Importance of shape invariance has been known for a long time however it is somewhat novel approach in machine vision. Invariant theory is not new and many of its principles were introduced in the nineteenth century. Shape descriptors discussed so far depend on viewpoint, meaning that object recognition may often be impossible as a result of changed object or observer position. Machine vision is especially concerned with the class of projective transforms. Collinearity is the simplest example of a projectively invariant image feature.
Any straight line is projected as a straight line under any projective transform.
Similarly, the basic idea of the projection-invariant shape description is to find such shape features that are unaffected by the transform between the object and the image plane. However, the pose must be hypothesized for each object and each image which makes this approach difficult and unreliable. Application of invariant theory , where invariant descriptors can be computed directly from image data without the need for a particular co-ordinate system, represents another approach. Let corresponding entities in two different co-ordinate systems be distinguished by large and small letters. In this definition, w is referred to as the weight of the invariant.