# A Multivariate Local Descriptor Registration Method for Surface Topography Evaluation
###### Abstract  
This paper illustrates a systematical surface topography measurement and evaluation method based on a 3D optical system. Firstly, the point cloud data of the workpiece are extracted by the use of a 3D structured light measurement system, and the STEP file of the design model is converted into point cloud data. Secondly, the local measurement point cloud (LMPC) and digital model point cloud (DMPC) are registered by a multivariate local descriptor registration scheme proposed in this study. Thirdly, the surface shapes extracted from the STEP file are applied as a reference to segment the measuring point cloud. Finally, an error analysis scheme is conducted on specific functional surfaces. An experiment was conducted to analyse the flatness, cylindricity and roughness to demonstrate the effectiveness and advantage of the method. The comparison results show that the proposed method outperforms other 3D optical surface topography analysis methods. STEP files; point cloud; surface topography; multivariate local descriptor registration; error evaluation +
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extracting the height information of objects from a single fringe image. In metrological studies, multiscale methods are used to analyse surface topography. [PERSON] et al. [10] investigated multiscale analyses and characterization to provide correlations between topography and the performance of parts. [PERSON] et al. [11] introduced geometric multiscale methods into electrical discharge machining; it is possible to shape surface microgeometry. [PERSON] et al. [12] presented a contact model to describe normal and tangential contact behaviors of rough interface with a multiscale method; this model provides an effective way for studying the contact response of rough interface. The 3D structured light system has the advantages of simple structure and low cost, hence quickly obtaining the measurement data of a workpiece [13]. In practice, the result of optical measurement data is in the form of a point cloud. Take a grating structured light measurement system as an example [14]; it processes the shot raster image to obtain the 3D point cloud of a workpiece, known as the measurement model. The classical error analysis method of 3D optical measurement calculates the distance between point pairs after completing the registration of the measurement model and corresponding CAD model. However, obtaining the entire measurement model requires a splice point cloud from multi-view because a point cloud can only photograph the data at a particular projection direction [15], which is high-cost and has splicing errors. To overcome the difficulty of error analysis from local data to whole CAD data, the common method in the industry is to post positioning markers [16]. Nevertheless, it is evident that this method will increase the time and introduce manual intervention errors. [PERSON] et al. [17; 18] investigated multiple global descriptors to enhance the description of the point cloud formed by the key points and their neighbourhood to complete the localisation of aircraft partial skin. However, for some small parts, the data is obtained at a specific projection direction, which accounts for a large proportion of the whole digital model, such extensive local measurement data is hard to be broken into patches of the point cloud. The local descriptor method [19] can complete small parts to complete registration, and the commonly used point cloud-based local descriptors depend on manual processes, such as Point Feature Histogram (PFH) [20], Signature of Histogram of Orientation (Shot) [21] and Ensemble of Shape Functions (ESF) [22]. These descriptors are challenging to accurately describe the characteristics of particular parts and have low generalisation. In addition to the global deformation analysis of the local point cloud, another critical issue to be addressed in implementing target surface error analysis is to split the point cloud into various functional surfaces accurately.