Measuring Surface and Volume of a Spheroid-Shaped 3D Object from a Single Image

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 ($<\delta>$) 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 ($<\delta>$ = 1.557%) and volume ($<\delta>$ = 2.365%). The estimation of the sub-region (mark) surface area over the modelled 3D object resulted in $<\delta>$ = 2.985%, much lower that what is obtained ignoring the fact that the mark is not on the reference (calibration) plane ($<\delta>$ = 50.7%), thus proving the effectiveness of the proposed iterative process to model the 3D object (spheroid).