Fuzzy Distance Transform for Trabecular Bone Thickness Measurement
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Solution Overview
Problem
Current methods for measuring trabecular bone thickness in low-resolution images, such as those from MRI and CT scans, face challenges due to partial volume blurring, which renders existing techniques ineffective for fuzzy images, necessitating a method that can segment and accurately measure structural thickness without relying on high-resolution segmentation.
Innovation Solution
The development of a dynamic programming-based algorithm for computing fuzzy distance transforms (FDT) in digital images, which extends the concept of distance transforms to fuzzy objects, allowing for the extraction of structural thickness from low-resolution images by considering membership values along paths, thus providing a robust and reproducible method for trabecular bone thickness measurement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional distance transform methods are used on low-resolution images, then computational simplicity is maintained, but measurement precision deteriorates due to partial volume blurring and fuzzy object boundaries
Solution Approach 1:
The patent transforms the binary distance transform into a fuzzy distance transform by changing the parameter representation from binary (0 or 1) to continuous membership values (0 to 1). This allows the algorithm to handle partial volume effects and fuzzy boundaries by computing distances weighted by membership values, thereby improving measurement precision in low-resolution images without requiring higher image resolution
Solution Approach 2:
The patent introduces membership values as an intermediary element between the binary object representation and the distance computation. These membership values serve as weights that mediate the distance calculation, allowing the algorithm to account for uncertain boundaries and partial volume effects while maintaining computational feasibility through dynamic programming
2Measurement precision
If image resolution is increased to reduce partial volume blurring, then measurement precision improves, but imaging time and resource requirements increase
Solution Approach 1:
The patent changes the parameter of image representation from high-resolution binary data to low-resolution fuzzy data with membership values. By working directly with the fuzzy membership information already present in low-resolution images, the method achieves accurate thickness measurements without requiring time-consuming high-resolution imaging
Solution Approach 2:
The patent creates a fuzzy representation copy of the object that preserves boundary information through membership values rather than requiring a high-resolution physical copy. This fuzzy copy contains sufficient information for accurate measurement while being computationally more efficient than processing high-resolution data
3Measurement precision
If segmentation is performed to isolate structures before measurement, then measurement accuracy improves, but device complexity and processing time increase
Solution Approach 1:
The patent extracts the essential measurement information (thickness) directly from the fuzzy distance transform without requiring separate segmentation steps. By computing the fuzzy distance from all points to the object boundary and then measuring along the skeleton, the method extracts thickness information directly, eliminating complex segmentation procedures
Solution Approach 2:
The fuzzy distance transform serves multiple functions simultaneously: it performs boundary detection, distance computation, and thickness measurement in a unified framework. This multi-functional approach eliminates the need for separate segmentation and measurement steps, reducing overall system complexity while maintaining measurement precision
Data Source
AI summary
Provided are fuzzy distance transform-based methods, and an algorithm therefor, for analyzing digital images defining a volumetric region of an object from a digital image comprising finding a set of points in the image to generate a fuzzy subset, and calculating the fuzzy distance transform (FDT) of the fuzzy subset. The methods deal with the extraction of object features from digital images acquired at low resolution, specifically, the measurement of structural thickness distribution along an object. Targeted applications comprise, but are not limited to, the measurement of trabecular bone thickness in magnetic resonance or computed tomography images. Also provided are systems and device for utilizing the disclosed methods and algorithm to extract the object features from the digital images.