Identification and Recovery of Injective Transforms

Image transforms are used extensively in image processing to convert one image form into another form. These transforms are either point-operation transforms or neighborhood-operation transforms. Injective transforms, also known as reversible or one-to-one transforms, are a subset of point-operation transforms where each intensity value maps to a distinct intensity value. In this paper we present a novel technique that can identify if an image was processed by an injective transform. The injective mapping is also recovered in the process. The technique is applicable to both linear and non-linear transforms. We introduce two measures that assess the degree of injective mapping and the degree of functional mapping of the transform. The technique is based on the attributes of the image variation number which is an entropysimilar informative measure. Tests are conducted on real images to show the validity of our technique.