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Staking out curves is an essential process in construction to ensure the accurate alignment of structures along a curved path. This task involves positioning stakes at calculated locations corresponding to the curve's design, effectively translating plans into physical markers in the field. The process begins by determining the geometric parameters of the curve, including the radius, central angle, and tangent distances. These parameters are critical for identifying key points such as the...
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Curve sketching is a systematic method for understanding the overall behavior of a function by analyzing its key mathematical features. A function defines a curve on the coordinate plane, where the horizontal axis represents the input variable and the vertical axis represents the output. The process begins by determining the domain, which specifies the set of input values for which the function is defined and establishes the horizontal extent of the graph.Intercepts with the horizontal and...
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Understanding the behavior of a function through its first and second derivatives is essential for analyzing its graph. Derivatives provide insight into where a function increases or decreases, where it attains local maxima or minima, and how its curvature behaves across different intervals.The first derivative of a function reveals the slope of the tangent line at any given point. Points where the derivative is zero or undefined are considered critical, as they often indicate potential extrema...
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Updated: Mar 23, 2026

Sit-to-stand-and-walk from 120% Knee Height: A Novel Approach to Assess Dynamic Postural Control Independent of Lead-limb
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Post-processing techniques for making reliable measurements from curve-skeletons.

Robert S Bradley1, Philip J Withers1

  • 1Henry Moseley X-ray Imaging Facility, School of Materials, The University of Manchester, Oxford Road, Manchester M13 9PL, UK.

Computers in Biology and Medicine
|April 2, 2016
PubMed
Summary
This summary is machine-generated.

New methods improve curve-skeleton analysis for biological networks. These techniques enhance accuracy in measuring lengths and thicknesses, making data more robust against imaging noise for applications like bone and tumor analysis.

Keywords:
Computed tomography (CT)Curve skeletonLocal thicknessMedial axis transform (MAT)TortuosityVascular network

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Area of Science:

  • Biomedical Engineering
  • Medical Imaging Analysis
  • Computational Biology

Background:

  • Interconnected 3-D biological networks are common.
  • Curve-skeletons quantify network geometry (e.g., path lengths, tortuosities, thicknesses).
  • Standard curve-skeletons are sensitive to small surface features and imaging noise.

Purpose of the Study:

  • To develop robust post-processing techniques for curve-skeletons.
  • To reduce sensitivity to small-scale surface features in geometric measurements.
  • To introduce a more reliable measure of cross-sectional dimension.

Main Methods:

  • Developed new post-processing techniques for curve-skeletons.
  • Utilized a minimal sphere-network representation for object sampling.
  • Defined a novel 'modal radius' for cross-sectional dimension measurement.
  • Achieved sub-voxel accuracy in measurements.

Main Results:

  • Measurements of lengths and thicknesses are less sensitive to surface noise.
  • The modal radius is more robust than the internal radius for cross-sectional dimension.
  • The techniques effectively quantify geometric parameters of complex networks.
  • Demonstrated application on trabecular bone and tumor vascular networks.

Conclusions:

  • The new techniques provide more reliable quantification of 3-D biological network geometry.
  • These methods improve the robustness of curve-skeleton analysis, particularly with noisy imaging data.
  • The modal radius offers a superior single-measure metric for local structure size.