LOG Transformation:

It is mathematically defined as, S=C log(1+r) where C is any constant and r, s are input and output pixel values. LOG transform enhances small magnitude input values into wider range of output pixel values and compresses large magnitude input values into narrow range of output values. It is useful to display Fourier Transformed images, The drawback for this transform is that the transformation function is fixed and cannot be changed as per requirement. Graphically the transform is represented as:

Power Law Transformation:

1. It is mathematically defined as s=$cr^ɣ$ where c is any constant and r, s are normalized input and output pixel values.
2. Let c=1 then s=$r^ɣ$

Power law transform overcomes the limitation of LOG transform by changing the value of ɣ we can get different transformation function.