Near regular textures are pervasive in man-made and natural world. Their global regularity and local randomness pose new difficulties to the state of the art texture analysis and synthesis algorithms. We carry out a systematic comparison study on the performance of four texture synthesis algorithms on near-regular textures. Our results confirm that faithful near-regular texture synthesis remains a challenging problem for the state of the art general purpose texture synthesis algorithms. In addition, we provide comparison of human perception with computer evaluations on the quality of the texture synthesis results.