We introduce an integrated method for processing depth maps measured by a laser profile sensor. It serves for the recognition and alignment of an object given by a single example. Firstly, we look for potential object contours, mainly using the Retinex filter. Then, we select the actual object boundary via shape comparison based on Triangle Area Representation (TAR). We overcome the limitations of the TAR method by extension of its shape descriptor. That is helpful mainly for objects with symmetric shapes but other asymmetric aspects like squares with asymmetric holes. Finally, we use point-to-point pairing, provided by the extended TAR method, to calculate the 3D rigid affine transform that aligns the scanned object to the given example position. For the transform calculation, we design an algorithm that overcomes the Kabsch point-to-point algorithm’s accuracy and accommodates it for a precise contour-to-contour alignment. In this way, we have implemented a pipeline with features convenient for industrial use, namely production inspection.