Measuring Surface and Volume of a Spheroid-Shaped 3D Object from a Single Image
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ORIGINAL RESEARCH
Measuring Surface and Volume of a Spheroid‑Shaped 3D Object from a Single Image André R. S. Marcal1 · Elisabete M. D. S. Santos2 Received: 4 May 2020 / Accepted: 16 October 2020 © Springer Nature Singapore Pte Ltd 2020
Abstract The extraction of accurate geometric measurements from images normally requires the use of metric cameras and stereoscopic observations. However, as good-quality digital cameras are widely available in mobile devices (smartphones, tablets), there is great interest to develop alternative approaches, suitable for these devices. This paper presents a methodology to compute the surface area and volume of a spheroid-shaped object, such as many types of fruit, from a single image acquired by a standard (non-metric) camera and a basic calibration target. An iterative process is used to establish a 3D spheroid out of the observed 2D ellipse, after which auxiliary images of height, resolution and surface area of each pixel on the 3D object surface are created. The method was tested with a data set of 2400 images, of 10 different objects, 2 calibration targets, 2 cameras and 2 mark types. The average relative errors ( < 𝛿 > ) in establishing the 3D object semi-diameters were 0.863% and 0.791%. The semi-diameters are used to compute the object’s surface area ( < 𝛿 > = 1.557%) and volume ( < 𝛿 > = 2.365%). The estimation of the sub-region (mark) surface area over the modelled 3D object resulted in < 𝛿 > = 2.985%, much lower that what is obtained ignoring the fact that the mark is not on the reference (calibration) plane ( < 𝛿 > = 50.7%), thus proving the effectiveness of the proposed iterative process to model the 3D object (spheroid). Keywords 3D modeling · Spheroid · Volume · Surface area · Non-metric camera
Introduction The widespread availability of good-quality digital cameras in mobile devices (smartphones, tablets) propelled the development of a variety of application to extract high-level information from images acquired by these devices. However, there are not many cases where these cameras have been used to make accurate geometric measurements of the observed 3D space, despite some attempts made to use advanced imaging and computational tools for shape detection and creation [3]. In fact, the extraction of quantitative geometric measurements from a single image is not straightforward, as the standard approach to measure 3D coordinates is to use metric cameras and stereoscopic observations.
* André R. S. Marcal [email protected] 1
Faculdade de Ciencias, Universidade do Porto, Rua do Campo Alegre, 687, 4169‑007 Porto, Portugal
INESC TEC, Porto, Portugal
2
One application that requires the geometric evaluation of a 3D object is the computation of volume and surface area of fruit. Also of considerable interest is the evaluation of the surface area of a sub-region or spot on a fruit. As an example, the presumptive diagnosis of a number of walnut diseases, which affect severely the walnut production worldwide [10], can be made by the observation of symptomatic
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