Abstract
Computer-aided detection of brain lesions from volumetric magnetic resonance imaging (MRI) is in demand for fast and automatic diagnosis of neural diseases. The template-matching technique can provide satisfactory outcome for automatic localization of brain lesions; however, finding the optimal template size that maximizes similarity of the template and the lesion remains challenging. This increases the complexity of the algorithm and the requirement for computational resources, while processing large MRI volumes with three-dimensional (3D) templates. Hence, reducing the computational complexity of template matching is needed. In this paper, we first propose a mathematical framework for computing the normalized cross-correlation coefficient (NCCC) as the similarity measure between the MRI volume and approximated 3D Gaussian template with linear time complexity, {mathbf{mathcal{O}}}left( {{varvec{a}}_{{{varvec{max}}}} {varvec{N}}} right), as opposed to the conventional fast Fourier transform (FFT) based approach with the complexity {mathbf{mathcal{O}}}left( {{varvec{a}}_{{{varvec{max}}}} {varvec{N}}log {varvec{N}}} right), where {varvec{N}} is the number of voxels in the image and {varvec{a}}_{{{varvec{max}}}} is the number of tried template radii. We then propose a mathematical formulation to analytically estimate the optimal template radius for each voxel in the image and compute the NCCC with the location-dependent optimal radius, reducing the complexity to {mathbf{mathcal{O}}}left( {varvec{N}} right). We test our methods on one synthetic and two real multiple-sclerosis databases, and compare their performances in lesion detection with FFT and a state-of-the-art lesion prediction algorithm. We demonstrate through our experiments the efficiency of the proposed methods for brain lesion detection and their comparable performance with existing techniques.
Highlights
We have proposed a new mathematical framework to compute a radius-optimized normalized cross-correlation coefficient (NCCC) similarity measure for 3D template matching, with application for automatic lesion detection
Our alternative way to compute the NCCC exploits the approximation of Gaussian smoothing with multiple convolutions with a box kernel
We further proposed an analytical solution for the template radius that replaces the costly exhaustive search, thereby achieving the computational complexity of O(N), which is not possible with the FFT-based method
Summary
Our goal is to maximize NCCC with respect to both a and X , to accurately localize the lesions. We aimed to determine how accurately the enhancing spheres could be detected with their approximated radii from the respective volumes. The lower DICE in the three detection methods that we tested is mainly attributed to the facts that: (1) we used a single image, (2) we performed no post-processing, (3) we employed no supervision, but most importantly (4) our goal was to detect as opposed to segment the lesion
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