Your description is too unclear. Here are several examples.
What does an image have to do with a sphere? A sphere is a three-dimensional body; an image is a flat picture. What is a 3D axis? An axis is a line; how is it 3D? Orthogonal to what? Or do you mean axes? Most importantly, what does it mean to "define"?Given a black sphere (binary image so black sphere and white background) I need to define a orthogonal 3D axis on it.
Do you mean a plan or a plane?with the point in the middle of the sphere, I make a plan that contains that point and with this plan, I can have the normal vector.
I am not an expert on this, but are you familiar with ways to describe the orientation of a rigid body, such as Euler angles? Do they help?