Nonlinear Complementary Filter for Attitude Estimation by Fusing Inertial Sensors and a Camera

Using a standalone camera for pose estimation has been quite a standard task. However, the point correspondence-based algorithms require at least four feature points in the field of view. This paper considers the situation that there are only two feature points. Focusing on the attitude estimation, we propose to fuse a camera with low-cost inertial sensors based on a nonlinear complementary filter design. An implicit geometry measurement model is derived using two feature points in an image. This geometry measurement is fused with the angle rate measurement and vector measurement from inertial sensors using the proposed nonlinear complementary filter with only two parameters to be adjusted. The proposed nonlinear complementary filter is posed directly on the special orthogonal group SO(3). Based on the theory of nonlinear system stability analysis, the proposed filter ensures locally asymptotic stability. A quaternion-based discrete implementation of the filter is also given in this paper for computational efficiency. The proposed algorithm is validated using a smartphone with built-in inertial sensors and a rear camera. The experimental results indicate that the proposed algorithm outperforms all the compared counterparts in estimated accuracy and provides competitive computational complexity.

Form Defects Tolerancing by Natural Modes Analysis

The form defects quality needs methods to express allowable deviations. We propose a new language for form defects expression. This one is based on natural mode shapes of a discretized feature. The finite element method is used in order to compute those modes. Then a basis of defects is built with the natural modes. A defect is projected in this basis and thus the coordinates (modal coefficient) represent it. Hence, tolerancing is possible, by limiting those coordinates. The methods proposed in the literature can be applied on elementary geometries or there is a need to express the set of possible features (explicit geometry). Our method is versatile because it is based on the discretization of the feature (implicit geometry). The modal tolerancing method proposes two ways to express specifications of form defects: (1) The spectral tolerancing shows the modal coordinates and their limits in a bar chart graph by drawing the limits. In this method, we can see the decomposition of the measured feature and express tolerancing on each coordinate. (2) When a specification needs to link coordinates, we propose the modal domain method. An inclusion test of the feature coordinates gives the result of the metrology. Those methods are presented in an example.

A Computational Approach to the Reconstruction of Surface Geometry from Early Temple Superstructures

Recovering the control or implicit geometry underlying temple architecture requires bringing together fragments of evidence from field measurements, relating these to mathematical and geometric descriptions in canonical texts and proposing “best-fit” constructive models. While scholars in the field have traditionally used manual methods, the innovative application of niche computational techniques can help extend the study of artefact geometry. This paper demonstrates the application of a hybrid computational approach to the problem of recovering the surface geometry of early temple superstructures. The approach combines field measurements of temples, close-range architectural photogrammetry, rule-based generation and parametric modelling. The computing of surface geometry comprises a rule-based global model governing the overall form of the superstructure, several local models for individual motifs using photogrammetry and an intermediate geometry model that combines the two. To explain the technique and the different models, the paper examines an illustrative example of surface geometry reconstruction based on studies undertaken on a tenth century stone superstructure from western India. The example demonstrates that a combination of computational methods yields sophisticated models of the constructive geometry underlying temple form and that these digital artefacts can form the basis for in depth comparative analysis of temples, arising out of similar techniques, spread over geography, culture and time.

Implicit Methods for Geometry Creation

In this paper, we briefly review the existing direct implicit geometry generation methods, which include creation of blending surfaces, a limited family of sweeps, and reconstruction of solid geometry from a sample set of surface data points. A broader approach is presented, utilizing the properties of the graph of the implicit defining function, to systematically construct swept solids and perform morphing between sections by implicit methods.