pgradient

Computes the gradient magnitude and direction.

Synopsis

pgradient halfsize [-m mask] [im_in|-] [im_out1|-] [im_out2|-]

Description

pgradient computes the first derivative of the input image im_in. The result is two grayscale images, where each im_out1's pixel is set to the magnitude value of the gradient at this point and each im_out2's pixel is set to the direction of the gradient.

The gradient magnitude value reflects the amount of grayscale variation in this point. The more is the variation the greater is the value. The magnitude is the maximum between x derivative and y derivative (+ z derivative in 3D). The variation is computed inside a given neighborhood space size specified by the parameter halfsize.

The direction is the atan(dy/dx) follows by a discretization to get values in the freeman codes. So the output image is set with values from [0..7] in 2D and [0..25] in 3D.

Freeman codes are:

   2D:            3D:
                  z-1:		   z:		    z+1:
 1 2 3           2  3  4	10 11 12	 19 20 21
 0   4           1  0  5	9     22	 18 13 14
 7 6 5           8  7  6	25 24 23	 17 16 15

The derivative is computed by convolution with the kernel in all directions and the magnitude is set with the maximum value:

-1, 0, 1

For color images, the Di Zenzo algorithm is used. It is based on the calculus of the eigen-values of the matrix:

  | p t |
  | t q |
où p=gxR*gxR+gxG*gxG+gxB*gxB
où q=gyRy*gyR+gyG*gyG+gyB*gyB
où t=gxR*gyR+gxG*gyG+gxB*gyB

The gradient magnitude is given by:

magnitude=sqrt(lambda1 + lambda2)
with lambda1=1/2 * (p+q + sqrt((p-q)*(p-q)-4*t*t)) 
     lambad2=1/2 * (p+q - sqrt((p-q)*(p-q)-4*tt))

and direction is given by:

direction = 1/2 *arctan (2*t / (p-q))

followed by a discretization according to Freeman encoding.

Parameters

halfsize specifies the half size of the convolution kernel.

Inputs

im_in: an image.

Outputs

im_out1: an image of the same type as im_in.
im_out2: a Uchar image.

Result

Returns SUCCESS or FAILURE.

Examples

Performs an edge detection based on hysteresis threshold:

   pgradient 1 tangram.pan i1.pan i2.pan
   pbinarization 30 1e30 i1.pan i3.pan
   pbinarization 60 1e30 i1.pan i4.pan
   pgeodesicdilation 1 1 -1 i4.pan i3.pan i4.pan
   psuperimposition 1 tangram.pan i4.pan out.pan

C++ prototype

Errc PGradient( const Img2duc &im_in, Img2duc &im_out1, Img2duc &im_out2, int halfsize );

Version française

Calcul du module et de la direction du gradient par convolution.

Author: Régis Clouard