To determine the thickness from MR images, segmentation, that is, boundary detection, of the two adjacent thin structures (e.g., femoral cartilage and acetabular cartilage in the hip joint) is needed before thickness determination. Traditional techniques such as zero-crossings of the second derivatives are not suitable for the detection of these boundaries. A theoretical simulation analysis reveals that the zero-crossing method yields considerable biases in boundary detection and thickness measurement of the two adjacent thin structures from MR images. This paper studies the accurate detection of hip cartilage boundaries in the image plane, and a new method based on a model of the MR imaging process is proposed for this application. Based on the newly developed model, a hip cartilage boundary detection algorithm is developed. The in-plane thickness is computed based on the boundaries detected using the proposed algorithm. In order to correct the image plane thickness for overestimation due to oblique slicing, a three-dimensional (3-D) thickness computation approach is introduced. Experimental results show that the thickness measurement obtained by the new thickness computation approach is more accurate than that obtained by the existing thickness computation approaches.