A geometric model for estimating the volume and surface area of apples

Scarmana, Gabriel and McDougall, Kevin ORCID: https://orcid.org/0000-0001-6088-1004 and Stepanyants, Yury ORCID: https://orcid.org/0000-0003-4546-0310 (2020) A geometric model for estimating the volume and surface area of apples. In: Smart Surveyors for Land and Water Management, 10–14 May 2020, Amsterdam, Netherlands.


Agricultural and food technology research and science studies frequently require estimates of surface area (SA) and volume (V) of fruits, nuts and vegetables. These estimates are essential for supporting important processes such as storage, sorting, shipping practices, respiration rates, water loss or absorption, use and extent of pesticides and heat transfer.

In this research, low-cost laser scanning and conventional close range photogrammetric methods (for SA) are combined with standard hydro-static techniques (for V) so as to create accurate and scaled 3D models of apples of different sizes and shapes. Based on these models a novel geometric representation for a quick estimation of V and SA of an apple cultivar (i.e. granny smith) is presented. In essence, this geometric model relates to a particular mathematical function referred to as the cardioid.

Accurate statistical figures of V and SA values as obtained via the proposed cardioid representation are determined by comparing the developed model to the points of truth V and SA values obtained from the afore-mentioned 3D models. Results show that for the relatively large apple samples considered the predicted (via the cardioid representation) and the 'true' figures for V and SA agree within 2.8% and 3.4% respectively.

The proposed cardioid representation can be defined with simple but precise measurements which comply with international quality standards for size and volume characteristics of apple cultivars in general, that is, apple axial dimensions such as length (L) and diameter (T). Hence, the proposed cardioid model constitutes a practical and effective tool for many applications related to apple measuring, processing and handling.'
In particular it may lead to valid applications in orchard management, production and forecasting. In this context, an example describing a field data collection/capture system for apples is carried out in a real environment using a purpose made digital calliper integrating an on-board data-logger and a GPS receiver.

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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: Due to COVID 19 this event was physically cancelled. However, all accepted contributions/papers were published and included in the conference proceedings/program.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Civil Engineering and Surveying (1 Jul 2013 -)
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 -)
Date Deposited: 08 Jun 2020 06:17
Last Modified: 15 Feb 2021 23:34
Uncontrolled Keywords: 3D modeling, laser scanning, land management, GPS, metrology
Fields of Research (2008): 09 Engineering > 0908 Food Sciences > 090805 Food Processing
09 Engineering > 0909 Geomatic Engineering > 090905 Photogrammetry and Remote Sensing
07 Agricultural and Veterinary Sciences > 0701 Agriculture, Land and Farm Management > 070105 Agricultural Systems Analysis and Modelling
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
09 Engineering > 0909 Geomatic Engineering > 090999 Geomatic Engineering not elsewhere classified
Fields of Research (2020): 30 AGRICULTURAL, VETERINARY AND FOOD SCIENCES > 3006 Food sciences > 300604 Food packaging, preservation and processing
40 ENGINEERING > 4013 Geomatic engineering > 401304 Photogrammetry and remote sensing
30 AGRICULTURAL, VETERINARY AND FOOD SCIENCES > 3002 Agriculture, land and farm management > 300207 Agricultural systems analysis and modelling
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490101 Approximation theory and asymptotic methods
40 ENGINEERING > 4013 Geomatic engineering > 401399 Geomatic engineering not elsewhere classified
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
URI: http://eprints.usq.edu.au/id/eprint/38678

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