Gradient




In short, gradient is a measure for changes of the color intensity of an image. Of course, it does not have to be limited to 2-D images and it can be applied to any n-D functions. For the general definition, see wikipedia > Gradient.

For a 2-D function, the gradient can be computed using the given formula on the right. The formula simply asks for the rate of changes in the x direction (i) and the rate of changes in the y direction (j).

In my project, I followed the algorithm given in MathWorks > Gradient. The general idea is to calculate the gradient horizontally and vertically:

  1. Horizontal gradient
    1. internal pixels:
      • G[i][j] = (m[i+1][j] + m[i-1][j]) * 0.5
    2. pixels along the edges
      • G[i][j] = m[i+1][j] + m[i][j] <<< on the left edge
      • G[i][j] = m[i-1][j] + m[i][j] <<< on the right edge
  2. Vertical gradient
    1. internal pixels:
      • G[i][j] = (m[i][j+1] + m[i][j-1]) * 0.5
    2. pixels along the edges:
      • G[i][j] = m[i][j+1] + m[i][j] <<< on the bottom edge
      • G[i][j] = m[i][j-1] + m[i][j] <<< on the top edge

Code

The output of my Gradient filter is:

  • gradientCalculator.calculateGradientCart(image);
      • double[][] gx: Horizontal gradient
      • double[][] gy: Vertical gradient
  • gradientCalculator.calculateGradientPolar(image);
      • double[][] gx: angles of gradient vectors
      • double[][] gy: Magnitude of gradient vectors

Original 4096-by-4096 SDO image

Horizontal Gradient

Vertical Gradient

Angles of Gradient (theta)

Magnitudes of Gradient (radius) [Increased contrast for visualization]