An Adaptive Clustering Algorithm For Image Segmentation

Pappas, Thrasyvoulos N.; Jayant, N.

doi:10.1109/ccv.1988.590006

Cited by 83 publications

(144 citation statements)

References 10 publications

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“…Many algorithms have been developed to accomplish this, including statistical methods (Besag, 1986; Pieczynski, 1992), edge detection (Canny, 1986; Ma and Manjunath, 1997; Bellon and Silva, 2002), and region growing (Mumford and Shah, 1989; Adams and Bischof, 1994; Chan and Vese, 2001) methods. Here we consider three frequently used approaches: active contour evolution (Vese and Chan, 2002), k-means clustering (Kanungo et al ., 2002; Gibou and Fedkiw, 2005), and adaptive clustering (Pappas, 1992; Ashton and Parker, 1995). These three approaches are well suited to delivering geometries in the form of level set information drawn from image intensity values and have been employed in the image processing community to segment images obtained from various modalities.…”

Section: Image Segmentationmentioning

confidence: 99%

“…Pappas (1992) made significant improvements to clustering-based segmentation by proposing a multi-level adaptive clustering framework, which we have extended to 3D for this study. The method applies Bayes’ theorem to an image signal I composed of x segments, so that:

p (x ∣ I) \propto p (I ∣ x) p (x)

The a priori probability p(x) indicates the likelihood of a pixel/voxel s belonging to the same segmentation region as its neighbors, and the conditional density p(I|x) compares local pixel/voxel characteristics with those of the different segmentation regions distributed in the observed image.…”

Section: Image Segmentationmentioning

confidence: 99%

“…Unlike k -Means, however, the mean intensity of each segment x s is considered to be a smoothly varying mean field μ s , calculated using an interpolation window approach outlined in (Pappas, 1992). This smoothly varying field allows for pixels/voxels to be compared to the statistics of local regions, making the method more robust to global intensity variations.…”

Section: Image Segmentationmentioning

confidence: 99%

“…This smoothly varying field allows for pixels/voxels to be compared to the statistics of local regions, making the method more robust to global intensity variations. The combined distribution is then:

p (x ∣ I) α \exp true{- \sum_{s} \frac{1}{2 σ^{2}} {[I_{s} - μ_{s}^{x_{s}}]}^{2} - \sum_{q \in {scriptN}_{s}} V_{C} (x_{q}) true}

Pappas’ algorithm was later modified by Ashton and Parker (1995) to improve the reliability of segmentation results on images that are heavily polluted by speckle noise, such as those acquired via ultrasound, by allowing for the intensity variance σ 2 to be calculated adaptively in each region x s , for each window at all levels of resolution:

p (x ∣ I) α \prod_{s} true(\frac{1}{σ_{x_{s}}} true) \exp true{- \sum_{s} \frac{1}{2 σ_{x_{s}}^{2}} {[I_{s} - μ_{s}^{x_{s}}]}^{2} - \sum_{q \in {scriptN}_{s}} V_{C} (x_{q}) true}

Maximizing this probability function is equivalent to maximizing its natural logarithm, so that it can be viewed alternatively in terms of an energy minimization function:

E (x ∣ I) = \sum_{s} true{\ln (σ_{x_{s}}) + \frac{1}{2 σ_{x_{s}}^{2}} {[I_{s} - μ_{s}^{x_{s}}]}^{2} true} + \sum_{q \in {scriptN}_{s}} V_{C} (x_{q})

E(x|I) is minimized using the iterated conditional modes (ICM) approach put forth by Besag (1986) and within the adaptive framework presented by Pappas (1992). The complete algorithm consists of two iterative loops; an outer loop, which computes σ x s and

…”

Section: Image Segmentationmentioning

confidence: 99%

“…The complete algorithm consists of two iterative loops; an outer loop, which computes σ x s and

μ_{s}^{x_{s}}

given the current configuration of regions x s in the image, and an inner loop, which executes a raster scan update of the pixels/voxels in the image, whereby the regional x s label assigned to each pixel/voxel is the one which minimizes the energy function (21). The inner raster scan loop is considered converged when the number of updates is less than some inner threshold ( T inner = W /2 nlev –1 is suggested in (Pappas, 1992)), with adaptive clustering window width W and image coarsening level nlev ( nlev = 1 is the original image). The outer iterative loop is converged when the number of raster scan updates in the inner loop becomes smaller than an outer threshold (e.g.…”

Section: Image Segmentationmentioning

confidence: 99%

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Techniques to derive geometries for image-based Eulerian computations

Dillard

Buchholz

Vigmostad

et al. 2014

Engineering Computations

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Purpose The performance of three frequently used level set-based segmentation methods is examined for the purpose of defining features and boundary conditions for image-based Eulerian fluid and solid mechanics models. The focus of the evaluation is to identify an approach that produces the best geometric representation from a computational fluid/solid modeling point of view. In particular, extraction of geometries from a wide variety of imaging modalities and noise intensities, to supply to an immersed boundary approach, is targeted. Design/methodology/approach Two- and three-dimensional images, acquired from optical, X-ray CT, and ultrasound imaging modalities, are segmented with active contours, k-means, and adaptive clustering methods. Segmentation contours are converted to level sets and smoothed as necessary for use in fluid/solid simulations. Results produced by the three approaches are compared visually and with contrast ratio, signal-to-noise ratio, and contrast-to-noise ratio measures. Findings While the active contours method possesses built-in smoothing and regularization and produces continuous contours, the clustering methods (k-means and adaptive clustering) produce discrete (pixelated) contours that require smoothing using speckle-reducing anisotropic diffusion (SRAD). Thus, for images with high contrast and low to moderate noise, active contours are generally preferable. However, adaptive clustering is found to be far superior to the other two methods for images possessing high levels of noise and global intensity variations, due to its more sophisticated use of local pixel/voxel intensity statistics. Originality/value It is often difficult to know a priori which segmentation will perform best for a given image type, particularly when geometric modeling is the ultimate goal. This work offers insight to the algorithm selection process, as well as outlining a practical framework for generating useful geometric surfaces in an Eulerian setting.

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Section: Image Segmentationmentioning

confidence: 99%

p (x ∣ I) \propto p (I ∣ x) p (x)

Section: Image Segmentationmentioning

confidence: 99%

Section: Image Segmentationmentioning

confidence: 99%

p (x ∣ I) α \exp true{- \sum_{s} \frac{1}{2 σ^{2}} {[I_{s} - μ_{s}^{x_{s}}]}^{2} - \sum_{q \in {scriptN}_{s}} V_{C} (x_{q}) true}

p (x ∣ I) α \prod_{s} true(\frac{1}{σ_{x_{s}}} true) \exp true{- \sum_{s} \frac{1}{2 σ_{x_{s}}^{2}} {[I_{s} - μ_{s}^{x_{s}}]}^{2} - \sum_{q \in {scriptN}_{s}} V_{C} (x_{q}) true}

Maximizing this probability function is equivalent to maximizing its natural logarithm, so that it can be viewed alternatively in terms of an energy minimization function:

E (x ∣ I) = \sum_{s} true{\ln (σ_{x_{s}}) + \frac{1}{2 σ_{x_{s}}^{2}} {[I_{s} - μ_{s}^{x_{s}}]}^{2} true} + \sum_{q \in {scriptN}_{s}} V_{C} (x_{q})

…”

Section: Image Segmentationmentioning

confidence: 99%

“…The complete algorithm consists of two iterative loops; an outer loop, which computes σ x s and

μ_{s}^{x_{s}}

Section: Image Segmentationmentioning

confidence: 99%

See 3 more Smart Citations

Techniques to derive geometries for image-based Eulerian computations

Dillard

Buchholz

Vigmostad

et al. 2014

Engineering Computations

View full text Add to dashboard Cite

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On estimation of bias field in MRI images: polynomial vs Gaussian surface fitting method

Kahali

Adhikari

Sing

2016

Journal of Chemometrics

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Surface fitting is one of the well‐known retrospective methods for bias field estimation from magnetic resonance imaging (MRI) images. Bias field in MRI images is primarily caused because of radio frequency–coil nonuniformity, improper image acquisition process, patient movement, and so on. The bias field can be characterized by any slow variant and smooth function because of its slow variant nature. In this paper, we present a comparative study between polynomial and Gaussian surface fitting methods. In particular, we have used both the second‐ and third‐order polynomial functions to estimate the bias field. In this study, we approximate the bias field in two different ways. In the first method, the surfaces are fitted on the anatomical tissue regions individually and then fused to estimate the bias field. Conversely, in the second method, we have done the same over the entire image region. We have tested on three volumes of simulated and one volume of real‐patient MRI brain images and validated the results by both the qualitative and quantitative analyses. The quantitative analyses are presented in standard deviation and coefficient of joint variation. The analysis of the simulation results show that the Gaussian surface fitting method yields better results in both the cases, where the surface fitting is done on entire image and individual tissue regions.

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Unsupervised segmentation of predefined shapes in multivariate images

Noordam

Broek²,

Buydens

2003

Journal of Chemometrics

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Fuzzy C-means (FCM) is an unsupervised clustering technique that is often used for the unsupervised segmentation of multivariate images. In traditional FCM the clustering is based on spectral information only and the geometrical relationship between neighbouring pixels is not used in the clustering procedure. In this paper, the spatially guided FCM (SG-FCM) algorithm is presented which segments multivariate images by incorporating both spatial and spectral information. Spatial information is described by a geometrical shape description and can vary from a local neighbourhood to a more extended shape model such as Hough circle detection. A modified FCM objective function uses the spatial information as described by the shape model. This results in a segmented image in which the construction of the cluster prototypes is influenced by spatial information. The performance of SG-FCM is compared with both FCM and the sequence of FCM and a majority filter. The SG-FCM segmented image shows more homogeneous regions and less spurious pixels.

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An Adaptive Clustering Algorithm For Image Segmentation

Cited by 83 publications

References 10 publications

Techniques to derive geometries for image-based Eulerian computations

Techniques to derive geometries for image-based Eulerian computations

On estimation of bias field in MRI images: polynomial vs Gaussian surface fitting method

Unsupervised segmentation of predefined shapes in multivariate images

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