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This paper exploits Geometric (Clifford) Algebra (GA) theory in order to devise and introduce a new adaptive filtering strategy. From a least-squares cost function, the gradient is calculated following results from Geometric Calculus (GC), the extension of GA to handle differential and integral calculus. The novel GA least-mean-squares (GA-LMS) adaptive filter, which inherits properties from standard adaptive filters and from GA, is developed to recursively estimate a rotor (multivector), a hypercomplex quantity able to describe rotations in any dimension. The adaptive filter (AF) performance is assessed via a 3D pointclouds registration problem, which contains a rotation estimation step. Calculating the AF computational complexity suggests that it can contribute to reduce the cost of a full-blown 3D registration algorithm, especially when the number of points to be processed grows. Moreover, the employed GA/GC framework allows for easily applying the resulting filter to estimating rotors in higher dimensions.

In this paper, we extend the concept of model-mediated teleoperation (MMT) for complex environments and six degrees of freedom interaction using point cloud surface models. In our system, a time-of-flight camera is used to capture a high resolution point cloud model of the object surface. The point cloud model and the physical properties of the object (stiffness and surface friction coefficient) are estimated at the slave side in real-time and transmitted to the master side using the modeling and updating algorithm proposed in this work. The proposed algorithm adaptively controls the updating of the point cloud model and the object properties according to the slave movements and by exploiting known limitations of human haptic perception. As a result, perceptually irrelevant transmissions are avoided, and thus the packet rate in the communication channel is substantially reduced. In addition, a simple point cloud-based haptic rendering algorithm is adopted to generate the force feedback signals directly from the point cloud model without first converting it into a 3D mesh. In the experimental evaluation, the system stability and transparency are verified in the presence of a round-trip communication delay of up to 1000ms. Furthermore, by exploiting the limits of human haptic perception the presented system allows for a significant haptic data reduction of about 90% for teleoperation systems with time delay. Index Termsmodel-mediated teleoperation, model-update, packet rate reduction, point cloud-based haptic rendering.

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Consensus-based Cross-correlation (ConCor) is a recently presented algorithm for robust synchronization of noisy and corrupted signals. ConCor has a number of interdependent parameters that need to be set correctly to guarantee good performance. In this paper we analyse the effects of the individual parameters on ConCor's behaviour and performance. As a second contribution, we show that a parameter sweep with subsequent majority voting can be used to boost ConCor's performance and produce a trustworthy confidence measure. As a final contribution we show how the proposed extension also allows performing multi-modal (joint audio-video) synchronization of casual multi-perspective video recordings enabling superior matching performance.