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Areas Within Irregular Boundaries

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Calculating areas within irregular boundaries, such as along rivers or curved roads, is crucial in various fields, including surveying, engineering, and environmental management. Surveyors often begin by creating a traverse, a connected series of straight lines approximating the area's boundary. The coordinates of each traverse point are essential for calculating the enclosed area. The double meridian distance formula is a widely used technique for this purpose. This method utilizes the...

State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Transfer Function to State Space

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
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Related Experiment Video

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In vitro Synthesis of Native, Fibrous Long Spacing and Segmental Long Spacing Collagen

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Published on: September 20, 2012

Optimal surface segmentation with convex priors in irregularly sampled space.

Abhay Shah¹, Michael D Abámoff², Xiaodong Wu³

¹Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, 52242, USA.

Medical Image Analysis

|March 6, 2019

Summary

This study introduces a generalized graph-based method for medical image segmentation, achieving subvoxel accuracy by utilizing partial volume information. The enhanced approach enables non-equidistant node spacing for superior surface segmentation in volumetric datasets.

Keywords:

Convex smoothness constraints Graph search Image segmentation Intravascular ultrasound (IVUS)Irregularly sampled Minimum s-t cut Optical coherence tomography (OCT)Optimal surface Retina Subvoxel

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Area of Science:

Medical image analysis
Computer vision
Computational anatomy

Background:

Optimal surface segmentation methods typically use uniformly distributed voxels, limiting accuracy to unit voxel resolution.
Existing graph-based methods struggle with irregularly sampled data and achieving subvoxel precision.

Purpose of the Study:

To develop a generalized graph-based multiple surface segmentation method for achieving subvoxel accuracy.
To enable segmentation in irregularly sampled spaces by exploiting partial volume information.

Main Methods:

A generalized graph-based method with convex priors for multiple surface segmentation.
Utilizing partial volume information to compute a displacement field for subvoxel-accurate centers.
Employing an edge-based graph representation and minimum s-t cut for global optimization.

Main Results:

Achieved subvoxel segmentation accuracy by allowing non-equidistant spacing between graph nodes.
Validated on 10 intravascular multi-frame ultrasound image datasets, yielding highly accurate results.
Demonstrated the method's capability to handle irregularly sampled spaces.

Conclusions:

The proposed method significantly enhances surface segmentation accuracy beyond unit voxel resolution.
The approach effectively utilizes partial volume information for precise localization of surfaces.
The generalized method is robust, accurate, and extensible to higher-dimensional segmentation problems.