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Related Concept Videos

Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...
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Boundary detection in multidimensions.

J K Udupa1, S N Srihari, G T Herman

  • 1Medical Image Processing Group, Department of Computer Science, State University of New York at Buffalo, Amherst, NY 14226; Medical Image Processing Group, Department of Radiology.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

This study generalizes image processing concepts like adjacency and connectivity to multidimensional spaces for analyzing time-varying and computerized tomography data. Algorithms for boundary detection in these complex spaces are presented and evaluated.

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Area of Science:

  • Computer vision
  • Image processing
  • Computational geometry

Background:

  • Standard image processing relies on 2D/3D concepts.
  • Analyzing dynamic or volumetric data requires higher dimensions.
  • Existing methods lack generalization for multidimensional spaces.

Purpose of the Study:

  • To generalize fundamental image processing concepts (adjacency, connectivity, boundary) to 3D and 4D discrete spaces.
  • To develop and present algorithms for boundary detection in multidimensional image data.
  • To analyze the performance and complexity of these novel algorithms.

Main Methods:

  • Definition of generalized adjacency and connectivity in N-dimensional spaces.
  • Development of boundary detection algorithms for multidimensional discrete spaces.
  • Theoretical complexity analysis and simulation using computerized tomography data.

Main Results:

  • Unified terminology for multidimensional image analysis concepts established.
  • Novel algorithms for boundary detection in 3D and 4D spaces demonstrated.
  • Performance evaluation shows effectiveness with simulated computerized tomography data.

Conclusions:

  • The proposed framework successfully extends image processing concepts to higher dimensions.
  • The developed algorithms provide efficient boundary detection for complex datasets.
  • This work is crucial for advancing image analysis in fields like medical imaging.