This paper presents a comparative study of four pattern recognition algorithms which are invariant to translations, rotations, and scale changes of the input object; namely, object shape features (OSF), geometrica fourier mellin transform (GFMT), moment invariants (MI), and centered polar exponential transform (CPET). Pattern description is obviously one of the most important aspects of pattern recognition, which is useful to describe the object shape independently of translation, rotation, or size. We first discuss problems that arise in the conventional invariant pattern recognition algorithms, or size. We first discuss problems that arise in the coventional invariant pattern recognition algorithms, then we analyze their performance using the same criterion. Computer simulations with several distorted images show that the CPET algorithm yields better performance than the other ones.