Mid-Sagittal Plane Detection in Brain MRI Using Entropy Optimization
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Solution Overview
Problem
Existing methods for determining the location of the mid-sagittal plane in three-dimensional brain images require a priori information and are time-consuming, orientation-dependent, and limited to small tilts in data.
Innovation Solution
A method that defines volumes of interest in three-dimensional brain images, determines measures such as entropy or energy for slices in these volumes, identifies the sagittal direction, and uses optimization techniques like Nelder-Mead optimization to find the mid-sagittal plane without requiring prior information on slice orientation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If a priori information about slice direction is used to determine the mid-sagittal plane, then the determination process is simplified, but the method becomes orientation-dependent and limited to small tilts in data
Solution Approach 1:
The method enables the system to automatically determine slice orientation and identify the mid-sagittal plane without requiring external a priori information about slice direction. The algorithm self-adapts to the data by computing orientation from the volume itself, making the system autonomous and eliminating the need for manual orientation specification.
Solution Approach 2:
The invention changes the approach from using fixed a priori orientation parameters to dynamically computing orientation parameters from the data. By calculating the normal vector to the mid-sagittal plane from the volume data itself, the method adapts to any orientation and tilt, removing the limitation of small tilts while maintaining computational efficiency.
2Measurement precision
If traditional symmetry-based methods are used to find the mid-sagittal plane, then the method is theoretically sound, but it becomes time-consuming due to exhaustive search through all possible planes
Solution Approach 1:
The method performs preliminary computation by directly calculating the mid-sagittal plane from the volume data using a closed-form solution based on symmetry principles. Instead of exhaustively searching through all possible planes, the algorithm computes the optimal plane in a single step, eliminating the time-consuming iterative search while preserving the theoretical accuracy of symmetry-based methods.
Solution Approach 2:
The invention replaces the mechanical exhaustive search process with a mathematical closed-form solution. By substituting the iterative mechanical search through all possible planes with a direct computational formula that calculates the mid-sagittal plane from symmetry properties of the volume data, the method achieves both precision and efficiency.
3Ease of manufacture
If the interhemispheric fissure is segmented and used as a landmark, then the mid-sagittal plane can be determined using orthogonal regression, but the method requires the fissure to be clearly visible and planar
Solution Approach 1:
The method provides a universal approach that works regardless of the visibility or clarity of the interhemispheric fissure. By using symmetry properties of the entire brain volume rather than relying on specific anatomical landmarks, the algorithm can determine the mid-sagittal plane in cases where the fissure is not clearly visible, is curved, or shows anatomical variations, thereby achieving greater reliability and robustness.
Data Source
AI summary
Volumes of interest may be defined, within a three-dimensional brain image, for each of three orthogonal directions. Measures, which may, for example, be energy or entropy measures, are determined for slices of the volumes of interest in the three directions. The volume of interest corresponding to the sagittal direction is then identified. The slice, among the slices in the volume of interest corresponding to the identified sagittal direction, having the optical measure is used to define a first estimate of the mid-sagittal plane. The first estimate of the mid-sagittal plane may then be used to build an input to an optimization technique, which operates until a convergence criterion is satisfied, at which point a final estimate of the mid-sagittal plane may be produced.125