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Related Concept Videos

Convolution Properties II01:17

Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
Deconvolution01:20

Deconvolution

Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
Convolution Properties I01:20

Convolution Properties I

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:

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Related Experiment Video

Updated: May 23, 2026

Measuring the Shape and Size of Activated Sludge Particles Immobilized in Agar with an Open Source Software Pipeline
09:27

Measuring the Shape and Size of Activated Sludge Particles Immobilized in Agar with an Open Source Software Pipeline

Published on: January 30, 2019

Robust interactive image segmentation using convex active contours.

Thi Nhat Anh Nguyen, Jianfei Cai, Juyong Zhang

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |March 29, 2012
    PubMed
    Summary

    This study introduces a new interactive image segmentation method using a continuous-domain convex active contour model. The robust algorithm accurately segments images with minimal user input, outperforming existing methods.

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    Area of Science:

    • Computer Vision
    • Image Processing
    • Computational Geometry

    Background:

    • Current interactive image segmentation algorithms are sensitive to user input, requiring extensive manual refinement.
    • Existing methods often struggle to achieve accurate segmentation boundaries with limited user interaction.

    Purpose of the Study:

    • To develop a robust and accurate interactive image segmentation method.
    • To overcome the limitations of state-of-the-art algorithms regarding user input sensitivity and boundary refinement.

    Main Methods:

    • Utilized a recently developed continuous-domain convex active contour model.
    • Implemented an interactive approach for image segmentation.

    Main Results:

    • The proposed method demonstrates robustness to user inputs and various initializations.
    • Achieved smooth and accurate boundary contours, effectively handling topological changes.
    • Outperformed existing state-of-the-art interactive image segmentation algorithms on a benchmark dataset.

    Conclusions:

    • The proposed continuous-domain convex active contour model offers a superior interactive image segmentation solution.
    • The method provides an effective and efficient alternative for accurate image segmentation tasks.