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Related Concept Videos

Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
Difference from Background: Limit of Detection01:05

Difference from Background: Limit of Detection

The limit of detection (LOD) is the smallest amount of analyte that can be distinguished from the background noise. The LOD value corresponds to the concentration at which the analyte signal is three times larger than the standard deviation of the blank signal. Below this value, the analyte signal cannot be differentiated from the background noise. It is calculated by dividing the calibration slope by 3 times the standard deviation of the blank signals.
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Range00:59

Range

The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
15.9; 16.1; 15.2; 14.8; 15.8; 15.9; 16.0; 15.5
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Quantifying and Rejecting Outliers: The Grubbs Test01:02

Quantifying and Rejecting Outliers: The Grubbs Test

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Related Experiment Video

Updated: Jun 12, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Edge detecting for range data using Laplacian operators.

Sonya A Coleman, Bryan W Scotney, Shanmugalingam Suganthan

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |May 25, 2010
    PubMed
    Summary

    This study introduces novel Laplacian operators for direct edge detection on irregularly distributed 3D range data. This method is robust to data irregularity and less sensitive to noise compared to traditional intensity image processing.

    Related Experiment Videos

    Last Updated: Jun 12, 2026

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
    13:44

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

    Published on: August 30, 2013

    Area of Science:

    • Computer Vision
    • Image Processing
    • Geometric Data Analysis

    Background:

    • Irregularly distributed data in range images presents challenges for direct image processing, particularly edge detection.
    • Traditional methods often require interpolation to a regular grid, losing information or introducing approximations.
    • Existing direct methods like scan-line approximation do not fully utilize exact data locations.

    Purpose of the Study:

    • To develop and present novel Laplacian operators for direct application to irregularly distributed data.
    • To specifically address the challenge of edge detection in 3D range images with irregular data distributions.
    • To evaluate the performance of these operators across varying levels of data irregularity.

    Main Methods:

    • Development of novel Laplacian operators designed for irregularly sampled data.
    • Application of these operators directly to 3D range data without prior interpolation.
    • Testing across diverse datasets exhibiting different degrees of data distribution irregularity.

    Main Results:

    • The proposed Laplacian operators effectively perform edge detection directly on irregularly distributed 3D range data.
    • The method demonstrates robustness across a spectrum of data distribution irregularities.
    • Laplacian operators applied to range data exhibit significantly lower susceptibility to noise compared to those used on intensity images.

    Conclusions:

    • Novel Laplacian operators provide an effective solution for edge detection in irregularly sampled 3D range data.
    • The approach overcomes limitations of interpolation-based methods and offers improved noise resilience.
    • This work advances direct image processing techniques for complex, real-world range data acquisition scenarios.