## Adaptive Regularization for Image Segmentation using Local Image Curvature Cues

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Citations: | 3 - 3 self |

### BibTeX

@MISC{Rao_adaptiveregularization,

author = {Josna Rao and Rafeef Abugharbieh and Ghassan Hamarneh},

title = {Adaptive Regularization for Image Segmentation using Local Image Curvature Cues},

year = {}

}

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### Abstract

Abstract. Image segmentation techniques typically require proper weighting of competing data fidelity and regularization terms. Conventionally, the associated parameters are set through tedious trial and error procedures and kept constant over the image. However, spatially varying structural characteristics, such as object curvature, combined with varying noise and imaging artifacts, significantly complicate the selection process of segmentation parameters. In this work, we propose a novel approach for automating the parameter selection by employing a robust structural cue to prevent excessive regularization of trusted (i.e. low noise) high curvature image regions. Our approach autonomously adapts local regularization weights by combining local measures of image curvature and edge evidence that are gated by a signal reliability measure. We demonstrate the utility and favorable performance of our approach within two major segmentation frameworks, graph cuts and active contours, and present quantitative and qualitative results on a variety of natural and medical images. 1

### Citations

3310 | Snakes: Active contour models
- Kass, Witkin, et al.
- 1988
(Show Context)
Citation Context ...nergy terms are weighted, the resulting segmentation can greatly differ. Examples of widely used optimizationbased segmentation methods with this sensitive tradeoff include active contours techniques =-=[1,2,3,4]-=-, graph cut methods [5], optimal path approaches [6] and numerous variations thereof. In fact, addressing the issue of how to best balance competing cost terms is of great importance to many related a... |

1509 | Fast approximate energy minimization via graph cuts
- Boykov, Veksler, et al.
- 2001
(Show Context)
Citation Context ... does not require any prior knowledge or preprocessing steps. In order to showcase the utility of our approach, we incorporate this structural cue into two popular segmentation frameworks, graph cuts =-=[22,23]-=- and active contours [24]. We validate our method on real natural and medical images, and compare its performance against two alternative approaches for regularization: using the best possible spatial... |

1150 | Geodesic active contours
- Casselles, Kimmel, et al.
- 1995
(Show Context)
Citation Context ...nergy terms are weighted, the resulting segmentation can greatly differ. Examples of widely used optimizationbased segmentation methods with this sensitive tradeoff include active contours techniques =-=[1,2,3,4]-=-, graph cut methods [5], optimal path approaches [6] and numerous variations thereof. In fact, addressing the issue of how to best balance competing cost terms is of great importance to many related a... |

873 | Active contours without edges
- Chan, Vese
- 2001
(Show Context)
Citation Context ...knowledge or preprocessing steps. In order to showcase the utility of our approach, we incorporate this structural cue into two popular segmentation frameworks, graph cuts [22,23] and active contours =-=[24]-=-. We validate our method on real natural and medical images, and compare its performance against two alternative approaches for regularization: using the best possible spatially uniform (fixed) weight... |

331 | Motion of level sets by mean curvature
- Evans, Spruck
- 1991
(Show Context)
Citation Context ...under one of two classes. One class uses the curvature of an evolving contour as an internal energy to locally control the contour evolution in order to smoothen high curvature contour segments, e.g. =-=[1,21]-=-. The other class treats image curvature as an external energy in order to attract the evolving contour to high curvature regions in the image, e.g. [1,18]. In contrast, our proposed method uses estim... |

323 | C.: Evaluation of interest point detectors
- Schmid, Mohr, et al.
- 2000
(Show Context)
Citation Context ...an be smooth while other parts exhibit highly curved features. It is therefore inappropriate to enforce the same level of regularization in these different regions of varying degrees of curvature. In =-=[18,19,20]-=-, for example, it was observed that high curvature points are anatomically and structurally important and thus form a good basis for feature matching over a set of data for image registration. Therefo... |

317 | Contour and texture analysis for image segmentation
- Malik, Belongie, et al.
(Show Context)
Citation Context ...re used to distinguish between texture edges and edges between different objects. Only the latter edges were then used to dampen the curve evolution and define the segmentation boundary. Malik et al. =-=[16]-=- proposed Normalized Cuts to regularize segmentation in textured regions through the use of local texture and orientation cues. Gilboa et al. [17] presented a graph-cut based segmentation framework wi... |

197 | Brainweb: Online interface to a 3D MRI simulated brain database
- Cocosco, Kollokian, et al.
- 1997
(Show Context)
Citation Context ...ral images where structural features play an important role and which are available at the McGill Calibrated Color Database [29]. We also tested on magnetic resonance imaging (MRI) data from BrainWeb =-=[30]-=-. To8 Rao, Abugharbieh, and Hamarneh (a) (b) (c) (d) (e) (f) Fig. 1. (color figure) Segmentation of grey object in synthetic image corrupted by AWGN with increasing standard devation. (a), (b), (c) O... |

160 | Graph cuts and efficient N-D image segmentation
- Boykov, Funka-Lea
- 2006
(Show Context)
Citation Context ... resulting segmentation can greatly differ. Examples of widely used optimizationbased segmentation methods with this sensitive tradeoff include active contours techniques [1,2,3,4], graph cut methods =-=[5]-=-, optimal path approaches [6] and numerous variations thereof. In fact, addressing the issue of how to best balance competing cost terms is of great importance to many related algorithmic2 Rao, Abugh... |

130 |
Gray-level corner detection
- Kitchen, Rosenfeld
- 1982
(Show Context)
Citation Context ...where Ix,σ and Iy,σ are the image derivatives along x and y, respectively, at scale σ. Denoting the Hessian matrix of I(x, y; σ) by Hσ(x, y), the local image curvature K(x, y; σ) can be calculated as =-=[25,26]-=-: K(x, y; σ) = ∣ ∣t T Hσt ∣ ∣ . (3) Note that we used the absolute value on the right hand side of (3) since we are not concerned with differentiating between convex and concave curvature. We follow t... |

82 | Tracking points on deformable objects using curvature information
- Cohen, Ayache, et al.
- 1992
(Show Context)
Citation Context ...an be smooth while other parts exhibit highly curved features. It is therefore inappropriate to enforce the same level of regularization in these different regions of varying degrees of curvature. In =-=[18,19,20]-=-, for example, it was observed that high curvature points are anatomically and structurally important and thus form a good basis for feature matching over a set of data for image registration. Therefo... |

79 | Learning CRFs using graph cuts
- Szummer, Kohli, et al.
- 2008
(Show Context)
Citation Context ...e variability present in real image data. Although an optimal regularization weight can be found for a single image in a set [10], the same weight may not be optimal for all regions of that image. In =-=[11]-=-, a max-margin approach is used to learn the optimal parameter setting. In [12], Kolmogorov et al. solved the optimization problem for a range of parameters. In recent years, spatially adaptive regula... |

64 | Interactive live-wire boundary extraction
- Barret, Mortensen
- 1997
(Show Context)
Citation Context ...reatly differ. Examples of widely used optimizationbased segmentation methods with this sensitive tradeoff include active contours techniques [1,2,3,4], graph cut methods [5], optimal path approaches =-=[6]-=- and numerous variations thereof. In fact, addressing the issue of how to best balance competing cost terms is of great importance to many related algorithmic2 Rao, Abugharbieh, and Hamarneh formulat... |

61 | N.: Geometric Level Set Methods
- Osher, Paragios
- 2003
(Show Context)
Citation Context ...nergy terms are weighted, the resulting segmentation can greatly differ. Examples of widely used optimizationbased segmentation methods with this sensitive tradeoff include active contours techniques =-=[1,2,3,4]-=-, graph cut methods [5], optimal path approaches [6] and numerous variations thereof. In fact, addressing the issue of how to best balance competing cost terms is of great importance to many related a... |

50 | On scale selection for differential operators
- Lindeberg
- 1993
(Show Context)
Citation Context ...= ∣ ∣t T Hσt ∣ ∣ . (3) Note that we used the absolute value on the right hand side of (3) since we are not concerned with differentiating between convex and concave curvature. We follow the method in =-=[27]-=- where equation (3) is enhanced to have a stronger response near edges by multiplication with the gradient magnitude raised to some power, which we chose as 2. The enhanced curvature estimate becomes ... |

41 | Applications of parametric maxflow in computer vision
- Kolmogorov, Boykov, et al.
- 2007
(Show Context)
Citation Context ...ight can be found for a single image in a set [10], the same weight may not be optimal for all regions of that image. In [11], a max-margin approach is used to learn the optimal parameter setting. In =-=[12]-=-, Kolmogorov et al. solved the optimization problem for a range of parameters. In recent years, spatially adaptive regularization has been acknowledged as a necessary requirement for improving the acc... |

32 | Boosted lasso
- Zhao, Yu
- 2004
(Show Context)
Citation Context ...2 Rao, Abugharbieh, and Hamarneh formulations in computer vision. More generally, this tradeoff is seen in likelihood versus prior in Bayesian methods [7] and loss versus penalty in machine learning =-=[8]-=-. Determining the optimum balance between regularization and adherence to image content has predominantly been done empirically and in an ad-hoc manner. However, natural and medical images commonly ha... |

27 | STACS: New active contour scheme for cardiac MR image segmentation
- Pluempitiwiriyawej, Moura, et al.
- 2005
(Show Context)
Citation Context |

21 |
Matlab wrapper for graph cut
- Bagon
- 2006
(Show Context)
Citation Context ... does not require any prior knowledge or preprocessing steps. In order to showcase the utility of our approach, we incorporate this structural cue into two popular segmentation frameworks, graph cuts =-=[22,23]-=- and active contours [24]. We validate our method on real natural and medical images, and compare its performance against two alternative approaches for regularization: using the best possible spatial... |

18 | Texture Analysis and Segmentation Using Modulation Features, Generative Models and Weighted Curve Evolution
- KOKKINOS, EVANGELOPOULOS, et al.
(Show Context)
Citation Context ...hah segmentation approaches through the use of data-driven local cues and contextual feedback, specifically focusing on edge (gradient) consistency, edge continuity, and texture cues. Kokkinos et al. =-=[15]-=- proposed a spatially adaptive texture estimation measure through an amplitude/frequency modulation model of images that allows for a probabilistic discrimination between edges, textured and smooth re... |

16 |
Nonlocal convex functionals for image regularization
- Gilboa, Darbon, et al.
- 2006
(Show Context)
Citation Context ...on and define the segmentation boundary. Malik et al. [16] proposed Normalized Cuts to regularize segmentation in textured regions through the use of local texture and orientation cues. Gilboa et al. =-=[17]-=- presented a graph-cut based segmentation framework with spatially varying regularization through edge weights in the graph using a gradient magnitude-based cue.Adaptive Regularization using Image Cu... |

12 | Is a single energy functional sufficient? Adaptive energy functionals and automatic initialization
- McIntosh, Hamarneh
- 2007
(Show Context)
Citation Context ...ntation keep a uniform level of regularization across the image or along an object boundary, i.e. one that does not vary spatially and is determined empirically. As addressed in McIntosh and Hamarneh =-=[10]-=-, adapting the regularization weights across a set of images is necessary for addressing the variability present in real image data. Although an optimal regularization weight can be found for a single... |

8 | Noise-Adaptive Nonlinear Diffusion Filtering of MR Images With Spatially Varying Noise Levels
- Samsonov, Johnson
(Show Context)
Citation Context ...ted and spatially varying boundary behavior, and often suffer from significant inhomogeneous image artifacts, e.g. the spatially varying bias field commonly observed in magnetic resonance (MR) images =-=[9]-=-. Compensating for such image deteriorations by uniformly increasing the level of regularization, until the most degraded region of the image is properly regularized, may result in excessive smoothing... |

6 | R.: Prior knowledge driven multiscale segmentation of brain MRI
- Akselrod-Ballin, Galun, et al.
- 2007
(Show Context)
Citation Context ... of great importance to many related algorithmic2 Rao, Abugharbieh, and Hamarneh formulations in computer vision. More generally, this tradeoff is seen in likelihood versus prior in Bayesian methods =-=[7]-=- and loss versus penalty in machine learning [8]. Determining the optimum balance between regularization and adherence to image content has predominantly been done empirically and in an ad-hoc manner.... |

6 | Mumford-Shah regularizer with contextual feedback
- Erdem, Tari
- 2008
(Show Context)
Citation Context ...tion We first incorporated our adaptive weights1 w(p) into a graph cuts (GC) based segmentation [22,23]. The segmentation energy in this case becomes: E(f) = ∑ w(p)Eint(fp, fq) + ∑ (1 − w(p))Eext(fp) =-=(14)-=- p,q∈N where f ∈ L is the labeling for all pixels p ∈ P , L is the space of all possible labellings, and P is the set of pixels in image I. In GC, Eint is the interaction penalty between pixel pairs (... |

6 |
McGill calibrated colour image database. http://tabby.vision.mcgill.ca
- Olmos, Kingdom
- 2004
(Show Context)
Citation Context ...ch were modified as proposed in Sections 2.4 and 2.5. We tested various natural images where structural features play an important role and which are available at the McGill Calibrated Color Database =-=[29]-=-. We also tested on magnetic resonance imaging (MRI) data from BrainWeb [30]. To8 Rao, Abugharbieh, and Hamarneh (a) (b) (c) (d) (e) (f) Fig. 1. (color figure) Segmentation of grey object in syntheti... |

3 | Adaptive contextual energy parameterization for automated image segmentation
- Rao, Hamarneh, et al.
- 2009
(Show Context)
Citation Context ...ge of parameters. In recent years, spatially adaptive regularization has been acknowledged as a necessary requirement for improving the accuracy of energy-minimizing segmentations. In an earlier work =-=[13]-=-, we proposed an adaptive regularization framework based on estimating the level of image reliability through local data cues reflecting both structure gradient and noise. Our approach in [13] demonst... |

3 | Approximated Curvature Penalty in Non-rigid Registration Using Pairwise MRFs
- Glocker, Komodakis, et al.
- 2009
(Show Context)
Citation Context ...an be smooth while other parts exhibit highly curved features. It is therefore inappropriate to enforce the same level of regularization in these different regions of varying degrees of curvature. In =-=[18,19,20]-=-, for example, it was observed that high curvature points are anatomically and structurally important and thus form a good basis for feature matching over a set of data for image registration. Therefo... |

3 |
N.: Curvature of oriented patterns: 2-D and 3-D estimation from differential geometry
- Donias, Baylou, et al.
- 1998
(Show Context)
Citation Context ...where Ix,σ and Iy,σ are the image derivatives along x and y, respectively, at scale σ. Denoting the Hessian matrix of I(x, y; σ) by Hσ(x, y), the local image curvature K(x, y; σ) can be calculated as =-=[25,26]-=-: K(x, y; σ) = ∣ ∣t T Hσt ∣ ∣ . (3) Note that we used the absolute value on the right hand side of (3) since we are not concerned with differentiating between convex and concave curvature. We follow t... |

1 |
D.: (Learning CRFs using Graph Cuts) 2
- Szummer, Kohli, et al.
(Show Context)
Citation Context ...e variability present in real image data. Although an optimal regularization weight can be found for a single image in a set [10], the same weight may not be optimal for all regions of that image. In =-=[11]-=-, a max-margin approach is used to learn the optimal parameter setting. In [12], Kolmogorov et al. solved the optimization problem for a range of parameters. In recent years, spatially adaptive regula... |

1 |
MATLAB wrapper for graph cuts. http://www.wisdom.weizmann.ac.il/ ˜ bagon (2006
- Bagon
(Show Context)
Citation Context ... does not require any prior knowledge or preprocessing steps. In order to showcase the utility of our approach, we incorporate this structural cue into two popular segmentation frameworks, graph cuts =-=[22,23]-=- and active contours [24]. We validate our method on real natural and medical images, and compare its performance against two alternative approaches for regularization: using the best possible spatial... |

1 |
Vese active contours without edges
- Wu
- 2009
(Show Context)
Citation Context ...the method. (17) 3 Results and Discussion Using MATLAB code on a PC with 3.6 GHz Intel Core Duo processor and 2GB of RAM, we ran a series of tests using a GC wrapper [22], and an implementation of AC =-=[28]-=-, both of which were modified as proposed in Sections 2.4 and 2.5. We tested various natural images where structural features play an important role and which are available at the McGill Calibrated Co... |