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Related Concept Videos

Convolution Properties II01:17

Convolution Properties II

176
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...
176
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

236
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...
236
Convolution Properties I01:20

Convolution Properties I

142
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:
142

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Optimisation of Convolution-Based Image Lightness Processing.

D Andrew Rowlands1, Graham D Finlayson1

  • 1Colour & Imaging Lab, School of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UK.

Journal of Imaging
|August 28, 2024
PubMed
Summary
This summary is machine-generated.

A new statistical approach to convolutional retinex objectively mitigates image shading using autocorrelation statistics. This method optimizes filters in closed form, improving image processing without subjective enhancements.

Keywords:
convolution filterleast squares optimisationlightnessretinex

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Area of Science:

  • Computer Vision
  • Image Processing
  • Statistical Modeling

Background:

  • Convolutional retinex methods use center/surround operators to reduce shading and dynamic range.
  • Existing methods often tune parameters for visual appeal and include enhancement functions like logarithmic mapping.

Purpose of the Study:

  • To introduce and detail a statistical approach to convolutional retinex based on autocorrelation statistics.
  • To objectively mitigate shading without subjective image enhancement components.

Main Methods:

  • Modeling autocorrelation matrices for image albedo and shading.
  • Solving a linear regression to obtain optimal filters in closed form.
  • Analyzing the impact of autocorrelation matrix shape on optimal filter shape.

Main Results:

  • The statistical approach yields an objectively optimal filter.
  • Demonstrated effectiveness in shading removal from text documents.
  • Validated performance on a challenging image dataset.

Conclusions:

  • The statistical convolutional retinex method provides an objective approach to shading mitigation.
  • Autocorrelation statistics are crucial in determining optimal filter characteristics.
  • The method shows promise for various image processing applications, including document analysis.