Overview of Critical Feature Techniques

This section presents a general overview of the techniques that have been proposed, and extensively employed, to extract the “critical” features for a given 3D surface with respect to different applications. The critical features (sometimes called “sharp” feature) are the corners and edges within a given 3D surface. In the context of grid representations we refer to “critical points”, grid centre points that represent edges or corners. The Local Distance Measure (LDM) representation presented later in this thesis uses the concept of critical points (see Chapter 4). Point cloud representation and mesh representation are two examples of different 3D representations. Examples of detection techniques used with each approach are discussed in further detail below.

Generally speaking, critical feature detection and extraction from 3D surfaces is an area of research interest with respect to different applications such as: (i) 3D imaging and modelling [105], (ii) movement tracking [28], (iii) image matching [80] and (iv) im- age recognition [8, 46, 118, 139, 160]. It also finds application with respect to domains such as the automotive part manufacturing industry where it is used for fault detec- tion in assembly line processes [165, 220]. From the listed applications, we can argue that the accurate detection of critical features is of primary interest for most of these applications. From the above we have seen that there exists a wide variety of 3D rep- resentation techniques. There is a similar range of critical feature detection techniques many dependent on the nature of the adopted 3D representation. In the following the various critical feature detection methods have been grouped according to whether they are: (i) cloud based, (ii) mesh based or (iii) normal analysis based.

In the context of point cloud representations, the lack of information concerning connectivity and neighbourhoods in the point cloud makes direct detection of critical features a challenging task [32]. However, there is some reported research directed at extracting critical feature points from point clouds, examples include [87, 127, 210, 231]. In Gumhold et al. [87] the authors generated a local neighbourhood graph for each point in the point cloud, then identified critical points usingeigenvector and eigenvalue analysis. The technique attempted not only to detect the critical points but also to

classify effectively the point according to whether they were: edges, crease lines, corners or flat surfaces. This work was extended and improved in [165] by the inclusion of better surface smoothing and noise reduction techniques. In Zhao et al. [231] a technique to extract edges (and corners) from point clouds was proposed whereby the point cloud is first converted into a 2D image format where the z values are used as the image pixel value. Well known 2D image edge extraction techniques can then be applied, such as: Canny edge detection [31], the Sobel operator [171] and the Prewitt operator [170]. However the approach is expensive in terms of computation time and storage requirements [142]. Moreover, using the image processing detection techniques with point cloud representations has the disadvantages that: (i) it requires the user to specify certain parameters, (ii) it is difficult to know the real location of points belonging to edges and (iii) it tends to be very sensitive to the presence of “noise”.

With respect to mesh representations, as noted above, these are popular in the context of CAD/CAM systems. Many mesh based critical feature detection techniques have been proposed such as [70, 103, 161, 196]. Most of these mesh based techniques are founded on curvature analysis. Curvature describes the shape of a local region within a given 3D surface and thus it is often used as a local shape descriptor [9]. A number of mechanisms have been proposed for determining curvature. For example there is reported work where the mesh representation is converted into a mathematical surface representation (an “implicit representation”) anddifferentialgeometry employed to calculate the curvatures such as in the case of [172]. Further discussion regarding different types of curvature analysis, and their computation and estimation, can be found in [7, 163]. Eigen analysis has been extensively used in combination with curvature analysis to determine the direction of bending for a given 3D surface, see for example [162, 193]. Despite the accurate detection of critical features offered by the combination of curvature analysis and the eigen analysis, the major limitation is the complex nature of the required mathematical calculation founded on the second derivative of a surface; this is difficult to calculate in the context of 3D surface representation other than where specific mathematical representations are used [163].

The Identification of critical features based on the calculation and comparison of normals with respect to “neighbourhood areas” has been reported by a number of au- thors [151, 229, 232]. The basic idea is the consider the angle between the normals of adjacent points, if this angle is above some threshold a critical feature can be said to exist. The ease and simplicity of the approach are its main advantages. Some authors (for example [49]) recommend this type of critical feature detection. The nature of the generic grid representation proposed with respect to the work described in this thesis is will suited to critical feature identification using normal analysis because:

• The surrounding neighbourhood of a given grid point can be clearly and easily identified.

• By ordering the neighbours of a given grid point in (say) a clockwise direction,

cross product approach, and (i) identification of the direction of the calculated normals using the “right hand rule”.

The normal analysis approach to critical feature selection was thus adopted. Fur- ther detail concerning the adopted normal analysis critical feature detection method is presented in Chapter 5 and thus will not be considered further here.