Related Experiment Video
Updated: May 29, 2026
13:44
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
An optimal frequency domain filter for edge detection in digital pictures
K S Shanmugam1, F M Dickey, J A Green
1SENIOR MEMBER, IEEE, Department of Electrical Engineering, Wichita State University, Wichita, KS 67208.
IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
Summary
This study introduces an optimal spatial frequency domain filter for edge detection in digital images. The proposed filter maximizes energy within a resolution interval, effectively enhancing noisy and blurred edges.
Area of Science:
- Image Processing
- Digital Signal Processing
Background:
- Edge detection and enhancement are crucial in image processing.
- Existing methods face challenges with noisy and blurred image data.
Purpose of the Study:
- To optimize spatial frequency domain filters for edge detection in digital images.
- To develop a filter that maximizes energy within a specified resolution interval near edges.
Main Methods:
- Derivation of the filter transfer function in the continuous case using prolate spheroidal wave functions.
- Specification of the discrete case filter using sampled prolate spheroidal wave functions or their asymptotic approximation.
- Implementation of both filter versions using the fast Fourier transform (FFT).
Main Results:
- The derived filter transfer function is specified by prolate spheroidal wave functions.
- The filter can be efficiently implemented using the fast Fourier transform (FFT).
- The optimum filter demonstrates high effectiveness in detecting blurred and noisy edges.
Conclusions:
- The proposed optimum filter provides superior performance for edge detection, particularly in challenging image conditions.
- The filter's design based on prolate spheroidal wave functions offers a robust approach to edge enhancement.
- Comparison with other filters indicates the effectiveness of the optimized spatial frequency domain approach.
Related Concept Videos
01:22Upsampling
Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
01:18Aliasing
Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
01:10Reconstruction of Signal using Interpolation
Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...
01:26Linear 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.
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.
01:15Discrete 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...
01:10Fast Fourier Transform
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
The computational efficiency of the FFT becomes...