Trace Projection Transformation: a new method for measurement of debris flow surface velocity fields

doi:10.1007/s11707-015-0576-6

Front. Earth Sci.

2016, Vol. 10

Issue (4) : 761-771 https://doi.org/10.1007/s11707-015-0576-6

RESEARCH ARTICLE

Trace Projection Transformation: a new method for measurement of debris flow surface velocity fields

Yan YAN^1,²,Peng CUI^1,³(

),Xiaojun GUO^1,²,Yonggang GE¹

¹. Key Laboratory of Mountain Surface Process and Hazards/Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, China
². University of Chinese Academy of Sciences, Beijing 100049, China
³. Center for Excellence in Tibetan Plateau Earth Sciences, Chinese Academy of Sciences, Beijing 100101, China

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Abstract

Spatiotemporal variation of velocity is important for debris flow dynamics. This paper presents a new method, the trace projection transformation, for accurate, non-contact measurement of a debris-flow surface velocity field based on a combination of dense optical flow and perspective projection transformation. The algorithm for interpreting and processing is implemented in C++ and realized in Visual Studio 2012. The method allows quantitative analysis of flow motion through videos from various angles (camera positioned at the opposite direction of fluid motion). It yields the spatiotemporal distribution of surface velocity field at pixel level and thus provides a quantitative description of the surface processes. The trace projection transformation is superior to conventional measurement methods in that it obtains the full surface velocity field by computing the optical flow of all pixels. The result achieves a 90% accuracy of when comparing with the observed values. As a case study, the method is applied to the quantitative analysis of surface velocity field of a specific debris flow.

Keywords debris flow surface velocity field spatiotemporal variation dense optical flow perspective projection transformation

Corresponding Author(s): Peng CUI

Online First Date: 18 September 2016 Issue Date: 04 November 2016

Cite this article:

Yan YAN,Peng CUI,Xiaojun GUO, et al. Trace Projection Transformation: a new method for measurement of debris flow surface velocity fields[J]. Front. Earth Sci., 2016, 10(4): 761-771.

URL:

https://academic.hep.com.cn/fesci/EN/10.1007/s11707-015-0576-6
https://academic.hep.com.cn/fesci/EN/Y2016/V10/I4/761

Fig.1 Schematic of the comparator coordinates, x y z , and the object-space coordinates, x'y'z' . Arrows indicate the direction of flow; x o y is the imaging plane of the video; x' o y ' is the real plane of the flow.

Fig.2 (a) Positioning of quadrilateral, (b) projection mapping of the projection rectangle’s area in the perspective projection transformation algorithm.

Fig.3 Flowchart of the trace projection transformation algorithm (loop computation).

Tab.1 Comparison of velocities measured by TPT and field observations for the debris flow event on July 8, 2001 (Wei et al., 2002)

Fig.4 Schematic diagram of the measurement of surge 1 on July 8, 2001, obtained by using the method described in the text ((a) stands for channel sections; while (b), (c), and (d) represent flow patterns with surface velocity vectors of the surge front at sections 1?1', 2?2', and 3?3', in the observation video, respectively).

Tab.2 Comparison of velocities measured by TPT and by field observations for the debris flows on August 25, 2004 (Hu et al., 2011b)

Tab.3 Comparison of observed and TPT-measured data in large-scale flume experiments

Fig.5 Schematic diagram of the measurement of the surge 19 front on August 25, 2004, obtained by using the method proposed in this study ((a) represents sections in the channel, while (b), (c), and (d) represent the flow pattern with surface velocity vectors of the surge front at sections 1?1', 2?2', and 3?3', in the observation video, respectively).

Tab.4 Comparison of observed and TPT-measured data in large-scale flume experiments

Tab.5

Fig.6 Schematic diagram of the measurement of the surge front in the second experiment of a series of large-scale flume experiments, measured using the method proposed in this study ((a) denotes channel sections, while (b), (c), and (d) represent flow patterns with surface velocity vectors of the surge front at sections 1?1’, 2?2’ and 3?3’, in the observation video, respectively).

Fig.7 Spatio-temporal distribution of debris flow surface velocity at section S?S’ in Fig. 6(a) ((a) represents spatio-temporal distribution (3D) of debris flow surface velocity; (b) represents a two-dimensional map of the spatio-temporal distribution in debris flow surface velocity; (c) represents the surface velocity at time 2.0 s and 6.0 s; and (d) represents variations in mean surface velocity measured by the proposed method (TPT)).

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