In this tutorial we prepare a texture map suitable for rendering to a sphere using Photoshop's Polar Co-ordinates filter.
1/. Left, the orignal texture should be of  2:1 ratio and have the left and right edges tile. The image should now be cropped into a top and bottom half, saving each half as seprate files. Note the bottom half has to be rotated 180 degrees as the polar co-ordinates filter only works from one direction.

2/. Now the top half image is resized horizontaly to make it square, the hieght now matching the original width.

3/. Apply the polar co-ordinates filter, with 'Rectangular to Polar' button checked. The filter has compressed the upper edge of the image down to meet in the center.

4/.  Here, a roughly circular area has been taken from the original picture in 1/. and pasted as a layer. This should be large enough to cover the central, over pinched, area

5/. Use the eraser tool to rub away the edges to blend the layer in with the image below. You might need to use other tools like the smudge tool as well, depending on the individual picture.

6/. When happy with the blend the layer can be merged down and the polar co-ordinates filter applied again. This time however use the 'Polar to Rectangular' option.

7/. Next the image should now be resized back to its original size. Now you will need to repeat the whole operation again for the other half. Remember to rotate the lower half back again when finished.

8/. Finally the two halves can be rejoined as above.

9/. When rendered to a sphere the difference can be clearly seen here with our treated map on the right.