Area and volume measurements of objects withirregular shapes using multiple silhouettesD. J. Lee, MEMBER SPIEXiaoqian XuBrigham Young UniversityDepartment of Electrical and ComputerEngineering459 CB Provo, Utah 84602E-mail: [email protected] EifertVirginia Polytechnic Institute andState UniversityDepartment of Food Science andTechnologyBlacksburg, Virginia 24061Pengcheng ZhanBrigham Young UniversityDepartment of Electrical and ComputerEngineering459 CB Provo, Utah 84602Abstract. Surface area and volume measurements provide importantinformation for agriculture and food-processing applications. A machinevision system that uses a nondestructive method to measure volume andsurface area of objects with irregular shapes is presented in this paper.The system first takes a series of silhouettes of the object from differentdirections by rotating the object at a fixed angular interval. The boundarypoints of each image are then extracted to construct a silhouette. A three-dimensional wire-frame model of the object can be reconstructed by in-tegrating silhouettes obtained from different view angles. Surface areaand volume can then be measured by means of surface fitting and ap-proximation on the wire-frame model. System calibration and surfaceapproximation were two major challenges for the design of this machinevision system. A unique centerline calibration method is introduced in thispaper. Surface approximation and calculation are also discussed. Ex-amples of applications in agriculture and food processing using this vi-sion system for surface area measurement are included, and its accu-racy is verified.© 2006 Society of Photo-Optical Instrumentation Engineers. 关DOI: 10.1117/1.2166847兴Subject terms: machine vision; silhouette-based reconstruction; radial projection;surface area measurement; surface approximation; 3-D wire-frame model.Paper 040483R received Jul. 22, 2004; revised manuscript received Apr. 14,2005; accepted for publication Jun. 19, 2005; published online Feb. 3, 2006. Thispaper is a revision of a paper presented at the SPIE conference on VisionGeometry, Jul. 2002, Seattle, Washington. The paper presented there appearsunrefereed in SPIE proceedings Vol. 4794.1 IntroductionIn many applications, physical attributes of fresh produce,such as surface area, volume, density, and weight, havebeen used to calculate water loss, heat transfer, quantity ofpesticide applications, respiration rates, and so on. Forfood-processing systems, rapid and nondestructive tech-niques for measurement of these physical attributes are use-ful for size sorting, quality grading, and microbial concen-tration estimation. Among all these attributes, surface areais one of the most important factors in all these applicationfields. Research work has been done to determine the rela-tionship between surface area and more easily measuredattributes such as weight, volume, and 2-D measures.1–6Different mathematical models and numerical analysismethods have been applied to extract a representation ofsurface area.From a deterministic point of view, Clayton et al.1,2de-veloped nonlinear regression models where both fruit massand volume were used to predict the surface area of apples.Humeida and Hobani3used weight or mean diameter inpredictive equations to estimate the surface area and vol-ume of pomegranates. Baten and Marshall4found that theweight of fruit 共apples, pears, and plums兲 could be used topredict surface area for picked fruit. But the transverse di-ameter, which was perpendicular to the core, gave the bestsurface area predictions for unpicked fruit. Frechette andZahradnik5developed equations to predict surface areafrom weight and density for McIntosh apples. To predictsurface area from weight, they developed the relationshipA = 7.82 + 0.11W, 共1兲where A is the area in square inches, and W is the weight ingrams. Another equation was developed to predict surfacearea from density measurements:A = 0.878W0.667. 共2兲By resorting to a statistical model, Thomas7developed re-lationships between poultry carcass surface area and weightfor two weight categories. For turkey carcasses weighingless than 7 kg, the relationship wassurface area 共cm2兲 = 0.45 ⫻ weight 共g兲 + 1293. 共3兲For turkey carcasses weighing more than 7 kg, the relation-ship wassurface area 共cm2兲 = 0.13 ⫻ weight 共g兲 + 3480. 共4兲However, a nondestructive system to rapidly measurethe area of raw, intact food has not been reported. Duringthe course of developing the preceding equations, Frechetteand Zahradnik5cut apples into slices, peeled them, andtraced the outlines of the peels on paper. The paper wasthen dried, cut, and weighed to estimate the fruit surfacearea. Clayton et al.1covered apples with electrical tape,0091-3286/2006/$22.00 © 2006 SPIEOptical Engineering 45共2兲, 027202 共February 2006兲Optical Engineering February 2006/Vol. 45共2兲027202-1which was then sectioned and removed. The surface area ofthe cut tape pieces was determined with a planimetric areameter. Sakai and Yonekawa8developed a structured lightsystem for measuring the surface area and volume of soy-bean seeds. They developed regression equations relatingseed mass to surface area and seed mass to volume. Noneof these methods is suitable for rapid surface area measure-ment in industrial food processing with large quantities.This paper presents a nondestructive way to measure thesurface area of selected raw produce, which aids the devel-opment of accurate assessments of the pathogen load onproduce and consumer exposure to pathogens from fresh orminimally processed fruits and vegetables.Applications such as 3-D visualization, volumetric mea-surement, and surface area measurement require some formof 3-D surface reconstruction. However, the irregularshapes of the objects involved in these applications make3-D surface reconstruction a very challenging task. Re-search work on silhouette-based 3-D model reconstructionhas been done to demonstrate a nondestructive way to solvethe problems. Radial projections have been used to gener-ate 3-D human face graphics models.9A continuous imagesequence was taken while rotating the object. However, theaccuracy and consistency of the c-axis of rotation was notaddressed. In other medical imaging applications, serialcross sections of an object were employed for 3-D recon-struction and visualization.10–12Several surface interpola-tion algorithms were developed or examined and haveshown very promising
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