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Abstract::We present a novel approach to 3D object recognition by using 3D orthonormal moments of a given 3D shape in order to find the pose of the object in a scene. This is an attempt to solve the problem of 3D object recognition by using only the available 3D representation of the object. The problem we are addressing is that of finding the pose of an unknown 3D shape in a scene, consisting of a number of known 3D shapes. An important motivation to address this problem comes from the need to quickly recognize 3D shapes encountered in medical images. Once the pose of the unknown shape is found, its 3D shape can be easily recognized by matching the moments of the unknown shape to the ones of known shapes. To find the pose of the unknown shape, we use a previously defined tensor that gathers and organizes the projections of a 3D shape from different points of view. The shape is therefore represented by an orthonormal vector of moments, lying on a plane of the tensor. The moments are arranged in a square tensor that can be computed off-line, and the pose of the shape is found by a simple two-step process. In the first step, the moments are arranged in a matrix that is used to solve a linear least squares problem, where the unknown shape has to be inserted. Once the pose of the object is found, the shape is recognized by matching the moments of the known object. This method is the natural extension of the PLACONEX 3D shape search engine , where a query shape is inserted and a position is found in order to guide the user to the object. The ability of this method for 3D object recognition is analytically proved, showing that it does not rely on experimental work to apply a generic technique to these problems. However, an additional strength of the algorithm is its easy implementation. Three different kinds of experiments have been conducted in order to perform a thorough validation of the proposed approach: recognition and pose estimation under z axis (yaw) rotations, the same estimation but with the addition of y axis rotations (pitch), and estimation of the pose of objects in real images downloaded from the Internet. In all these cases, results are encouraging, at a similar level to those of state-of-the art algorithms.

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