Following is a tutorial on how I produced spherical pictures. I use Photoshop so I`m not sure how, or if this is possible in other photo manipulation packages.

Start with your picture open

First I use canvas size to resize the image to a square format. Play around with the sizing to suit the picture. I use Image>Canvas size >set to 35cm x 35cm for this image. Change the values to suit

With the image active I use the slice tool and make a square selection within the picture.

I select slice tool>fixed size. Set the sizes to typically 25cmx25cm for this picture ( play with these sizes to suit image

Now drag a square over your selected part of the picture.

Then, with my square selection active, I click on Filter>Distort >Polar Coordinates.
Then I clicked on the Polar to Rectangular and click ok
This is the result;

Next, I went to the Image>rotate canvas>180
Now it looks like this

Now go back to the Filter>Distort>polar coordinates and this time select Rectangular to Polar

Click OK and thats it! This is the final picture.

Now you can crop and enhance as much as you desire. Dont forget to save it as with a different file name.