- DIP - Computer Vision and Graphics
- DIP - Optical Character Recognition
- DIP - JPEG compression
- DIP - Introduction to Color Spaces
- DIP - High Pass vs Low Pass Filters
- DIP - Convolution theorm
- DIP - Fourier series and Transform
- DIP - Frequency Domain Analysis
- DIP - Laplacian Operator
- DIP - Krisch Compass Mask
- DIP - Robinson Compass Mask
- DIP - Sobel operator
- DIP - Prewitt Operator
- DIP - Concept of Edge Detection
- DIP - Concept of Blurring
- DIP - Concept of Masks
- DIP - Concept of convolution
- DIP - Gray Level Transformations
- DIP - Histogram Equalization
- DIP - Introduction to Probability
- DIP - Histogram Stretching
- DIP - Histogram Sliding
- DIP - Image Transformations
- DIP - Brightness and Contrast
- DIP - Histograms Introduction
- DIP - Concept of Dithering
- DIP - ISO Preference curves
- DIP - Concept of Quantization
- DIP - Gray Level Resolution
- DIP - Pixels Dots and Lines per inch
- DIP - Spatial Resolution
- DIP - Zooming methods
- DIP - Concept of Zooming
- DIP - Pixel Resolution
- DIP - Concept of Sampling
- DIP - Grayscale to RGB Conversion
- DIP - Color Codes Conversion
- DIP - Types of Images
- DIP - Concept of Bits Per Pixel
- DIP - Perspective Transformation
- DIP - Concept of Pixel
- DIP - Camera Mechanism
- DIP - Image Formation on Camera
- DIP - Concept of Dimensions
- DIP - Applications and Usage
- DIP - History of Photography
- DIP - Signal and System Introduction
- DIP - Image Processing Introduction
- DIP - Home
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Convolution Theorem
In the last tutorial, we discussed about the images in frequency domain. In this tutorial, we are going to define a relationship between frequency domain and the images(spatial domain).
For example
Consider this example.
The same image in the frequency domain can be represented as.
Now what’s the relationship between image or spatial domain and frequency domain. This relationship can be explained by a theorem which is called as Convolution theorem.
Convolution Theorem
The relationship between the spatial domain and the frequency domain can be estabpshed by convolution theorem.
The convolution theorem can be represented as.
It can be stated as the convolution in spatial domain is equal to filtering in frequency domain and vice versa.
The filtering in frequency domain can be represented as following:
The steps in filtering are given below.
At first step we have to do some pre – processing an image in spatial domain, means increase its contrast or brightness
Then we will take discrete Fourier transform of the image
Then we will center the discrete Fourier transform, as we will bring the discrete Fourier transform in center from corners
Then we will apply filtering, means we will multiply the Fourier transform by a filter function
Then we will again shift the DFT from center to the corners
Last step would be take to inverse discrete Fourier transform, to bring the result back from frequency domain to spatial domain
And this step of post processing is optional, just pke pre processing , in which we just increase the appearance of image.
Filters
The concept of filter in frequency domain is same as the concept of a mask in convolution.
After converting an image to frequency domain, some filters are appped in filtering process to perform different kind of processing on an image. The processing include blurring an image, sharpening an image e.t.c.
The common type of filters for these purposes are:
Ideal high pass filter
Ideal low pass filter
Gaussian high pass filter
Gaussian low pass filter
In the next tutorial, we will discuss about filter in detail.
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