The osteophyte shows only on some particular locations on the vertebra. This indicates that other locations on the vertebra shape contain that are not of interest hinder the spine x-ray image retrieval relevance precision, which motivates our research in partial shape matching (PSM). This paper presents PSM methods for matching shapes with variable number of points and with different data point distributions. Dynamic Programming (DP) is proposed for matching partial shapes by allowing merging of the data points in the process of PSM. DP is implemented based on two shape representation methods: line segments and multiple open triangles. The performance evaluation, which is based on human relevance judgements of these two shape representations in PSM is also presented.