In this paper, we introduce a method of extracting and comparing geometric structures within images for content based query-by-sketch image retrievals. These structures are modeled by a set of curvelets, i.e., line segments, circular arcs, and higher degree implicit polynomials (IPs). A similarity computation based on this geometric representation is also introduced. It is more robust and tolerant towards distortions in query sketches. We show experiment results for the image query applications where inaccurate or only partial sketch information is provided for the search.