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Related Concept Videos

Discrete Fourier Transform01:15

Discrete Fourier Transform

The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
Relation of DFT to z-Transform01:20

Relation of DFT to z-Transform

The Discrete Fourier Transform (DFT) is a crucial tool for analyzing the frequency content of discrete-time signals. It converts a sequence of N samples from the time domain into its corresponding sequence in the frequency domain, where each sample represents a specific frequency component.
To understand how the DFT works, it's helpful to consider the z-transform, which is a method for representing discrete sequences in the complex frequency domain. The z-transform involves summing the terms of...
IR Frequency Region: Fingerprint Region01:03

IR Frequency Region: Fingerprint Region

IR spectra are divided into two main regions: the diagnostic region and the fingerprint region. The diagnostic region of the spectrum lies above 1500 cm−1. The absorptions resulting from single-bond vibrations of the N–H, C–H, and O–H stretch at higher wavenumbers and appear on the left side of the spectrum. The stretching absorptions of the C≡C and C≡N occur between 2100–2300 cm−1. In contrast, those arising from stretching absorptions of the C=O, C=N, and C=C occur between 1600–1850 cm−1.
The...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

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

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Published on: August 30, 2013

Entropy-based texture analysis in the spatial frequency domain.

M E Jernigan1, F D'Astous

  • 1Department of Systems Design, University of Waterloo, Waterloo, Ont., Canada N2L 3G1.

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

This study introduces regional entropy measures for texture discrimination, offering new information beyond traditional methods. These entropy features demonstrate comparable performance to existing techniques and are invariant to subimage size.

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Area of Science:

  • Image analysis
  • Texture analysis
  • Digital signal processing

Background:

  • Texture discrimination is crucial for image analysis.
  • Traditional methods often rely on summed energy or gray-level co-occurrence matrices.
  • Existing features may not capture all relevant texture information.

Purpose of the Study:

  • To present a novel approach for texture discrimination using regional entropy measures in the spatial frequency domain.
  • To demonstrate that these measures provide unique discriminating information.
  • To ensure the developed measures are robust and comparable to existing methods.

Main Methods:

  • Utilizing regional entropy in the spatial frequency domain for texture analysis.
  • Calculating texture discriminating information independent of summed energy features.
  • Employing a between-to-within-class scatter criterion for performance evaluation.
  • Introducing a frequency scaling method for subimage size invariance.

Main Results:

  • Regional entropy measures provide texture discriminating information distinct from traditional frequency domain features.
  • The performance of entropy features is comparable to traditional frequency domain and gray-level co-occurrence contrast features.
  • A frequency scaling method allows for size-invariant texture comparisons.

Conclusions:

  • Regional entropy measures offer a valuable addition to texture discrimination techniques.
  • The proposed method is robust and performs comparably to established approaches.
  • The size-invariant nature of the measures enhances their applicability across different image scales.