CONVOL Function

Convolves an array with a kernel (or another array).

TIP: When using CONVOL with image data, make sure the data has been first converted to floating-point type.

The kernel parameter is an array whose dimensions describe the size of the neighborhood surrounding the value in array that is analyzed. The kernel also includes values that give a weighting to each point in its array. These weightings determine the average that is the value in the output array. If kernel is not of the same type as array, a copy is made and converted into the same type before being used.

Using the scale_factor parameter allows you to simulate fractional kernel values and avoid overflow with byte parameters.

In many signal and image processing applications, it is useful to center a symmetric kernel over the data, to align the result with the original array. The Center keyword controls the alignment of the kernel with the array and the ordering of the kernel elements.

Sample Usage

In the convolution of any two functions, r(t) and s(t), for most applications function s is typically a signal or data stream, which goes on indefinitely in time, while r is a response function, typically a peaked function that falls to zero in both directions from its maximum.

In terms of CONVOL parameters, s corresponds to array and r corresponds to kernel. The effect of convolution is to smear the signal s(t) in time according to the "recipe" provided by the response function r(t).

One-Dimensional Convolution

For the example below, assume the following equation:

R = CONVOL(A, K, S)

where A is an n-element vector, K is an m-element vector (m n), and S is the scale factor.

If the Center keyword is set to 0, the results are as follows.

Otherwise, R_t = 0.

If the Center keyword is omitted or set to 1, the results are shown as follows.

Otherwise, R_t = 0.

Two-Dimensional Convolution

For the second example, assume the same equation:

R = CONVOL(A, K, S)

where A is an m-by-n element array, K is an l-by-l element kernel, S is the scale factor, and the result R is an m-by-n element array.

If the Center keyword is set to 0, the results are as follows.

Otherwise, R_t,u = 0.

The centered two-dimensional case is similar, except the t -i and u - j subscripts are replaced by t + i - l/2 and u + j - l/2.

Example

This example demonstrates what a 512-by-512 mandrill image looks like before and after applying the CONVOL function. The following parameters were used:

result = CONVOL(mandril_img, kernel, /Center)

where kernel is a 3-by-3 array. This array has the following value:

This kernel value represents a commonly-used algorithm for edge enhancement.

Figure 2-23 The CONVOL function has been used to enhance the edges of this 512-by-512 mandrill image. In other words, after CONVOL is applied, the dark colors change quickly to light ones.

Figure 2-24 The CONVOL function has been used to enhance the edges of this 512-by-512 mandrill image. In other words, after CONVOL is applied, the dark colors change quickly to light ones.

CONVOL Function

Usage

Input Parameters

Returned Value

Keywords

Discussion

Sample Usage

One-Dimensional Convolution

Two-Dimensional Convolution

Example

See Also