In order to improve the discrimination ability and robustness of contour noise and deformation of Height Functions (HF) descriptor in the process of shape retrieval, a feature description algorithm of exact height functions is proposed in shape retrieval. Firstly, contour outside the target shape is extracted, and then exact height functions type descriptors of sampling points are constructed for dimensionality reduction. And then, the optimized parallel dynamic programming algorithm is employed in matching stage. Finally, shape complexity analysis is used to improve matching effect. Based on point geometric feature saliency, the shape precision theory is proposed to further analyze the influence of the local deformation and the edge noise on shape feature description. The matching experiment has been conducted on the database of MPEG-7, Swedish Leaf, Tools, ETH-80 and noise experiment has been conducted on Kimia99 database. Experimental results indicate that the proposed algorithm in this paper is highly efficient and the matching time of it is only 12.5% of the original HF descriptor. The highest retrieval ratio can reach 90.38% on MPEG-7, 9007% on ETH-80, 95.07% on Swedish Leaf and 94.86% on Tools respectively and retrieval performance and robustness are better than HF and other important algorithms; on Kimia99 with adding noise, the anti-noise performance of the proposed algorithm is superior to the original HF descriptor, and even in the case of noise level of 2.0, the algorithm can still keep a retrieval rate of 91.92%. The proposed algorithm, with high accuracy, high efficiency, great robustness and noise immunity and good scalability, can be effectively applied to shape retrieval field.