The Alignment of Arbitrary Contours Using Area Difference Distance Measurement

Advancements in medical imaging have allowed for analyzing the anatomy of the human body without the risks of surgery. One can use the methods in this paper to determine the health of a patient’s brain or heart by comparing the anatomical contour to its ideal shape. Registration is an approach towards imaging which determines an optimal alignment between multiple images. In particular, the Area Difference Distance measurement is applied towards image registration to numerically determine an optimal alignment between arbitrary contours. The purpose of this paper is to propose the proof that the Area Difference Distance measurement[4] is a metric, illustrate optimal alignment using the Area Difference Procrustes method[2], and to show numerical simulations. This distance function takes into account two sets containing data points which represent their respective contours. The Area Difference Procrustes method is applied by aligning the arbitrary contour to a fixed contour. This optimal alignment requires minimizing the distance function in terms of rotating, scaling, and translating the arbitrary contour. The succeeding proof presented validates that these values, which optimize the distance between two contours, can be found with the sets of data points representing each contour. Once aligned, we can calculate the optimal Area Difference Distance between the contours. Through the use of MATLAB, synthetic data is applied to test the effectiveness of the optimization of the Area Difference Distance measurement.