CartToPolar and PolarToCart

The functions cvCartToPolar() and cvPolarToCart() are employed by more complex routines such as cvLogPolar() (described later) but are also useful in their own right. These functions map numbers back and forth between a Cartesian (x, y) space and a polar or radial (r, θ) space (i.e., from Cartesian to polar coordinates and vice versa). The function formats are as follows:

void cvCartToPolar(
  const CvArr* x,
  const CvArr* y,
  CvArr*       magnitude,
  CvArr*       angle            = NULL,
  int          angle_in_degrees = 0
);
void cvPolarToCart(
  const CvArr* magnitude,
  const CvArr* angle,
  CvArr*       x,
  CvArr*       y,
  int angle_in_degrees = 0
);

Figure 6-14. Perspective and affine mapping of an image

In each of these functions, the first two two-dimensional arrays or images are the input and the second two are the outputs. If an output pointer is set to NULL then it will not be computed. The requirements on these arrays are that they be float or doubles and matching (size, number of channels, and type). The last parameter specifies whether we are working with angles in degrees (0, 360) or in radians (0, 2π).

For an example of where you might use this function, suppose you have already taken the x- and y-derivatives of an image, either by using cvSobel() or by using convolution functions via cvDFT() or cvFilter2D(). If you stored the x-derivatives in an image dx_img and the y-derivatives in dy_img, you could now create an edge-angle recognition histogram. That is, you could then collect all the angles provided the magnitude or strength of the edge pixel to some desired threshold. To calculate this, we create two destination images of the same type (integer or float) as the derivative images and call them img_mag and img_angle. If you want the result to be given in degrees, then you would use the function cvCartToPolar( dx_img, dy_img, img_mag, img_angle, 1 ). We would then fill the histogram from img_angle as long as the corresponding "pixel" in img_mag is above our desired threshold.