixel

6594: 4295: 514: 6164:, Proc. of ICIAP 97, Florence, Italy, Lecture Notes in Computer Science, pages 6–13. Springer Verlag, September 1997. 5914: 5354:

Ohlander, Ron; Price, Keith; Reddy, D. Raj (1978). "Picture Segmentation Using a Recursive Region Splitting Method".

5380: 613:(MDL) principle, but here the length of the data given the model is approximated by the number of samples times the 368:

method. This method is based on a clip-level (or a threshold value) to turn a gray-scale image into a binary image.

6565: 6072:

Witkin, A. P. "Scale-space filtering", Proc. 8th Int. Joint Conf. Art. Intell., Karlsruhe, Germany,1019–1022, 1983.

5005:

Yi, Jingru; Wu, Pengxiang; Jiang, Menglin; Huang, Qiaoying; Hoeppner, Daniel J.; Metaxas, Dimitris N. (July 2019).

4237: 3197: 1827: 864:{\displaystyle \nabla ^{2}f(x,y)={\frac {\partial ^{2}f}{\partial x^{2}}}+{\frac {\partial ^{2}f}{\partial y^{2}}}} 610: 565:. They use a robot to poke objects in order to generate the motion signal necessary for motion-based segmentation. 563: 208: 5746: 6265: 5532:, Vadim V. Maximov, Alex Pashintsev Gestalt and Image Understanding. GESTALT THEORY 2012, Vol. 34, No.2, 143–166. 5528: 5472: 4309: 2767:. The Potts model is often called piecewise constant Mumford-Shah model as it can be seen as the degenerate case 2260: 578: 545: 6118: 5424:

Visual Taxometric approach Image Segmentation using Fuzzy-Spatial Taxon Cut Yields Contextually Relevant Regions

93:). Each of the pixels in a region are similar with respect to some characteristic or computed property, such as 6599: 5078:

Batenburg, K J.; Sijbers, J. (2009). "Adaptive thresholding of tomograms by projection distance minimization".

4270: 4058: 2822: 2671:{\displaystyle \operatorname {argmin} _{u,K}\gamma |K|+\mu \int _{K^{C}}|\nabla u|^{2}\,dx+\int (u-f)^{2}\,dx.} 2431:

is a piecewise constant image which has an optimal tradeoff between the squared L2 distance to the given image

1823:

selection of the similarity criterion is significant and the results are influenced by noise in all instances.

43: 3678:

2. E step: Estimate class statistics based on the random segmentation model defined. Using these, compute the

5057:

Alexander Kirillov; Kaiming He; Ross Girshick; Carsten Rother; Piotr Dollár (2018). "Panoptic Segmentation".

4028:

intensity minimum (LIM). Pixels draining to a common minimum form a catch basin, which represents a segment.

6500:

Frucci, Maria; Sanniti di Baja, Gabriella (2008). "From Segmentation to Binarization of Gray-level Images".

6478:

Connectivity-based segmentation of the substantia nigra in human and its implications in Parkinson's disease

6003: 4042: 3679: 2243: 268: 85:

The result of image segmentation is a set of segments that collectively cover the entire image, or a set of

6149: 4784:

Building façade detection, segmentation and parameter estimation for mobile robot localization and guidance

1579:{\displaystyle g(x,y)={\begin{cases}1&{\text{if }}|R(x,y)|\geq T\\0&{\text{otherwise}}\end{cases}}} 6107: 5915:"An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation" 5688: 5543: 5284: 5095: 4253: 4225: 4197: 4190: 4152: 3838: 2809: 2794: 2039: 295: 5423: 5310: 4691: 4429:

Pham, Dzung L.; Xu, Chenyang; Prince, Jerry L. (2000). "Current Methods in Medical Image Segmentation".

4417:

Color-and texture-based image segmentation using EM and its application to content-based image retrieval

4024: 3166:

Iterate over new prior probabilities and redefine clusters such that these probabilities are maximized.

3160: 2855: 2818: 2230: 6350: 6325: 5897: 4137:

segmentation, overcome these issues by modeling the domain knowledge from a dataset of labeled pixels.

6184:

Vincken, K.L.; Koster, A.S.E.; Viergever, M.A. (1997). "Probabilistic multiscale image segmentation".

6161: 4491:

Reznikov, Natalie; Buss, Dan J.; Provencher, Benjamin; McKee, Marc D.; Piché, Nicolas (October 2020).

4256: – Type of image segmentation, jointly segmenting semantically similar objects in multiple images 2114:-connected if there is a path linking those two pixels and the connectedness of this path is at least 6376: 5814: 5680: 5556: 5383: 5334: 5087: 4953: 4886: 4815: 4661: 4404:

3D reconstruction of individual anatomy from medical image data: Segmentation and geometry processing

4205: 4201: 2988:

and the class statistics calculated earlier. A Gaussian model is used for the marginal distribution.

2770: 2272: 2067: 556:

Motion based segmentation is a technique that relies on motion in the image to perform segmentation.

242: 6545: 5546:, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 26, No 11, pp 1452–1458, 2004. 5289: 5100: 3955:{\displaystyle P(\lambda )={\frac {\Sigma _{\lambda \in \Lambda }P(\lambda \mid f_{i})}{|\Omega |}}} 3492: 1508: 602:

of the contours in an image. Thus, the smoother a boundary is, the shorter coding length it attains.

5693: 5608: 5403: 4872:"Segment-Tube: Spatio-Temporal Action Localization in Untrimmed Videos with Per-Frame Segmentation" 4372:

2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings

4275: 4265: 4217: 3409: 2851: 2239: 2481: 6411: 5838: 5784: 5631: 5302: 5274: 5207: 5152: 5058: 5036: 4987: 4849: 4763: 4744: 4679: 4575: 4528: 4290: 4281: 4038: 1859: 693: 380: 290: 176: 144: 98: 4416: 4155:

are neural models proposed by modeling a cat's visual cortex and developed for high-performance

2171: 5724: 5461:

Barghout, Lauren, and Lawrence Lee. "Perceptual information processing system." Google Patents

5399: 2744: 424: 6555: 6444: 6392: 6331: 6246: 6134: 6055: 5830: 5728: 5706: 5445: 5407: 5197: 5144: 5028: 4979: 4971: 4922: 4904: 4841: 4833: 4799:

Liu, Ziyi; Wang, Le; Hua, Gang; Zhang, Qilin; Niu, Zhenxing; Wu, Ying; Zheng, Nanning (2018).

4736: 4641: 4633: 4567: 4547: 4520: 4512: 4446: 4383: 4345: 3988: 3683: 2985: 2137: 2117: 2097: 2077: 2049: 1592: 606: 533:

solution. The quality of the solution depends on the initial set of clusters and the value of

446: 110: 71: 4870:

Wang, Le; Duan, Xuhuan; Zhang, Qilin; Niu, Zhenxing; Hua, Gang; Zheng, Nanning (2018-05-22).

3968: 1993: 1899: 1841: 6536: 6511: 6436: 6384: 6296: 6238: 6193: 6047: 6038:

Staib, L.H.; Duncan, J.S. (1992). "Boundary finding with parametrically deformable models".

5822: 5802: 5776: 5698: 5623: 5588:

The lambda-connected segmentation and the optimal algorithm for split-and-merge segmentation

5484: 5363: 5294: 5238: 5189: 5136: 5105: 5018: 4961: 4912: 4894: 4823: 4728: 4671: 4623: 4559: 4504: 4473: 4438: 4375: 4209: 4159: 4130: 2814: 2525: 2255: 2219: 1440: 877: 717: 643: 454: 376: 279: 273: 263: 237: 200: 79: 6578: 5931: 5125:"Optimal Threshold Selection for Tomogram Segmentation by Projection Distance Minimization" 4419:." Sixth International Conference on Computer Vision (IEEE Cat. No. 98CH36271). IEEE, 1998. 2454: 2407: 1966: 1939: 1872: 572: 568:

Interactive segmentation follows the interactive perception framework proposed by Dov Katz

6572: 6549: 6465:

Connectivity-based segmentation of human amygdala nuclei using probabilistic tractography.

6217: 5938: 5594: 5525: 5341: 4704: 4403: 4344:

and George C. Stockman (2001): "Computer Vision", pp 279–325, New Jersey, Prentice-Hall,

4259: 3370: 2035: 400: 196: 153: 106: 47: 6082: 5587: 3367:

is the penalty for difference in label between neighboring pixels and chosen pixel. Here

3158:

Calculate the probability of each class label given the neighborhood defined previously.

6380: 6210: 6131:

Lindeberg, Tony, Scale-Space Theory in Computer Vision, Kluwer Academic Publishers, 1994

5993:", IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 689–700, Vol. 16. 5990: 5860:

Optimal approximations by piecewise smooth functions and associated variational problems

5818: 5684: 5091: 4957: 4890: 4819: 5876: 5227:"Real-world scene perception and perceptual organization: Lessons from Computer Vision" 4917: 4141: 4134: 3174: 2724: 2704: 2684: 2507: 2434: 2291: 1919: 1866: 1834: 1819: 1637: 1236:{\displaystyle {\frac {\partial ^{2}f(x,y)}{\partial y^{2}}}=f(x,y+1)+f(x,y-1)-2f(x,y)} 1089:{\displaystyle {\frac {\partial ^{2}f(x,y)}{\partial x^{2}}}=f(x+1,y)+f(x-1,y)-2f(x,y)} 932: 912: 681: 670: 595: 530: 247: 191: 157: 114: 90: 6431:

Vicente, Sara; Rother, Carsten; Kolmogorov, Vladimir (2011). "Object cosegmentation".

4011:

Reliable estimation of parameters for EM is required for global optima to be achieved.

4008:

Extension to multi-class labeling degrades performance and increases storage required.

2478:

defines a segmentation. The relative weight of the energies is tuned by the parameter

2394:{\displaystyle \operatorname {argmin} _{u}\gamma \|\nabla u\|_{0}+\int (u-f)^{2}\,dx.} 6588: 6477: 6464: 6300: 5855: 5702: 5367: 5040: 4991: 4683: 4532: 4341: 4298: – Extraction of information from images via digital image processing techniques 4241: 2235: 102: 55: 5880: 5306: 5156: 4940:

Guo, Dazhou; Pei, Yanting; Zheng, Kang; Yu, Hongkai; Lu, Yuhang; Wang, Song (2020).

4853: 4748: 4579: 6353:& Ö Göl (2004): "Edge-end pixel extraction for edge-based image segmentation", 6098:

Koenderink, Jan "The structure of images", Biological Cybernetics, 50:363–370, 1984

5842: 5788: 5426:. Communications in Computer and Information Science (CCIS). Springer-Verlag. 2014 5211: 4477: 4442: 497:

Repeat steps 2 and 3 until convergence is attained (i.e. no pixels change clusters)

86: 5635: 4801:"Joint Video Object Discovery and Segmentation by Coupled Dynamic Markov Networks" 6242: 6230: 5955: 5109: 4133:

database which does not currently exist. Trainable segmentation methods, such as

1684:); the second space is the dual 3-dimensional space of the original image itself 482: 5510:

Digital Image Processing (2007, Pearson) by Rafael C. Gonzalez, Richard E. Woods

5501:

Digital Image Processing (2007, Pearson) by Rafael C. Gonzalez, Richard E. Woods

5023: 5006: 4666: 4628: 4611: 4173: 4146: 4054: 2285: 167: 5188:. Vol. 2. IEEE Congress on Image and Signal Processing. pp. 110–114. 4493:"Deep learning for 3D imaging and image analysis in biomineralization research" 4492: 2874: 6440: 5780: 5627: 5298: 4732: 4675: 4563: 4508: 4379: 4181:

which combines these two tasks to provide a more complete scene segmentation.

4156: 2681:

The functional value is the sum of the total length of the segmentation curve

2071: 2031: 651: 599: 541: 510: 125: 6059: 5710: 5140: 4975: 4966: 4941: 4908: 4837: 4828: 4786:", International Conference on Intelligent Robots and Systems, pp. 1632–1639. 4637: 4516: 1419:{\displaystyle \nabla ^{2}f(x,y)=f(x+1,y)+f(x-1,y)+f(x,y+1)+f(x,y-1)-4f(x,y)} 17: 635: 544:

algorithm is a technique that is used to partition an image into an unknown

526: 494:

Re-compute the cluster centers by averaging all of the pixels in the cluster

478: 462: 450: 302: 6396: 5834: 5488: 5148: 5032: 4983: 4926: 4845: 4740: 4645: 4571: 4524: 4450: 1811:

is mean gradient on the borders). Maximum of MDC defines the segmentation.

5193: 4594:

MR Brain image segmentation using Bacteria Foraging Optimization Algorithm

4014:

Based on method of optimization, segmentation may cluster to local minima.

1963:. If not, then the pixel is considered different from all current regions 6388: 5956:"Graph-theoretical methods for detecting and describing gestalt clusters" 2161: 2027: 502: 488: 6575:

by Yu-Hsiang Wang (王昱翔), National Taiwan University, Taipei, Taiwan, ROC

6130: 5258:

Hossein Mobahi; Shankar Rao; Allen Yang; Shankar Sastry; Yi Ma. (2011).

4794: 4792: 3682:

of belonging to a label given the feature set is calculated using naive

3171:

Stop when probability is maximized and labeling scheme does not change.

3168:

This is done using a variety of optimization algorithms described below.

2887:

Define the neighborhood of each feature (random variable in MRF terms).

562:

Improving on this idea, Kenney et al. proposed interactive segmentation

109:, the resulting contours after image segmentation can be used to create 6237:. Lecture Notes in Computer Science. Vol. 5994. pp. 123–134. 2882:

The generic algorithm for image segmentation using MAP is given below:

204: 130: 6463:

Saygin, ZM, Osher, DE, Augustinack, J, Fischl, B, and Gabrieli, JDE.:

6197: 6051: 5826: 5557:

Fuzzy subfiber and its application to seismic lithology classification

5335:

Natural Image Segmentation with Adaptive Texture and Boundary Encoding

4899: 529:. This algorithm is guaranteed to converge, but it may not return the 6086: 5243: 5226: 4005:

Approximate MAP estimates are computationally expensive to calculate.

2164:

partition of an image. It is sometimes called quadtree segmentation.

1246:

These partial derivatives are then used to compute the Laplacian as:

522: 474: 134: 5260:"Segmentation of Natural Images by Texture and Boundary Compression" 211:, as well as volume electron microscopy techniques such as FIB-SEM. 6515: 6416: 5063: 4768: 1803:

is difference in brightness between the object and the background,

5559:, Information Sciences: Applications, Vol 1, No 2, pp 77–95, 1994. 5384:

https://www.cs.technion.ac.il/~ron/PAPERS/Paragios_chapter2003.pdf

5333:

Shankar Rao, Hossein Mobahi, Allen Yang, Shankar Sastry and Yi Ma

5279: 4546:

Wu, Wei; Chen, Albert Y. C.; Zhao, Liang; Corso, Jason J. (2014).

4165: 3987: 2873: 1430:

when we assume that all pixels have unit spacing along each axis.

639: 124: 94: 75: 35: 29: 1658:

Application of Isolated Point Detection in X-ray Image Processing

487:

Assign each pixel in the image to the cluster that minimizes the

6085:," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing ( 6083:

Scale-space filtering: A new approach to multi-scale description

5404:

https://www.cs.technion.ac.il/~ron/PAPERS/laplacian_ijcv2003.pdf

4552:

International Journal of Computer Assisted Radiology and Surgery

2961:

Compute the marginal distribution for the given labeling scheme

2830:. Some popular algorithms of this category are normalized cuts, 622:

length cannot be more than what the algorithm tries to minimize.

255:

Locate objects in satellite images (roads, forests, crops, etc.)

4942:"Degraded Image Semantic Segmentation With Dense-Gram Networks" 4278: – Classical quantization technique from signal processing 2504:. The binary variant of the Potts model, i.e., if the range of 6476:

Menke, RA, Jbabdi, S, Miller, KL, Matthews, PM and Zarei, M.:

6186: