Conversion at constant angle

The course is carried out on rays that cross in the center of the eye.

General description:

Description of the methods:

= > Conversion = > 

Then, we need an approximation in order to restore, their initial aspect of unit squares. The choice of a method of conversion corresponds to the choice of an approximation.
 

• 1st method: Whole part.

Simplest. No approximation. The polar coordinates are transformed into rectangular directly. We keeps only the whole part of these coordinates. No interpolation.

• 2nd method: Local approximation.

We collects the values of the close points. Then, we use a linear approximation :
       Ex: Value with 22.4 = >
                                       0.4 * value of the item 22
                                    + 0.6 * value of the item 23.

This method is extensible in the plan, the values of 4 points (and not 2) are then used.

• 3rd method: Interpolations.

The transform is identical to the first method (one can also use the 2nd method). It is followed of an interpolation 1D (or 2D). This corresponds to has a resampling, where the missing values are deduced by interpolation.

Comparison of the methods:

	Transformation with method 1: Whole part. With 200x200, the " pixellized " aspect is not very visible (except on the top of the image).  The colors used here are used to emphasize the details and do not represent the average variations (present in dark blue).  Realized with pol2rec2, option 1: Truncation
	Transformation with method 2: Local approximation.  The approximation is significant and gives the aspect of blur to the whole of the image. However, the number of columns is the half, which makes the image more approximate.  It does not seem to have losses, the contour of the details is fuzzy but the details (including smallest) remain present.  Realized with pol2rec2, option 2: Approximation
	Transformation with method 3: Unidimensional interpolation (according to the columns) cubic.  The vertical features, in bottom of the image are due to a bad redimensioning. The visible " waves " in top of the image, are due to the cubic aspect of the interpolation.  That gives similar result with the 1st method. The details are finer and more precise. The image appears clearer.  Realized with pol2rec2, option 6: Cubic interpolation

If the methods with interpolation can appear better, it should be considered that the computing time is more significant and a simple transformation can be enough.