An efficient level set method for simultaneous intensity inhomogeneity correction and segmentation of MR images

doi:10.1016/j.compmedimag.2015.11.005

Computerized Medical Imaging and Graphics

Volume 48, March 2016, Pages 9-20

https://doi.org/10.1016/j.compmedimag.2015.11.005 Get rights and content

Highlights

•
We propose a novel method for simultaneous intensity inhomogeneity correction and segmentation.
•
Energy functional includes total variation regularization for bias field and level set function.
•
The minimization procedure searches the global minimum and does not depend on initialization.
•
The method was tested on synthetic and real images and evaluated qualitatively and quantitatively.
•
The approach produces results, similar or superior in quality compared to other techniques.

Abstract

Intensity inhomogeneity (bias field) is a common artefact in magnetic resonance (MR) images, which hinders successful automatic segmentation. In this work, a novel algorithm for simultaneous segmentation and bias field correction is presented. The proposed energy functional allows for explicit regularization of the bias field term, making the model more flexible, which is crucial in presence of strong inhomogeneities. An efficient minimization procedure, attempting to find the global minimum, is applied to the energy functional. The algorithm is evaluated qualitatively and quantitatively using a synthetic example and real MR images of different organs. Comparisons with several state-of-the-art methods demonstrate the superior performance of the proposed technique. Desirable results are obtained even for images with strong and complicated inhomogeneity fields and sparse tissue structures.

Introduction

Intensity inhomogeneity is a common artefact that often occurs in medical images and is caused by imperfect image acquisition. For example, radio frequency field inhomogeneities appear due to either a non-uniform field itself or a non-uniform sensitivity of the receiver and transmitter coils. Such artefacts lead to undesired intensity variations in the same tissue types across the image. They hinder successful automated image segmentation, especially if the segmentation algorithms rely only on image intensities [15]. Therefore, efficient and reliable techniques for intensity inhomogeneity correction are required.

In general, there are two main directions in this area [18], [47]. First, the correction can be done prospectively based on adjustments of hardware and acquisition methods, such as phantom-based calibration and multichannel transmit scanning. Such techniques can remove scanner-dependent inhomogeneities. Nonetheless, they are not applicable for already acquired data. Second, the retrospective correction is done on a post-processing level. Such methods are rather general and mainly rely on the information from acquired images and prior knowledge about imaged anatomies, including methods based on filtering, histogram analysis, surface fitting, statistical modeling, and segmentation [18]. Approaches that allow for simultaneous image segmentation and bias field correction are especially attractive, since the processes of segmentation and correction are interleaved to benefit from each other [47].

Level set methods, which are based on calculus of variations and partial differential equations, are naturally able to represent contours with complex topology and to change their topology during evolution. In the last decade, level set methods have become increasingly popular in image processing for segmentation [22], [42], [43], denoising, and enhancement [23], [45]. Region-based level set models [22], [37] aim to evolve the contour such that a certain region of interest is identified. A classical example is the well-known Chan and Vese model [7], which uses a region homogeneity assumption. Other methods based on piecewise smooth models might overcome the problem of intensity inhomogeneity. However, they are usually more computationally expensive and sensitive to initialization [27].

In this paper, we propose a novel region-based level set method, which allows for simultaneous intensity inhomogeneity correction and two-phase image segmentation. Using a generally accepted model of images with intensity inhomogeneity, we apply a local intensity clustering property proposed by Li et al. [26] and extend the energy functional to enable an explicit regularization of the bias field component. The functional consists of two parts related to segmentation and bias field correction. We reformulate the level set functional using a convexification procedure [6] and minimize each part with the Split Bregman algorithm [3], [14], which attempts to find the global minimum and does not depend on initialization. The algorithm is implemented with CUDA [36], a general-purpose computing platform on graphics processing units (GPGPU), to guarantee fast computations.

The paper is organized as follows. First, a review of related works is given in Section 2. In Section 3, we shortly introduce the model and the basic level set formulation. In Section 4, we present our extended functional. The level set formulation and the minimization procedure are described in Section 4.3. The implementation is elaborated in Section 4.4. The results and findings are discussed in Section 5. This paper is summarized in Section 6.

Section snippets

Related work

Recently, multiple retrospective algorithms for bias field correction applied to MR data have been proposed [18], [47]. These algorithms have become an essential part of segmentation pipelines. Such approaches as the nonparametric non-uniformity normalization (N3) method of Sled et al. [44] and its extension, the N4 approach, by Tustison et al. [46] have become popular due to their performance. They are applied in numerous studies, where the intensity inhomogeneity correction is introduced in a

Image model

The 2D image $Im : Ω \to ℝ$ is defined on a continuous domain Ω, such that $Im = bJ + n,$ where J is the true image, b is the intensity inhomogeneity component, and n is the additive zero-mean Gaussian noise. This is a standard multiplicative model that originates from MR physics [4] and is used in multiple works on intensity inhomogeneity correction [47].

Similarly as in the model presented by Li et al. [26], we assume that the bias field component $b : Ω \to ℝ$ is slowly varying and essentially constant within a

Proposed model with explicit bias field smoothing parameter

In the original CLIC model, the truncated Gaussian function K serves for an implicit smoothing of the bias field term b. The level of smoothness is controlled by the standard deviation σ of the Gaussian kernel K, i.e., one can manipulate b only by changing σ, which can be insufficient in presence of complicated intensity inhomogeneities and organ structures. Moreover, such a smoothing term requires computation of four convolutions in each iteration, which is rather computationally expensive. We

Experimental results and discussion

The parameter selection in our model is rather straightforward. We have two data fidelity terms μ_ϕ and μ_b and two Bregman factors λ_ϕ and λ_b. Both data fidelity terms affect the segmentation results for the ϕ process, and only μ_b affects the bias field correction b process. The values of the fidelity terms define the amount of smoothing, i.e., the smaller the fidelity terms, the more impact has the other term (| ∇ ϕ(x)| in the level set ϕ process) and the smoother the contours will be. Generally,

Conclusions and future work

We present a variational level set method for simultaneous segmentation and intensity inhomogeneity correction. We formulate an energy by applying a generally accepted model for images with intensity inhomogeneities and a local coherent clustering criterion. We extend this criterion to include an explicit manipulation of the bias field component. The novel functional is minimized using the efficient Split Bregman method. It attempts to find the global minimum and is not sensitive to

Acknowledgments

The authors would like to thank Dr. C. Li, Dr. X. Bresson, Dr. D.-J. Kroon, and Dr. T. Goldstein for providing a research source code of the methods. This work was supported by the Ministry for Education, Science and Culture and the European Social Fund (Grant UG 11 035A). MR imaging examinations in SHIP are supported by the Federal Ministry of Education and Research (grant no. 03ZIK012) and a joint grant from Siemens Healthcare, Erlangen, Germany and the Federal State of Mecklenburg West

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An efficient level set method for simultaneous intensity inhomogeneity correction and segmentation of MR images

Highlights

Abstract

Introduction

Section snippets

Related work

Image model

Proposed model with explicit bias field smoothing parameter

Experimental results and discussion

Conclusions and future work

Acknowledgments

Comput Geosci

Comput Biol Med

Exp Syst Appl

Magn Reson Imaging

Comput Vis Image Underst

Pattern Recogn Lett

Physica D

Magn Reson Imaging

Neuroimage

Magn Reson Imaging

A modified fuzzy C-Means algorithm for bias field estimation and segmentation of MRI data

IEEE Trans Med Imaging

A short guide on a fast global minimization algorithm for active contour models

Magnetic resonance imaging: physical principles and sequence design

An algorithm for total variation minimization and applications

J Math Imaging Vis

Algorithms for finding global minimizers of image segmentation and denoising models

SIAM J Appl Math

Active contours without edges

IEEE Trans Image Process

A fuzzy C-Means (FCM) based algorithm for intensity inhomogeneity correction and segmentation of MR images

Evaluation of performance metrics for bias field correction in MR brain images

J Magn Reson Imaging

Mean shift: a robust approach toward feature space analysis

IEEE Trans Pattern Anal Mach Intell

Localized FCM clustering with spatial information for medical image segmentation and bias field estimation

J Biomed Imaging

Measures of the amount of ecologic association between species

Ecology

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J Sci Comput

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SIAM J Imaging Sci

Digital image processing

Breast segmentation and density estimation in breast MRI: a fully automatic framework

IEEE J Biomed Health Inform

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Int J Biomed Imaging