Peter Yuen

Multi-scale free-form 3D object recognition using 3D models

The recognition of free-form 3D objects using 3D models under different viewing conditions based on the geometric hashing algorithm and global verification is presented. The matching stage of the algorithm uses the hash-table prepared in the off-line stage. Given a scene of feature points, one tries to match the measurements taken at scene points to those memorised in the hash-table. The technique used for feature recovery is the generalisation of the CSS method (IEEE Trans. Pattern Anal. Mach. Intell., 14 (1992) 789–805), which is a powerful shape descriptor expected to be an MPEG-7 standard. Smoothing is used to remove noise and reduce the number of feature points to add to the efficiency and robustness of the system. The local maxima of Gaussian and mean curvatures are selected as feature points. Furthermore, the torsion maxima of the zero-crossing contours of Gaussian and mean curvatures are also selected as feature points. Recognition results are demonstrated for rotated and scaled as well as partially occluded objects. In order to verify match, 3D translation, rotation and scaling parameters are used for verification and results indicate that our technique is invariant to those transformations. Our technique for smoothing and feature extraction is more suitable than level set methods or volumetric diffusion for object recognition applications since it is applicable to incomplete surface data that arise during occlusion. It is also more efficient and allows for accurate estimation of curvature values.

Curvature Computation on Free-Form 3-D Meshes at Multiple Scales

A novel technique for multiscale curvature computation on a smoothed 3-D surface is presented. This is achieved by iteratively convolving local parameterizations of the surface with 2-D Gaussian filters. In our technique, semigeodesic coordinates are constructed at each vertex of the mesh which becomes the local origin. A geodesic from the origin is first constructed in an arbitrary direction such as the direction of one of the incident edges. The smoothing eliminates surface noise and small surface detail gradually and results in gradual simplification of the object shape. The surface Gaussian and mean curvature values are estimated accurately at multiple scales together with curvature zero-crossing contours. The curvature values are then mapped to colors and displayed directly on the surface. Furthermore, maxima of Gaussian and mean curvatures are also located and displayed on the surface. These features have been utilized by later processes for robust surface matching and object recognition. Our technique is independent of the underlying triangulation and is also more efficient than volumetric diffusion techniques since 2-D rather than 3-D convolutions are employed. Another advantage is that it is applicable to incomplete surfaces which arise during occlusion or to surfaces with holes.

Estimation of Error in Curvature Computation on Multi-Scale Free-Form Surfaces

A novel technique for multi-scale curvature computation on a free-form 3-D surface is presented. This is achieved by convolving local parametrisations of the surface with 2-D Gaussian filters iteratively. In our technique, semigeodesic coordinates are constructed at each vertex of the mesh. Smoothing results are shown for 3-D surfaces with different shapes indicating that surface noise is eliminated and surface details are removed gradually. A number of evolution properties of 3-D surfaces are described. Next, the surface Gaussian and mean curvature values are estimated accurately at multiple scales which are then mapped to colours and displayed directly on the surface. The performance of the technique when selecting different directions as an arbitrary direction for the geodesic at each vertex are also presented. The results indicate that the error observed for the estimation of Gaussian and mean curvatures is quite low after only one iteration. Furthermore, as the surface is smoothed iteratively, the error is further reduced. The results also show that the estimation error of Gaussian curvature is less than that of mean curvature. Our experiments demonstrate that estimation of smoothed surface curvatures are very accurate and not affected by the arbitrary direction of the first geodesic line when constructing semigeodesic coordinates. Our technique is independent of the underlying triangulation and is also more efficient than volumetric diffusion techniques since 2-D rather than 3-D convolutions are employed. Finally, the method presented here is a generalisation of the Curvature Scale Space method for 2-D contours. The CSS method has outperformed comparable techniques within the MPEG-7 evaluation framework. As a result, it has been selected for inclusion in the MPEG-7 package of standards.

Multi-scale 3-D Free-Form Surface Smoothing

A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Complete triangulated models of 3-D objects are constructed (through fusion of range images) and are then described at multiple scales. This is achieved by convolving local parametrizations of the surface with 2-D Gaussian filters iteratively. Our method for local parametrization makes use of semigeodesic or goedesic polar coordinates as a natural and efficient way of sampling the local surface shape. The smoothing eliminates surface noise and small surface detail gradually. Our technique for 3-D multi-scale surface smoothing is independent of the underlying triangulation. It is also argued that the proposed technique is preferrable to volumetric smoothing or level set methods since it is applicable to incomplete surface data which occurs during occlusion.

Curvature Estimation on Smoothed 3-D Meshes

13 - 16 September 1999, A novel technique for multi-scale curvature computation on a smoothed 3-D surface is presented. In our technique, semigeodesic coordinates are constructed at each vertex of themesh which becomes the local origin. A geodesic from the origin is first constructed in an arbitrary direction such as the direction of one of the incident edges. The surface Gaussian and mean curvatures are then estimated. Next, the curvature zero-crossing contours were recovered. Curvature features such as zero-crossing contours and maxima recovered at multiple scales are useful for surface matching and object recognition algorithms, as well as registration of 3-D medical data. The performance of our technique when selecting different directions as an arbitrary direction for the geodesic at each vertex is also evaluated. Our experiments demonstrate that estimation of smoothed surface curvatures are very accurate and not affected by the arbitrary direction of the first geodesic line when constructing semigeodesic coordinates. Our technique is independent of the underlying triangulation and is also more efficient than volumetric diffusion techniques since 2-D rather than 3-D convolutions are employed.

Free-Form 3-D Object Recognition at Multiple Scales.

The recognition of free-form 3-D objects using multi-scale features recovered from 3-D models, and based on the geometric hashing algorithm and global veri cation is presented. The feature points on the object are detected by smoothing its surface after construction of semigeodesic coordinates at each point (mesh vertex). This technique is the generalisation of the CSS method which is a powerful shape descriptor expected to be in the MPEG-7 standard. Smoothing is used to remove noise and to select multi-scale feature points to add to the eAEciency and robustness of the system. The local maxima of Gaussian and mean curvatures are selected as feature points. Furthermore the torsion maxima of the zero-crossing contours of Gaussian and mean curvatures are also selected as feature points. Recognition results are demonstrated for rotated and scaled as well as partially occluded objects. In order to con rm the match, 3D translation, rotation and scaling parameters are used for veri cation and results indicate that our technique is invariant to those transformations.

Free-Form Surface Description in Multiple Scales: Extension to Incomplete Surfaces

A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Diffusion of the surface is achieved through convolutions of local parametrisations of the surface with a 2-D Gaussian filter. Our method for local parametrisation makes use of semigeodesic coordinates as a natural and efficient way of sampling the local surface shape. The smoothing eliminates the surface noise together with high curvature regions such as sharp edges, therefore, sharp corners become rounded as the object is smoothed iteratively. During smoothing some surfaces can become very thin locally. Application of decimation followed by refinement removes very small/ thin triangles and segments those surfaces into parts which are then smoothed separately. Furthermore, surfaces with holes and surfaces that are not simply connected do not pose any problems. Our method is also more efficient than those techniques since 2-D rather than 3-D convolutions are employed. It is also argued that the proposed technique is preferable to volumetric smoothing or level set methods since it is applicable to incomplete surface data which occurs during occlusion. Our technique was applied to closed as well as open 3-D surfaces and the results are presented here.