C++ :: Design Image Class Which Should Work With Various Data Types (Multidimensional)

I have been thinking about this all day and I am yet to come up with a good solution. So, I need to design an image class which should work with various data types (int, float, double etc.) and can also be multidimensional (2, 3, 4, 5). So, what I did was generate a template image class as follows:

Code:
template<typename T, int dimensions=3>
class Image {
private:
T * data;
};

Anyway, now I have various image formats that I want to support, so the easy thing to do is create a Factory sort of object which will call eventually generate the correct image.

So I want to create various image classes called ImageType1, ImageType2 etc. which will take the input image and generate the correct Image object. However, I do not want these objects to be templated because they need to be passed from functions and be used in a generic way.

So, at run time I will need to be able to do this…

Code:
class ImageType {
public:
ImageType() {
PolymorphicImage * image = new Image<float, 3>();
}
private:
PolymorphicImage * image;
};

So, I want my ImageType classes to contain the Image object and be able to generate it with the right template arguments at run time. Is there any way to do this without having multiple specialised definitions for ImageType?