Horst Holstein

Gravimetric analysis of uniform polyhedra

Analytical formulas for the gravity anomaly of a uniform polyhedral body are subject to numerical error that increases with distance from the target, while the anomaly decreases. This leads to a limited range of target distances in which the formulas are operational, beyond which the calculations are dominated by rounding error. We analyze the sources of error and propose a combination of numerical and analytical procedures that exhibit advantages over existing methods, namely (1) errors that diminish with distance, (2) enhanced operating range, and (3) algorithmic simplicity. The latter is achieved by avoiding the need to transform coordinates and the need to discriminate between projected observation points that lie inside, on, or outside a target facet boundary. Our error analysis is verified in computations based on a published code and on a code implementing our methods. The former requires a numerical precision of one part in 1016 (double precision) in problems of geophysical interest, whereas our c...

Gravimagnetic anomaly formulas for polyhedra of spatially linear media

Formulas for the gravity potential, field, and field gradient tensor are derived for a polyhedral target body of a spatially linear density medium. The formulas also define the magnetic potential and field in the case of a medium of spatially linear magnetization. This work generalizes existing solutions for the gravity field of a polyhedral target of linearly varying density.The formulas are analyzed for singularities and for numerical error growth. Error growth with increasing target distance is found to be higher than in the corresponding uniform polyhedral case. Examination of the error sources reveals that some error reduction is possible. On this basis, new algorithms of improved error control over existing algorithms are proposed for the linear medium. Computational results confirm the expected improvement.

Gravimagnetic similarity in anomaly formulas for uniform polyhedra

Gravitational and magnetic anomalies of an arbitrary target body are linked through Poissons differential relation. For a uniform polyhedral target, Poissons relation reduces to an algebraic link between gravity and magnetic anomaly formulas.The derivation is given in tensor form. It identifies for each target facet edge a vector function, in terms of which the gravitational and magnetic potential and field anomaly formulas are similarly expressed as appropriately weighted linear combinations. This similarity unifies the theory of uniform polyhedral anomalies. It benefits analysis and construction of software that naturally embraces all anomalies in a single code.The analysis is exemplified by a discussion of singularities and by the adaptation of three gravity‐field algorithms to the remaining gravitational and magnetic cases, while retaining the respective computational advantages of the former gravity‐field algorithms.

Recognition of Human Periodic Movements From Unstructured Information Using A Motion-based Frequency Domain Approach

Feature-based motion cues play an important role in biological visual perception. We present a motion-based frequency-domain scheme for human periodic motion recognition. As a baseline study of feature based recognition we use unstructured feature-point kinematic data obtained directly from a marker-based optical motion capture (MoCap) system, rather than accommodate bootstrapping from the low-level image processing of feature detection. Motion power spectral analysis is applied to a set of unidentified trajectories of feature points representing whole body kinematics. Feature power vectors are extracted from motion power spectra and mapped to a low dimensionality of feature space as motion templates that offer frequency domain signatures to characterise different periodic motions. Recognition of a new instance of periodic motion against pre-stored motion templates is carried out by seeking best motion power spectral similarity. We test this method through nine examples of human periodic motion using MoCap data. The recognition results demonstrate that feature-based spectral analysis allows classification of periodic motions from low-level, un-structured interpretation without recovering underlying kinematics. Contrasting with common structure-based spatio-temporal approaches, this motion-based frequency-domain method avoids a time-consuming recovery of underlying kinematic structures in visual analysis and largely reduces the parameter domain in the presence of human motion irregularities.

Point pattern matching and applications-a review

Feature-based methods in vision analysis often encounter the problem of correspondences between features of two related patterns. The features may be points, lines, curves and surfaces/regions. Point pattern matching (PPM) is a primary and essential approach for establishing a correspondence within two related patterns. Applications exist in wide circumstances. Numerous techniques related to PPM have been studied within a rich and extensive literature, encompassing both theoretical and practical problem domains. In this paper, we provide a review of the PPM techniques and their applications from three aspects: 1) PPM under rigid/affine motion, 2) PPM under non-rigid/elastic motion, and 3) PPM in a dynamic sequence. We also anticipate the trend for the future in adapting existing techniques to novel algorithms for non-rigid PPM.

Innovative data processing methods for gradient airborne geophysical data sets

Have you ever wondered whether the data you have collected, or have had collected for you, have been distorted or contain misrepresentations due to poor software algorithms? Next-generation potential field data sets are arriving fast, yet few software providers have redesigned their code to deal properly and formally with the vector and tensor nature of these data. We present several informative examples to demonstrate how and why “noise” in the data may not be all due to the hardware and why radical “rethinking” of the software can aid in exploration efforts.

Invariance in gravimagnetic anomaly formulas for uniform polyhedra

The anomaly formulas of gravitation and magnetics for uniform polyhedral targets are related by the gradient operation. The relationship enforces an invariance among subexpressions of the formulas. Knowledge of the invariance is not new. However, its role as a simplifier in an abstract calculus of anomaly functions is novel. This is exemplified by the derivation of anomaly formula variants of practical value. The gravitational potential V of a uniform polyhedral target allows compact expression to terms of certain vector functions b ij , one associated with each edge j of every target facet i , as defined in Holstein (2002). The derivation requires integration of elementary volume and surface integrals associated with the Newtonian potential. Corresponding integrations of the derived integrands for the gravity field and gravity gradient tensor reveal anomaly formulas for ∇ V and ∇∇ V with reappearance of the same functions b ij . This phenomenon is described as gravimagnetic similarity, extensions to the magnetic case being immediate on account of Poisson9s relation.

Articulated pose identification with sparse point features

We propose a general algorithm for identifying an arbitrary pose of an articulated subject with sparse point features. The algorithm aims to identify a one-to-one correspondence between a model point-set and an observed point-set taken from freeform motion of the articulated subject. We avoid common assumptions such as pose similarity or small motions with respect to the model, and assume no prior knowledge from which to infer an initial or partial correspondence between the two point-sets. The algorithm integrates local segment-based correspondences under a set of affine transformations, and a global hierarchical search strategy. Experimental results, based on synthetic pose and real-world human motion data demonstrate the ability of the algorithm to perform the identification task. Reliability is increasingly compromised with increasing data noise and segmental distortion, but the algorithm can tolerate moderate levels. This work contributes to establishing a crucial self-initializing identification in model-based point-feature tracking for articulated motion.

Recognition of human periodic motion-a frequency domain approach

We present a frequency domain analysis technique for modelling and recognizing human periodic movements from moving light displays (MLDs). We model periodic motions by motion templates, that consist of a set of feature power vectors extracted from unidentified vertical component trajectories of feature points. Motion recognition is carried out in the frequency domain, by comparing an observed motion template with pre-stored templates. This method contrasts with common spatio-temporal approaches. The proposed method is demonstrated by some examples of human periodic motion recognition in MLDs.

Articulated motion reconstruction from feature points

A fundamental task of reconstructing non-rigid articulated motion from sequences of unstructured feature points is to solve the problem of feature correspondence and motion estimation. This problem is challenging in high-dimensional configuration spaces. In this paper, we propose a general model-based dynamic point matching algorithm to reconstruct freeform non-rigid articulated movements from data presented solely by sparse feature points. The algorithm integrates key-frame-based self-initialising hierarchial segmental matching with inter-frame tracking to achieve computation effectiveness and robustness in the presence of data noise. A dynamic scheme of motion verification, dynamic key-frame-shift identification and backward parent-segment correction, incorporating temporal coherency embedded in inter-frames, is employed to enhance the segment-based spatial matching. Such a spatial-temporal approach ultimately reduces the ambiguity of identification inherent in a single frame. Performance evaluation is provided by a series of empirical analyses using synthetic data. Testing on motion capture data for a common articulated motion, namely human motion, gave feature-point identification and matching without the need for manual intervention, in buffered real-time. These results demonstrate the proposed algorithm to be a candidate for feature-based real-time reconstruction tasks involving self-resuming tracking for articulated motion.