Keywords: lighting system, mandarins, fruit inspection, machine vision, image analysis.

The distribution of light reflected from objects depends, among other factors, on the position of the light source and the geometry of the object. The calibrations that are normally performed to correct the spatial and spectral inhomogeneities introduced by the lighting system are usually based on a plane model correction, using specific plates with known reflectance spectra. The problem arises when the object to be inspected can no longer be considered flat. This generally results in a darkening of the edges of the object, while the central part appears brighter. Such problems arise in the inspection of many products that are more or less spherical, as it is the case of several fruits such as oranges, peaches, tomatoes, mandarins, apples, and so forth. This darkening of the edges can even lead to confuse sound peel with damaged skin.

Some research has addressed the issue by setting up the lighting system in such a way that the light reaches the camera at an angle of 45° with respect to the light source, but this technique does not work properly with spherical objects. Various attempts have been made to solve this problem by applying spherical models with a constant curvature and variable radii. Such models are, however, very rigid. Another solution that has traditionally been employed to alleviate this problem is to erode the outline of the fruit, but this involves a loss of quality in the inspection because sometimes an important part of the object surface is not analysed.

This study proposes a method for correcting the adverse effects produced by the curvature of spherical objects in acquiring images with a computer vision system. The aim of this study is to develop a methodology for pre-processing images of spherical objects so that the adverse side effects caused by reflected light can be corrected. To fulfil this goal two corrections are performed: 1) Correction of the spatial variations of the light source by using a white reference; 2) Correction of the effects produced by the reflection of light on the spherical geometry of the fruit in flat images. To achieve this, we propose a methodology based on modelling the object as a three-dimensional spherical Lambertian surface that receives direct and diffuse lighting. Finally we will elaborate a digital elevation model (DEM) applied to the case of citrus fruits. Its suitability has been illustrated in the specific case of cuasi-spherical fruits such as citrus fruits but can be extended to other spherical objects.

To create the individual three-dimensional model of the objects from each two-dimensional image, some steps are followed: a) Determining the pixels that belong to the fruit in the scene. b) Determining the centre of mass of the object and the meridians of the interpolation network. c) Obtaining the elevations of the interpolation network. d) Obtaining the elevations of each pixel by interpolation. The height of each pixel is obtained from the interpolation network by performing a bilinear interpolation of all of them. e) Reflectance correction. The geometric parameters and the spatial coordinates of each pixel are used to calculate the cosine between the camera and the normal vector to the objects surface. Each pixel in the image can then be used to calculate their geometric correction factor.

To validate the model, some experiments were performed, consisting of comparisons of the spectra of four different regions of the object before and after the correction. The purpose of the experiments was to prove that at a difference from the uncorrected images, owing to the flattening of the histogram of the pixels from the fruit, pixels belonging to different regions of the fruit have a similar reflectance.

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