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Shape analysis is useful for a wide variety of disciplines and has many applications. There are many approaches to shape analysis, one of which focuses on the analysis of shapes that are represented by the coordinates of predefined landmarks on the object. This paper discusses Tridimensional Regression, a technique that can be used for mapping images and shapes that are represented by sets of three-dimensional landmark coordinates, for comparing and mapping 3D anatomical structures. The degree of similarity between shapes can be quantified using the tridimensional coefficient of determination (R2). An experiment was conducted to evaluate the effectiveness of this technique to correctly match the image of a face with another image of the same face. These results were compared to the R2 values obtained when only two dimensions are used and show that using three dimensions increases the ability to correctly match and discriminate between faces.