Bayesian and Variational Methods for Discontinuity Detection: Theory Overview and Performance Comparison

Benciolini, Battista; Reguzzoni, Mirko; Venuti, Giovanna; Vitti, Alfonso

doi:10.1007/978-3-642-22078-4_22

Cited by 4 publications

(4 citation statements)

References 13 publications

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“…This could be an indication of a further discontinuity with a small amplitude and therefore less visible when looking at the time series. The detection of the epoch and the amplitude of this possible discontinuity requires further investigations that could exploit more sophisticated techniques (Benciolini et al, 2012). Note that the same general behaviour can be seen in all the three components but with different relative amplitudes.…”

Section: Resultsmentioning

confidence: 91%

Cultural Heritage Monitoring by Low-Cost GNSS Receivers: A Feasibility Study for San Gaudenzio’s Cupola, Novara

Barzaghi

Reguzzoni

Gaetani

et al. 2019

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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<p><strong>Abstract.</strong> In this study the cupola of San Gaudenzio’s Basilica in Novara, Italy, has been monitored by using two low-cost GNSS receivers located on the East and West side of the spire. Time series of daily solutions for an observation period of about one year have been collected and interpolated by cubic splines. The minimum description length criterion has been used to optimize this interpolation. The results show that the building had an uplift with a maximum amplitude of about 2 cm during summer. Moreover, from a joint analysis of the two points, one can realize that the uplift is not homogeneous, but the structure made some oscillations (with an amplitude at most of 4&thinsp;mm) when rising up. As for the planimetric coordinates, the two antennas had a slightly different behaviour. The West point showed displacements at most of 1 cm and solutions with a very high repeatability of the order of few millimeters. The East point had a similar repeatability until a sudden jump occurred, followed by more noisy solutions in all the three directions. This noise degradation slowly dampened, till almost disappearing at the end of the recorded time series. This anomalous behaviour could be attributed to some structural movements. The test was successful in the sense that (1) it was proved that the millimeter accuracy can be reached by using GNSS low-cost receivers installed at San Gaudenzio’s cupola, even with a non-perfect sky visibility; (2) such an accuracy is able to show interesting movements of the cupola that can provide information about its stability.</p>

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Section: Resultsmentioning

confidence: 91%

Cultural Heritage Monitoring by Low-Cost GNSS Receivers: A Feasibility Study for San Gaudenzio’s Cupola, Novara

Barzaghi

Reguzzoni

Gaetani

et al. 2019

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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“…The 1D Blake-Zisserman the model has also been successfully applied to geodetic data of different kinds (A. Borghi, n.d.;B. Benciolini, 2009).…”

Section: Discussion and Outlooksmentioning

confidence: 99%

Polygonal Shapes Detection in 3d Models of Complex Architectures

Benciolini

Vitti

2015

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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Abstract. A sequential application of two global models defined on a variational framework is proposed for the detection of polygonal shapes in 3D models of complex architectures. As a first step, the procedure involves the use of the Mumford and Shah (1989) 1st-order variational model in dimension two (gridded height data are processed). In the Mumford-Shah model an auxiliary function detects the sharp changes, i.e., the discontinuities, of a piecewise smooth approximation of the data. The Mumford-Shah model requires the global minimization of a specific functional to simultaneously produce both the smooth approximation and its discontinuities. In the proposed procedure, the edges of the smooth approximation derived by a specific processing of the auxiliary function are then processed using the Blake and Zisserman (1987) 2nd-order variational model in dimension one (edges are processed in the plane). This second step permits to describe the edges of an object by means of piecewise almost-linear approximation of the input edges themselves and to detects sharp changes of the first-derivative of the edges so to detect corners. The Mumford-Shah variational model is used in two dimensions accepting the original data as primary input. The Blake-Zisserman variational model is used in one dimension for the refinement of the description of the edges. The selection among all the boundaries detected by the Mumford-Shah model of those that present a shape close to a polygon is performed by considering only those boundaries for which the Blake-Zisserman model identified discontinuities in their first derivative. The output of the procedure are hence shapes, coming from 3D geometric data, that can be considered as polygons. The application of the procedure is suitable for, but not limited to, the detection of objects such as foot-print of polygonal buildings, building facade boundaries or windows contours. v The procedure is applied to a height model of the building of the Engineering Faculty of the University of Trento and to other data. The obtained results show the effectiveness of the variational methods in handling geometric data describing complex objects. The most original and innovative contributions of this work are: - the consecutive and coordinated use of the proper variational models (of first and second order respectively) at first in two dimension and subsequently on the one dimensional sets arising in the first segmentation, - the application to geometrical data that represent a quite complex architecture.

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“…As an example, the Mumford-Shah model has been successfully applied for the detection of cycle slips in GPS measurement combinations (Benciolini et al 2012).…”

Section: Final Remarks and Future Developmentmentioning

confidence: 99%

Sigseg: a tool for the detection of position and velocity discontinuities in geodetic time-series

Vitti

2012

GPS Solut

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The detection of discontinuities in geodetic data is an ever more important topic due to both the influence of discontinuities on the results of models and analyses, and to the very meaning of discontinuities in physical phenomena. We consider and describe a mathematical model, originally formulated for the approximation of images by smooth functions, in one dimension (1D). The model had been designed to smooth the data while preserving and detecting its discontinuities following a variational approach. A second and more complex model for the approximation of images by functions with smooth first derivatives is also available. This second model had been designed to smooth the data while preserving and detecting the discontinuities of the data, but also those of the first derivative. Such interesting features suggest the chance to apply this second model to 1D geodetic data, in particular for the detection of discontinuities and velocity changes in position time-series rather than for signal smoothing. The sigseg (signal segmentation) program implements the two variational models in 1D and is presented with applications to geodetic data. The essential mathematical elements are sketched, and some details on the numerical implementation are given.

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Bayesian and Variational Methods for Discontinuity Detection: Theory Overview and Performance Comparison

Cited by 4 publications

References 13 publications

Cultural Heritage Monitoring by Low-Cost GNSS Receivers: A Feasibility Study for San Gaudenzio’s Cupola, Novara

Cultural Heritage Monitoring by Low-Cost GNSS Receivers: A Feasibility Study for San Gaudenzio’s Cupola, Novara

Polygonal Shapes Detection in 3d Models of Complex Architectures

Sigseg: a tool for the detection of position and velocity discontinuities in geodetic time-series

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