Discrete Convolution For Image Processing.

Several tasks associated with Image Processing can be procured by using discrete convolution. A 2- D digital filter (a discrete finite convolution) acts on an image, this is, a 3x3 (or 5x5) mask is stepped throughout the entire image (the coefficients can be variable). Each pixel colour is replaced by a weighted sum of the neighbouring pixels' colours, taking care not to overwrite pixel values before they are used in all calculations involved. If any of the coefficients are negative, you may have to adjust some of the results, to make sure all the output values lie within the availiable colour range.






A first attempt at edge detection is shown, including a scaled, low- resolution copy of the unprocessed image, for reference.
First attempt at Edge Detection


High- Pass mask:

-1-1-1
-1 9-1
-1-1-1

Low- Pass Filter:

1/161/161/16
1/161/21/16
1/161/161/16

Edge- Detector (as in the image above:)

-1-1-1
-1 8-1
-1-1-1

Strictly speaking, convolution is defined as the time integral from negative infinity to time t1 of the product of two signals, v1(t).v2(t1-t), where one of the signals has been folded and delayed by an amount of time t1; t1 is a constant as far as the integration is concerned.You are really interested in the value of the convolution for different values of t1. However, for digital signal processing, you are more likely to calculate a finite and discrete version.

The following image is intended to demonstrate that quite a lot of texture information can be retained in a binary (two- tone black- and- white) image, if the threshold is chosen well enough:


Electronics links:

  • Simplified Analog Electronics Simulation
  • Data converters
  • Video Digitizer
  • Thermionic valves look like depletion nMOS
  • Transient response
  • Under 50- chip discrete Microcontroller
  • 2x OverSampling Digital Filter Click Here!
  • More Simulation: Finite Elements For electrostatic Field Computation

    Computing Projects:
  • Computer Chess
  • Fractals! Click here!
  • Discrete Correlation
  • RLE For Image Compression
  • Newton's Method For Complex Polynomials

  • Non- frames version

    The distinction is rather loose: Most of the electronics sections involve use of a computer to some extent, and vice versa. 1