Thorough characterization and analysis of a multispectral imaging system developed for colour measurement

Lasarte Rigueiro, Marta de

doi:10.5821/dissertation-2117-94063

Thorough characterization and analysis of a multispectral imaging system developed for colour measurement

Lasarte Rigueiro, Marta de

Published: 2009-07-01
Publisher: Universitat Politècnica de Catalunya
DOI: 10.5821/dissertation-2117-94063
Repository: upcommons.upc.edu
Language: en

Abstract

Hoy en día, los sistemas de imagen basados en cámaras CCD son ampliamente utilizados en numerosos campos, en particular, en el campo de la imagen científica debido a su alta resolución, alta eficiencia cuántica, amplia respuesta espectral, aceptable razón señal-ruido, linealidad, fidelidad geométrica, rápida respuesta, tamaño reducido y durabilidad. A pesar de esto, si se quiere utilizar una cámara CCD como instrumento de medida, se debe tener en cuenta que las cámaras CCD no son detectores perfectos, si no que presentan diversas fuentes de ruido inherentes a su funcionamiento que alteran los niveles digitales correspondientes a cada píxel, distorsionan la imagen real adquirida de forma desconocida y reducen la precisión radiométrica, la calidad de la imagen y su resolución. Dos de las relativamente recientes aplicaciones de los sistemas de imagen basados en cámaras CCD son la medida del color, consistente, básicamente, en estimar los valores triestímulo XYZ asociados a una muestra de color a partir de los niveles digitales de respuesta del sistema, y la reconstrucción espectral, consistente en estimar el espectro de reflectancia de una muestra de color a partir de los niveles digitales correspondientes de la respuesta del sistema. No obstante, para llevar a cabo medidas de color o reconstrucciones espectrales mediante este tipo de dispositivos es necesario realizar una caracterización o calibración previa de estos sistemas de imagen, con el objetivo de determinar la transformación que define la correspondencia entre las repuestas digitales del sistema y, por un lado, un espacio de color independiente del dispositivo, como el XYZ o el CIELAB, ya que las respuestas digitales del sistema, incluso las señales de salida RGB de un sistema de imagen tricromático, no se corresponden con los valores triestímulo independientes del dispositivo basados en el observador colorimétrico estándar de la CIE, o bien, por otro lado, el espacio de reflectancias espectrales, respectivamente. Los métodos de caracterización colorimétrica se pueden dividir en dos categorías generales: los métodos basados en las sensibilidades espectrales del sistema, algunos de los cuales normalmente sólo se aplican a configuraciones colorimétricas, es decir, con tres canales de adquisición, debido a su creciente complejidad al incrementar el numero de canales de adquisición, y los métodos basados en una carta de colores. Los métodos basados en las sensibilidades espectrales del sistema requieren el conocimiento de dichas sensibilidades para cada canal de adquisición, las cuales deben haberse determinado previamente mediante la caracterización espectral del sistema. En cuanto a los métodos de reconstrucción espectral, su principal objetivo es reconstruir el espectro de reflectancia, transmitancia o radiancia de una muestra de color a partir de las correspondientes respuestas digitales del sistema de imagen. Estos métodos se aplican habitualmente a configuraciones multiespectrales ya que los modelos lineales de espectros de reflectancia utilizados requieren como mínimo cuatro canales de adquisición para ser capaces de estimar espectros de reflectancia reales. Para que un sistema de imagen basado en una cámara CCD pueda ser utilizado como un instrumento de medida con elevada resolución espacial, de forma que la totalidad del área de detección del sistema sea útil para medir, es necesario corregir la no-uniformidad espacial de la respuesta del sistema. Con este propósito se utilizan básicamente dos tipos de técnicas. En primer lugar, las técnicas basadas en la escena se fundamentan en aplicar un algoritmo a la imagen original con el objetivo de obtener una mejora considerable en la calidad de la imagen a expensas de la precisión radiométrica. En segundo lugar, las técnicas de corrección de campo uniforme o de la nouniformidad espacial se basan en la calibración del sistema mediante dos imágenes: una imagen oscura y una imagen de campo uniforme, que se combinan linealmente con la imagen original. Este segundo tipo de técnicas permiten llevar a cabo medidas radiométricas precisas utilizando una cámara CCD. En la literatura se pueden encontrar diversas variantes de estas técnicas de corrección de campo uniforme o de la no-uniformidad espacial. La más general de estas variantes permite llevar a cabo la corrección de la no-uniformidad espacial de la respuesta del sistema de forma independiente de la nouniformidad de la iluminación de la escena, lo que resulta particularmente útil en varias condiciones de medida como, por ejemplo, en el caso de imágenes de objetos radiantes. La utilización de un sistema de imagen basado en una cámara CCD para medidas de color o reconstrucciones espectrales con elevada resolución espacial requiere la aplicación del segundo tipo de técnicas de corrección de la no-uniformidad espacial. En este trabajo se presentan la metodología experimental desarrollada para corregir las fuentes de ruido inherentes a un sistema de imagen basado en una cámara CCD, y la optimización de un algoritmo de corrección de la no-uniformidad espacial para obtener la mejor corrección posible de la no-uniformidad espacial. El principal objetivo de este trabajo es desarrollar un sistema de imagen multispectral para la medida del color. En este trabajo se presentan el diseño y desarrollo de un prototipo de sistema multiespectral en el rango visible del espectro y su minuciosa caracterización y análisis. Con este propósito se utiliza un sistema de imagen basado en una cámara CCD, por lo que es necesario llevar a cabo, en primer lugar, la corrección del ruido de la respuesta del sistema, concretamente la corrección de la no-uniformidad espacial, y, en segundo lugar, la caracterización o calibración del sistema mencionada anteriormente, para poder obtener los valores triestímulo XYZ y/o los espectros de reflectancia, respectivamente, a partir de las respuestas digitales del sistema. En este trabajo se utilizan dos sistemas de imagen basados en una cámara CCD: uno basado en una cámara CCD 10-bits color, y uno basado en una cámara CCD 12-bits monocromática refrigerada. De este último sistema se consideran dos configuraciones: una configuración colorimétrica con 3 canales de adquisición, y una configuración multiespectral con 7 canales de adquisición. La caracterización espectral se lleva a cabo sólo para la configuración colorimétrica de ambos sistemas con el objetivo de aplicar el método de caracterización colorimétrica basado en las sensibilidades espectrales del sistema. Por otro lado, se aplican diversos métodos de medida del color y reconstrucción espectral a las dos configuraciones del sistema basado en una cámara CCD 12-bits monocromática refrigerada y se comparan utilizando todas las combinaciones posibles de las cartas GretagMacbeth ColorChecker Color Rendition (CCCR) y GretagMacbeth ColorChecker DC (CCDC) como conjuntos de entrenamiento y prueba del sistema, con el objetivo de determinar los métodos más adecuados para cada configuración, es decir, los métodos que permiten conseguir la mejor precisión tanto en la medida del color como en la reconstrucción espectral para cada configuración. Al mismo tiempo se compara también el comportamiento de ambas configuraciones en términos de precisión de la medida del color y de la reconstrucción espectral. El hecho de que las sensibilidades espectrales de la mayoría de las cámaras CCD color (3 canales de adquisición) no verifiquen la condición de Luther, es decir, no sean transformaciones lineales de las funciones de igualación del color de la CIE, limita seriamente las aplicaciones colorimétricas de los sistemas basados en cámaras CCD color, dando lugar a valores triestímulo estimados dependientes del iluminante. Esta propiedad de las sensibilidades espectrales motiva el uso de sistemas multiespectrales ya que la única forma de asegurar una igualación del color para todos los observadores y bajo cambios en la iluminación es consiguiendo la igualación espectral. El método más directo para obtener información espectral de las muestras medidas es incrementar el muestreo por encima de los tres canales de adquisición tradicionales mediante filtros de banda estrecha, lo que se conoce como un sistema de imagen multiespectral. Los campos de aplicación de los sistemas de imagen multiespectral se ha incrementado enormemente en los últimos años, fundamentalmente debido a la posibilidad que ofrecen de estimar con precisión el espectro de reflectancia en cada píxel y, a partir de éste, los valores triestímulo XYZ, evitando del metamerismo. El sistema de imagen multiespectral diseñado y desarrollado en este trabajo doctoral para la medida del color está compuesto por un cámara CCD 12-bits monocromática refrigerada, una rueda de filtros motorizada y controlada vía software con un conjunto de filtros interferenciales de banda estrecha y un objetivo de focal variable. En coherencia con los resultados obtenidos en trabajos previos [Vilaseca et al., 2006] en la región NIR del espectro y extrapolándolos al rango visible, se utiliza un conjunto de siete filtros interferenciales de banda estrecha cubriendo por completo el rango visible del espectro, con la misma FWHM y longitudes de onda de pico equidistantes. Cada filtro constituye un canal de adquisición del sistema multiespectral, que corresponde a la configuración multiespectral del sistema de imagen antes mencionado. El primer paso antes de poder utilizar un sistema de imagen basado en una cámara CCD como instrumento de medida con elevada resolución espacial es llevar a cabo la corrección de las diferentes fuentes de ruido inherentes a su funcionamiento, y muy concretamente la corrección de la nouniformidad espacial de la respuesta del sensor. Con esta objetivo, en este trabajo se ha desarrollado una metodología experimental para la corrección de dichas fuentes de ruido, y se ha llevado a cabo la optimización de un algoritmo de corrección de la no-uniformidad espacial. A lo largo de este trabajo doctoral se han realizado también diversos análisis con el objetivo de mejorar la precisión de la medida del color y de la reconstrucción espectral utilizando sistemas de imagen basados en cámaras CCD. En primer lugar, considerando los conceptos básicos aplicados en imagen de alto rango dinámico (HDRI) para obtener una representación del contenido visual de una escena real independiente del dispositivo, se propone un balance de adaptación luminosa para incrementar el rango dinámico del sistema mediante la captura de imágenes con diferentes tiempos de exposición obteniendo así niveles digitales útiles para todos los píxeles. La aplicación de este balance de adaptación luminosa permite determinar el color en todos los píxeles de la imagen, incrementando así el rango dinámico del sistema [Pujol et al., 2006]. En segundo lugar, se analiza la influencia del número de muestras del conjunto de entrenamiento en la precisión de la medida del color y la reconstrucción espectral con el objetivo de determinar si existe alguna relación entre la precisión y el tamaño del conjunto de entrenamiento. La precisión del sistema mejora incrementando el tamaño del conjunto de entrenamiento hasta alrededor de 110 muestras, y pasa a ser independientes del conjunto de entrenamiento utilizado para conjuntos de entrenamiento con un número de muestras igual o superior a 110. A continuación, se analizan la medida del color y la reconstrucción espectral llevadas a cabo utilizando las dos configuraciones del sistema, colorimétrica y multiespectral, en función de las gamas de colores medidas, es decir, conjuntos de muestras de color agrupadas en función de su tono, con el objetivo de determinar si estas configuraciones son especialmente sensibles a algunos tonos y/o a otras propiedades del color. En primer lugar se analizan las tendencias generales utilizando la carta CCDC como conjunto de entrenamiento y prueba y, en segundo lugar, se utilizan las 1269 muestras de color del Munsell Book of Color - Matte Collection, clasificadas en 10 tonos Munsell y cada uno de éstos en 4 sub-tonos, para analizar la influencia de la homogeneidad en tono del conjunto de entrenamiento. Se comprueba que la homogeneidad en tono del conjunto de entrenamiento permite mejorar de forma significativa la precisión del sistema tanto en la medida del color como en la reconstrucción espectral [de Lasarte et al., 2008 - 2]. Por otro lado, se utilizan tres combinaciones de conjuntos de entrenamiento y prueba de las muestras Munsell para variar el grado de homogeneidad en tono del conjunto de entrenamiento, obteniéndose los mejores resultados para los conjuntos de entrenamiento más homogéneos en tono. Los resultados obtenidos se analizan también en función de las características del color de las muestras medidas como son las coordenadas CIELAB, y las coordenadas Munsell de tono, 'value' y croma. No se observa ningún tipo de correlación entre la precisión del sistema y las coordenadas CIELAB, mientras que la precisión del sistema tiende a empeorar para muestras con valores de la coordenada Munsell Value V > 7 - 8. Se analiza también la influencia del iluminante mediante la comparación de los resultados obtenidos utilizando dos iluminantes: una lámpara incandescente y un simulador D65. Los mejores resultados se obtienen para la combinación configuración multiespectral del sistema y simulador D65 como iluminante. Seguidamente, la precisión de la medida del color y la reconstrucción espectral se analiza en función de los espectros de reflectancia de las muestras de color medidas para determinar si existe algún tipo de correlación entre ambos. Este estudio se lleva a cabo utilizando la configuración multiespectral del sistema y el iluminante D65, la carta CCDC y las muestras Munsell como conjuntos de entrenamiento y prueba. La precisión de la medida del color y la reconstrucción espectral se analizan en función de, por un lado, el área bajo la curva (AUC) de los espectros de reflectancia y, por otro lado, la suavidad de los espectros de reflectancia mediante su Transformada Discreta de Fourier (DFT), que se utiliza frecuentemente en análisis de espectros para determinar la suavidad de las curvas. Respecto al análisis del AUC, la precisión del sistema en la medida del color tiende a mejorar para muestras con AUC de sus espectros de reflectancia mayores, aunque no se puede establecer ninguna relación directa entre ambas. Esta tendencia no se observa en términos de la precisión de la reconstrucción espectral. Una mayor precisión en la reconstrucción espectral se asocia con frecuencia a espectros de reflectancia suaves, aunque tampoco se puede establecer ninguna correlación entre ambos. En cuanto al análisis de la DFT, la precisión en la medida del color parece ser independiente de la forma y/o la suavidad de los espectros de reflectancia, mientras que la mayor precisión en la reconstrucción espectral se asocia con frecuencia a un espectro de reflectancia suave, aunque no se puede establecer una correlación general entre ambas. Una vez completado el minucioso análisis del sistema multiespectral desarrollado y establecidas sus limitaciones en cuanto a precisión en la medida del color y la reconstrucción espectral, la siguiente etapa es determinar si algún otro número y/o combinación de filtros interferenciales disponibles comercialmente permitiría mejorar, al menos teóricamente, la precisión del sistema multiespectral. Con este propósito se lleva a cabo un estudio de simulación de un sistema multiespectral óptimo para la medida del color y la reconstrucción espectral. Este estudio se realiza considerando la respuesta espectral del la cámara CCD 12-bits refrigerada monocromática utilizada y una base de datos de filtros disponibles comercialmente seleccionados entre las bases de datos de Edmund Optics, OptoSigma y CVI. Se observa que la precisión del sistema se mejora al incrementar el número de filtros, aunque esta mejora está limitada y tiende a ser insignificante para un número de filtros superior a 8. Los filtros óptimos tienden a compensar la respuesta espectral de la cámara CCD sobre todo el rango visible pero teniendo en cuenta el inconveniente que suponen el desconocer las transmitancias reales de los filtros (las simulaciones dependen en gran medida de las transmitancias reales de los filtros, que no siempre se pueden simular fácilmente a partir de las especificaciones de los proveedores), la selección de un conjunto de filtros interferenciales con posiciones de pico equidistantes cubriendo todo el rango visible, iguales FWHM que permiten un ligero solapamiento entre ellos, y la mayor transmitancia posible, como se ha hecho en este trabajo, constituye una opción más que aceptable para obtener un sistema multiespectral útil. Finalmente, se comprueba la aplicabilidad del sistema multiespectral desarrollado utilizando, no sólo cartas de color estandarizadas, como son las CCDC, CCCR y las muestras Munsell, sino utilizando también un conjunto de 56 muestras textiles agrupadas en 28 parejas, que fueron especialmente fabricadas para comprobar la aplicabilidad de las fórmulas de diferencia de color, y el simulador D65 como iluminante. Se analizan diferentes combinaciones de conjuntos de entrenamiento y prueba. Los mejores resultados se obtienen, en promedio, utilizando conjuntos de entrenamiento homogéneos en tono y llevando a cabo una clasificación previa de las muestras textiles en tonos. Además, se comprueba la capacidad del sistema multiespectral desarrollado de detectar pequeñas diferencias, tanto en color como en el espectro de reflectancia, entre muestras reales, resultando así ser útil para aplicaciones que requieran discriminación, aunque se obtiene una escasa precisión en la determinación de las diferencias tanto de color como en las reflectancias espectrales entre los pares de muestras textiles considerados.

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UNIVERSITAT POLITÈCNICA DE CATALUNYA DEPARTAMENT DE ÒPTICA I OPTOMETRIA Thorough characterization and analysis of a multispectral imaging system developed for colour measurement Thesis Student: Marta De Lasarte Rigueiro Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 215 13 Conclusions and Future Work The main contributions achieved in the development of this work can be summarized in the following points: 1. An experimental methodology to correct the noise sources inherent to the performance of a CCD camera has been developed. This methodology establishes the fundamental stages to be followed in the correction of the several noise sources inherent to the performance of an imaging system based on a CCD camera. 2. A linear algorithm for the spatial non-uniformity correction of the system’s response has been optimized. The algorithm optimized is based on the calculation of gain and offset matrixes from a dark image and a uniform field image. The optimization of this algorithm has been carried out depending on the variables of these matrixes. A correction gain matrix calculated at a certain radiance level (preferably a high radiance level – low exposure time range) is proved to allow to achieve a high quality spatial non-uniformity correction when applying the optimized algorithm to images corresponding to any radiance level (any exposure time range) and radiance spectrum, therefore proving the wide applicability of the optimized linear correction algorithm. 3. The spectral characterization of an imaging system based on a colour 10-bits CCD camera QImaging QICAM, and of the colorimetric configuration (3 acquisition channels) of an imaging system based on a monochrome 12-bits cooled CCD camera QImaging QICAM Fast 1394, has been carried out to determine their absolute and relative spectral sensitivity functions, being these last necessary to perform the colorimetric characterization of the imaging system based on spectral sensitivities. 4. The colorimetric characterization based on spectral sensitivities has been only applied to the imaging system based on a colour 10-bits CCD camera QImaging QICAM, and to the colorimetric configuration (3 acquisition channels) of the imaging system based on a monochrome 12-bits cooled CCD camera QImaging QICAM Fast 1394, due to its growing complexity when the number of acquisition channels is increased. - A quite low accuracy on the estimation of the XYZ tristimulus values is obtained for most of colour samples of the GretagMacbeth ColorChecker DC (CCDC) chart, for the two imaging systems considered. - Slightly better results are achieved using the monochrome 12-bits cooled CCD camera than using the colour 10-bits CCD camera. - The quite low accurate results obtained are due to the fact that, despite of all the steps on this method are very clear conceptually, their application involved several fittings of experimental data and simulations using parameters obtained Conclusions and Future Work Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 216 from these fittings, which make it possible a considerably amount of errors to be easily accumulated on the estimations of the XYZ tristimulus values. - The colorimetric characterization based on spectral sensitivities applied results to be a non-advisable method for colorimetric characterization. 5. Apart from the previously mentioned method based on the spectral sensitivities, applied only to the colorimetric configuration, two methods for colour measurement (colorimetric characterization) based on a training set of colour samples have been compared for the two configurations (colorimetric and multispectral) of the imaging system based on a monochrome 12-bits cooled CCD camera QImaging QICAM Fast 1394: the pseudoinverse method for XYZ (PSEXYZ) and the second order non-linear method for XYZ (NLIN(2)XYZ). - Best results are always obtained using the CCDC chart as training and test set. - The most advisable methods for colour measurement for the colorimetric configuration are the NLIN(2)XYZ and the PSEXYZ methods. Both of them are recommended due to the fact that both lead to similar results when different sets of colour samples are used as training and test sets, which will be the more common situation for an imaging system that is going to be used as an instrument for colour measurement. - The most advisable method for colour measurement for the multispectral configuration is the PSEXYZ method. The NLIN(2)XYZ method would be also advisable but it presents some restrictions on the minimum number of colour samples of the training set depending on the number of acquisition channels of the imaging system. - Comparing both configurations, better results are obtained using the PSEXYZ and NLIN(2)XYZ methods for the multispectral configuration than for the colorimetric configuration. 6. Three methods for spectral reconstruction have been compared for the two configurations (colorimetric and multispectral) of the imaging system based on a monochrome 12-bits cooled CCD camera QImaging QICAM Fast 1394: the pseudoinverse method (PSE), the second order non-linear method (NLIN(2)), and the Principal Component Analysis (PCA). - Best results, in terms of accuracy of both colour measurement and spectral reconstruction, are always obtained using the CCDC chart as training and test set. - The most advisable method for spectral reconstruction for the colorimetric configuration, in terms of accuracy of both colour measurement and spectral reconstruction, is the NLIN(2), followed by the PSE method. - The most advisable methods for spectral reconstruction for the multispectral configuration, in terms of accuracy of both colour measurement and spectral reconstruction, are the PSE and the PCA methods. Just as for methods for Conclusions and Future Work Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 217 colour measurement, the NLIN(2) method would be also advisable but it is not considered because of having restrictions on the minimum number of colour samples of the training set, depending on the number of acquisition channels of the imaging system, which seriously limits its applicability. - Comparing both configurations, better results are obtained using the PSE, NLIN(2) and PCA methods for the multispectral configuration than for the colorimetric configuration. 7. Methods finally selected to characterize the imaging system are methods for spectral reconstruction for the two configurations of the imaging system. These methods allow one to perform not only colour measurement, but also spectral reconstruction of reflectance and/or radiance spectra, providing a complete information about the colour independently of the illuminant and the colour space used. The PSE method is selected for the colorimetric configuration for its wide applicability independently of the training set considered, and the PCA method is selected for the multispectral configuration because of performing rather similarly to the PSE method and being commonly used in literature for multispectral imaging systems. 8. The influence of the number of principal vectors considered as a basis of the reflectance spectra when applying the PCA method on system’s performance has been analyzed for the multispectral configuration. Neither the accuracy of colour measurement nor the accuracy of spectral reconstruction is significantly improved by increasing the number of principal components in the PCA basis from the number of acquisition channels on. Therefore, the minimum number of principal vectors that must be considered in the PCA basis in order to achieve the best system’s performance using the PCA method, in terms of accuracy of both colour measurement and spectral reconstruction, should be equal to the number of acquisition channels, as it is traditionally done in literature. 9. A Luminance Adaptation Model (LAM) has been proposed to increase the dynamic range of the imaging system which is actually limited by the useful (linear) dynamic range of the CCD camera used. This model is based on capturing images at different exposure times in order to obtain useful digital levels for all pixels in the image, which are subsequently transformed to a reference exposure time common to all pixels. - The LAM proposed, apart from its proved validity for limited exposure conditions, is also proved to be a very useful method to increase the dynamic range of the imaging system, allowing to widen its applicability to images having zones with extreme exposure conditions, for the two configurations of the imaging system. - The application of the LAM proposed is greatly advisable mainly on images having zones with an outstandingly wide range of exposures, in order to make useful all zones over the image, either for colour measurement or for spectral reconstruction. 10. The influence of the number of samples of the training set on the accuracy of colour measurement and spectral reconstruction has been analyzed, not only considering the system’s performance depending on the size of the training set, but also considering Conclusions and Future Work Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 218 the dependency of system’s performance on the concrete set of colour samples of the training set for each size. System’s performance seems to become independent of the training set used, in terms of both the number of samples of the training set and the training set itself, when increasing the number of samples over 110 samples for the colorimetric configuration, and over 120 samples for the multispectral configuration, proving the existence of a minimum and/or ‘sufficient number of colour samples’ for both configurations of the imaging system. These results hold in terms of accuracy of both colour measurement and spectral reconstruction. 11. Colour measurement and spectral reconstruction performed using both configurations of the imaging system have been analyzed depending on the colour ranges measured, using an incandescent lamp illuminant and a D65 simulator illuminant, and the same set of colour samples as training and test sets. - Accuracy of colour measurement and spectral reconstruction is proved to depend not only on the illuminant but also on the training and test sets considered. - Comparing results obtained using all Munsell’s colour patches and sets of Munsell’s colour patches grouped in hues and sub-hues as training and test sets, homogeneity in hue of the training set allows to improve outstandingly the accuracy of both colour measurement and spectral reconstruction for all colour ranges. - Comparing results obtained using a multi-colour range CCDC chart and sets of Munsell’s hues and sub-hues as training and test sets, homogeneity in hue of the training set does not assure an improvement in accuracy neither of colour measurement nor of spectral reconstruction, for all colour ranges. - The best combination of system’s configuration and illuminant is the multispectral configuration and the D65 simulator illuminant. 12. For the best combination of system’s configuration and illuminant, using the same sets of Munsell’s colour patches as training and test sets, and varying the degree of homogeneity in hue of the training set, the more homogeneous the training set is, the better results are obtained in terms of accuracy of both colour measurement and spectral reconstruction. 13. Using different training and test sets, the homogeneity in hue of the training set (Munsell’s hues) and the classification of the colour samples of the test set (CCDC chart) in hues tends to improve the accuracy of both colour measurement and spectral reconstruction, in general for all hues, with regard to results obtained using a multicolour range training set, as it is the set of all Munsell’s colour patches. 14. The complete training set (comprised by the training sets homogeneous in hue) must cover the whole CIELAB space and/or the reflectance spectra space of samples to be used as test set in order to be able to train the imaging system in the widest way possible hue by hue. Conclusions and Future Work Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 219 15. System’s performance depends on the classification of the test samples in hues. Methods tested in this work pretend to classify the colour samples of a known test set (known CIELAB coordinates, reflectance spectra) in hues in order to obtain the best system’s performance and prove that system’s performance is improved when different training sets homogeneous in hue are used. The best performance is obtained applying the a*b* classification method. 16. Analyzing the accuracy of colour measurement and spectral reconstruction depending on the Munsell value and chroma coordinates, larger CIELAB colour differences are obtained for samples having a Munsell value V < 5 – 6, and CIELAB colour differences tend to increase slightly for samples having a Munsell Value V > 7 - 8, as a general tendency for all Munsell sub-hues, both system’s configurations and both illuminants. RMSE values, although do not decrease with an increasing value of the Munsell value coordinate, also tend to increase slightly for samples having a Munsell Value V > 7 – 8, being not so sensitive to the Munsell value coordinate as the CIELAB colour difference is, for the low light and lower colourful patches (low Munsell value and chroma). 17. The accuracy of colour measurement and spectral reconstruction has been analyzed depending on the Area Under the Curve (AUC) and the Discrete Fourier Transform (DFT) of the reflectance spectra of the colour samples measured. - Considering the AUC analysis, the accuracy of colour measurement tends to improve for the colour samples with higher AUCs of their reflectance spectra, whereas this tendency is not observed for the accuracy of spectral reconstruction. Any direct relationship cannot be established either between the accuracy of colour measurement and the AUC of the reflectance spectra of colour samples. - Considering the DFT analysis, the accuracy of colour measurement seems to be independent of the shape and/or the smoothness of the reflectance spectra, whereas the best accuracy of spectral reconstruction is frequently associated to a smooth reflectance spectrum, although any general correlation cannot be established between them. 18. A simulation study of an optimum multispectral imaging system for colour measurement and spectral reconstruction has been carried out. It consists of an exhaustive search of the optimum set of commercially available interference filters, considering all possible combinations of filters on the database used, for a fixed number of filters or acquisition channels (from 3 to 9). The CIELAB colour difference has been used as the cost function for the accuracy of colour measurement, and the RMSE for the accuracy of spectral reconstruction. System’s performance is improved in terms of accuracy of both colour measurement and spectral reconstruction with an increasing number of interference filters. Nevertheless, this improvement is limited and tends to be insignificant for more than 8 filters. These results have been obtained using the CCDC chart as training and test set, but results could be notably different when using another set of colour samples. 19. When designing a multispectral imaging system, a simulation study of the optimum multispectral imaging system considering the commercially available filters can be Conclusions and Future Work Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 220 very useful in order to get an idea of the specific characteristics of the optimum filters, but not decisive in the sense that results of simulations depend greatly on the real spectral transmittances of filters, which not always can be easily simulated from the specifications provided by suppliers. 20. Optimum filters tend to make up for the spectral response of the CCD camera over the whole visible range, but considering the drawback the unknown real spectral transmittances of filters supposes, the selection of a set of gaussian interference filters having equidistant peak positions covering the whole visible range, equal FWHMs that allow a slight overlapping between them, and the higher transmittance possible, as it was done in this work, constitutes an acceptable option to obtain a worthy multispectral imaging system. 21. Regarding the number of filters in a multispectral imaging system, although increasing the number of filters tends to improve theoretically the accuracy of the system’s performance, it also introduces experimental errors involving a longer sequence of measurements, increases the mechanical complexity of the experimental setup to fit the filters in a wheel, or a similar assembly, and automate it, and also increases the final cost of the system. Therefore, some kind of compromise should also be reached among real accuracy, complexity, and cost. 22. The applicability of the multispectral imaging system developed has been tested using a set of 56 textile samples grouped in 28 pairs, which were made specifically to test the applicability of colour difference formulas to textile samples, and the D65 simulator illuminant. - Regarding the accuracy of system’s performance when applied to textile samples, best results in terms of both colour measurement and spectral reconstruction are obtained using the textile samples as training and test set. Using different training and test sets, best results are mostly obtained in average using the sets of Munsell’s hues as training sets, and classifying the textile samples in hues to reconstruct them. These results are even better than those obtained using the textile samples themselves as training set. - Regarding the accuracy of system’s performance in detecting both the colour and the spectral differences between pairs of textile samples, firstly, the multispectral imaging system developed is able to detect slight differences both in colour and in reflectance spectra between real samples, making it useful for applications that require discrimination. On the other hand, the accuracy of system’s performance in detecting both the colour differences and the spectral differences between pairs of textile samples obtained is quite low, and different in terms of the CIELAB colour difference values and the RMSE values depending on the training set used. - Deviations of general results and low accuracy in detecting both the colour differences and the spectral differences between pairs of textile samples are attributed firstly, to use different type of colour samples as training and test sets such are the textile samples and the standardized colour charts. Secondly, to the known limitations of the hue classification method applied and the limited gamut defined by the training sets homogeneous in hue used, which Conclusions and Future Work Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 221 cannot cover at all the gamut defined by the textile samples used as test set. Finally, to the differences between the textile samples and the rest of colour samples considered (CCDC’s and Munsell’s) in the measuring instruments and the measuring geometry used to determine the reflectance spectra of samples. Regarding the work developed in this PhD thesis, some research lines can be suggested for future work: 1. Considering the imaging system used in this work, studying the system’s performance when using the colorimetric configuration and the two illuminants as a multispectral imaging system, and studying if the performance of the multispectral imaging system developed could be improved considering combinations of the present acquisition channels and an illuminant as new acquisition channels constituting a new combined multispectral imaging system. 2. Defining and optimizing a general classification of colour samples in well delimited colour ranges, or hues, based on some measurable characteristic of colour and applicable to any kind of colour samples, in order that any measured colour sample (known XYZ tristimulus values, CIELAB coordinates, reflectance spectra, etc.) can be easily classified in some well defined colour range, independently of the type of colour samples it is. 3. Starting from standardized colour samples (CCDC, CCCR, and Munsell Book of Colour charts) and considering the properties of the colour samples of the training set that influence system’s performance, optimizing the homogeneous training sets associated to each previously defined and delimited colour ranges, in order to be able to train the imaging system in the widest way possible hue by hue, covering the whole CIELAB space and/or reflectance space of the samples to be used as test sets. 4. 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Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 236 Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 237 APPENDIXES Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 238 Appendix 1 Datasheets and specifications of instruments used Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 245 Tele-spectracolorimeter PhotoResearch PR650 Appendix 1 Datasheets and specifications of instruments used Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 246 Tele-spectracolorimeter PhotoResearch PR650 Appendix 1 Datasheets and specifications of instruments used Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 247 CVI Laser Digikrom DK 240 Monochromator Instrument Specifications Type. The Digikrom 240 is a Czerny-Turner Scanning Monochromator with a focal length of 240mm. Effective Aperture Ratio. The Digikrom 240 has an effective aperture ratio of f/3.9. Collimating/Focusing Mirrors. These mirrors are 84mm round aluminized with a protective overcoat. Gratings. Plane reflective gratings of 64mmx64mm, replicated are standard. 64mm(height)x84mm(width) replicated, or broadband holographic are available as options. Spectral Coverage. The grating is usable to ∼75 degrees angle of incidence with an 84mm-wide grating, and the aperture ratio is maintained to 42 degrees. The aperture ratio is maintained to approximately 1.2 microns, and with a 1200g/mm grating, the grating is usable to approximately 1.5 microns. Grating Mount. A reversible, two-grating mount with either one or two gratings mounted and calibrated is standard o the Digikrom 240. An optional three-grating turret mount is available. Any mounted grating may be stepped into position for use, autocalibrated, and used without opening the monochromator. Reciprocal Linear Dispersion. The reciprocal linear dispersion of the Digikro 240 is 3.2nm/mm with a 1200g/mm grating, in first order. Resolution. The spectral resolution of the Digikron 240 is 0.06nm with 20 micron slits and a 1200g/mm grating in first order. Stray Light. Stray light is less than 0.02% at 220nm (NaI). Wavelength Drive. A direct digital wavelength drive is standard. The Digikrom 240 has a self-contained, microprocessor controlled stepper motor drive. The motor is coupled to the rotating grating table via a worm/worm-wheel engagement. This mechanism is a new type for a monochromator drive. Bearings and Gears. All bearings and gears are precision quality and have been preloaded to optimize gear engagement and minimize backlash. Standard gear assembly, stepper motor, and driver electronics are configured to yield a grating rotational increment of 44 microradians per motor step. With a 1200g/mm grating in first order, the monochromator has a wavelength increment of approximately 0.07nm per step. A microstep option which permits operation of the stepper motor at 1/10 of a standard step is available. This option will produce a wavelength increment of 0.007nm per step. Appendix 1 Datasheets and specifications of instruments used Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 248 Wavelength Initialization. During power-up, the microprocessor invokes an initialization routine. This routine uses a two stage method to stablish a true ‘home’ position for the stepper motor. Using ‘home’ as the reference point, a look-up table located in the PROM permits the grating to be rotated to select the precise monochromator wavelength output. Wavelength Accuracy. After initialization, the microprocessor displays the output wavelength on the LCD display. The displayed output wavelength is accurate to plus-orminus one motor step (plus or minus 0.07nm for a 1200g/mm grating in first order – Digikrom 240). If, after long usage or severe treatment, the wavelength accuracy is not within one motor step, it can be returned to original accuracy by using a keyboard routine to adjust the ‘home’ wavelength offset. Wavelength Precision. The motor step differences between lines of the Hg spectrum are constant. Thus, wavelength precission is better than 0.07nm or one motor step. Wavelength Scan. The microprocessor controlled-motor combination has been designed for a maximum stepping rate of 1000 steps/sec., providing a slew speed of 84nm/sec. (with 1200g/mm grating in first order), or about 4000nm/min. Scan speeds are selected from the keypad by entering the desired value, in units of nm/min, and the user can specify any value from 1nm/min to 4000nm/min. Real-time display of the instantaneous wavelength is available only for scan speeds lees than 900nm/min, although output of the data to a computer is available for all scan speeds. Entrance/Exit Slits. Unilaterally adjustable-width curved jaw slits are standard on the Digikrom. Adjustable straight-jaw slits are also available. Adjustable slits are stepper motor driven with microprocessor control. Adjustable Slit Assembly. The microprocessor-controlled stepper motor-driven slits are adjustable in 1 micron increments from 20 microns to 2000 microns. Fail-safe electronic design prevents accidental closure of the slits to values less than 10microns. Slit jaws are 1 inch high and are photoetched from 0.0015” thick stainless steel. The etching process produces a sharp edge on the slit jaws. A thickness profile of the slit edge shows a decrease in metal thickness to a dimension of about 1/3 of the thickness, followed by a sharp truncation. Thus, the true ‘edge’ thickness is about 10 microns. Slit Width Accuracy. The slit is adjusted manually to produce a ‘home’ initialization value between 40 and 60 microns as measured by the diffraction of a HeNe laser beam. The exact value of this ‘home’ width for each slit assembly is stored in PROM. Selected slit width values are then offsets from this calibrated value. Adjusted slit width uniformity from top to bottom is better than 2 dust and other debris, and the user does not make his/her own adjustments, the slit width accuracy and uniformity is guaranteed to be plus-or-minus 3 microns. Slits having different resolutions (i.e. different increments of microns per motorstep) can be furnished on request. Appendix 1 Datasheets and specifications of instruments used Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 249 Optical Diagram The Digikrom 240 is a classical Czerny-Turner monochromator in its optical configuration, with a 240mm focal length. Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 250 Appendix 2 Fluctuations of system’s performance depending on the number of samples of the training set Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 251 Table A2.1 (1) Colorimetric Configuration: mean, minimum, maximum and standard deviation of the CIELAB colour difference values obtained using the five different training sets selected from an initial randomly selected colour sample for all sizes considered, and using the CCCR chart as test set. mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab Random 1 4.892 1.401 12.675 3.109 Random 1 5.428 1.380 13.054 3.321 Random 2 5.224 1.160 12.817 3.017 Random 2 5.593 1.231 13.500 3.406 Random 3 5.083 1.121 12.963 3.156 Random 3 6.389 0.753 18.228 4.243 Random 4 4.698 0.392 11.900 3.054 Random 4 5.877 1.580 14.125 3.441 Random 5 5.197 1.288 12.364 2.918 Random 5 6.041 1.627 14.601 3.527 mean 5.019 1.072 12.544 3.051 mean 5.866 1.314 14.702 3.588 std. dev. 0.222 0.396 0.423 0.091 std. dev. 0.378 0.352 2.058 0.374 10 colour samples % fluct. 4.422 36.932 3.369 2.988 20 colour samples % fluct. 6.439 26.759 13.996 10.418 mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab Random 1 5.897 1.032 14.319 3.580 Random 1 6.141 2.423 14.268 3.422 Random 2 5.860 1.145 14.248 3.545 Random 2 6.232 2.309 14.480 3.491 Random 3 5.694 1.046 13.805 3.495 Random 3 6.162 2.517 14.262 3.434 Random 4 5.963 1.562 14.682 3.560 Random 4 5.892 2.007 14.058 3.408 Random 5 5.872 1.255 14.256 3.542 Random 5 6.206 2.243 14.355 3.453 mean 5.857 1.208 14.262 3.544 mean 6.127 2.300 14.285 3.442 std. dev. 0.100 0.217 0.312 0.031 std. dev. 0.136 0.195 0.154 0.032 30 colour samples % fluct. 1.700 17.981 2.186 0.887 40 colour samples % fluct. 2.219 8.459 1.080 0.935 mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab Random 1 5.869 1.799 14.217 3.521 Random 1 5.732 2.197 14.077 3.452 Random 2 5.609 1.516 13.942 3.446 Random 2 5.653 2.117 13.912 3.455 Random 3 5.903 1.805 14.337 3.530 Random 3 5.772 2.331 14.100 3.465 Random 4 5.869 1.799 14.217 3.521 Random 4 5.782 2.329 14.110 3.466 Random 5 5.869 1.799 14.217 3.521 Random 5 5.800 2.308 14.148 3.478 mean 5.824 1.744 14.186 3.508 mean 5.748 2.256 14.069 3.463 std. dev. 0.121 0.127 0.146 0.035 std. dev. 0.059 0.095 0.092 0.010 50 colour samples % fluct. 2.077 7.299 1.029 0.991 60 colour samples % fluct. 1.019 4.231 0.651 0.297 Appendix 2 Fluctuations of system’s performance depending on the number of samples of the training set Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 252 Table A2.1 (2) Colorimetric Configuration: mean, minimum, maximum and standard deviation of the CIELAB colour difference values obtained using the five different training sets selected from an initial randomly selected colour sample for all sizes considered, and using the CCCR chart as test set. mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab Random 1 5.896 2.398 14.124 3.429 Random 1 5.736 2.236 13.994 3.451 Random 2 5.896 2.415 14.120 3.428 Random 2 5.682 2.235 13.943 3.434 Random 3 5.896 2.398 14.124 3.429 Random 3 5.682 2.235 13.943 3.434 Random 4 5.903 2.256 14.148 3.426 Random 4 5.682 2.235 13.943 3.434 Random 5 5.829 2.472 14.039 3.423 Random 5 5.677 2.257 13.948 3.429 mean 5.884 2.388 14.111 3.427 mean 5.692 2.240 13.954 3.436 std. dev. 0.031 0.080 0.042 0.003 std. dev. 0.025 0.010 0.022 0.008 70 colour samples % fluct. 0.525 3.338 0.296 0.074 80 colour samples % fluct. 0.436 0.435 0.160 0.246 mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab Random 1 5.710 2.291 13.891 3.411 Random 1 5.527 2.112 13.716 3.393 Random 2 5.681 2.261 13.815 3.368 Random 2 5.507 1.968 13.680 3.384 Random 3 5.710 2.291 13.891 3.411 Random 3 5.523 1.998 13.681 3.387 Random 4 5.720 2.279 13.918 3.421 Random 4 5.560 2.072 13.723 3.391 Random 5 5.710 2.291 13.891 3.411 Random 5 5.412 2.095 13.641 3.371 mean 5.706 2.282 13.881 3.404 mean 5.506 2.049 13.688 3.385 std. dev. 0.015 0.013 0.039 0.021 std. dev. 0.056 0.063 0.033 0.009 90 colour samples % fluct. 0.260 0.568 0.278 0.619 100 colour samples % fluct. 1.015 3.065 0.240 0.256 mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab Random 1 5.535 2.236 13.737 3.322 Random 1 5.575 2.224 13.788 3.359 Random 2 5.628 2.225 13.794 3.333 Random 2 5.623 2.265 13.833 3.365 Random 3 5.616 2.185 13.765 3.325 Random 3 5.627 2.248 13.832 3.363 Random 4 5.552 2.235 13.747 3.325 Random 4 5.621 2.246 13.826 3.362 Random 5 5.613 2.131 13.752 3.332 Random 5 5.621 2.246 13.826 3.362 mean 5.589 2.202 13.759 3.327 mean 5.613 2.246 13.821 3.362 std. dev. 0.043 0.045 0.022 0.005 std. dev. 0.022 0.014 0.019 0.002 110 colour samples % fluct. 0.761 2.045 0.159 0.145 120 colour samples % fluct. 0.385 0.638 0.134 0.053 Appendix 2 Fluctuations of system’s performance depending on the number of samples of the training set Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 253 Table A2.1 (3) Colorimetric Configuration: mean, minimum, maximum and standard deviation of the CIELAB colour difference values obtained using the five different training sets selected from an initial randomly selected colour sample for all sizes considered, and using the CCCR chart as test set. mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab Random 1 5.746 2.301 13.945 3.393 Random 1 5.712 2.264 13.855 3.408 Random 2 5.738 2.287 13.922 3.387 Random 2 5.728 2.260 13.901 3.420 Random 3 5.746 2.301 13.945 3.393 Random 3 5.726 2.255 13.858 3.409 Random 4 5.746 2.301 13.945 3.393 Random 4 5.726 2.255 13.858 3.409 Random 5 5.730 2.316 13.942 3.393 Random 5 5.726 2.255 13.858 3.409 mean 5.741 2.301 13.940 3.392 mean 5.724 2.258 13.866 3.411 std. dev. 0.007 0.010 0.010 0.003 std. dev. 0.007 0.004 0.020 0.005 130 colour samples % fluct. 0.125 0.446 0.072 0.079 140 colour samples % fluct. 0.114 0.181 0.141 0.148 mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab Random 1 5.749 2.211 13.877 3.404 Random 1 5.777 2.219 13.905 3.410 Random 2 5.749 2.211 13.877 3.404 Random 2 5.777 2.219 13.905 3.410 Random 3 5.749 2.211 13.877 3.404 Random 3 5.777 2.219 13.905 3.410 Random 4 5.749 2.211 13.877 3.404 Random 4 5.777 2.219 13.905 3.410 Random 5 5.749 2.211 13.877 3.404 Random 5 5.777 2.219 13.905 3.410 mean 5.749 2.211 13.877 3.404 mean 5.777 2.219 13.905 3.410 std. dev. 0.000 0.000 0.000 0.000 std. dev. 0.000 0.000 0.000 0.000 150 colour samples % fluct. 0.000 0.000 0.000 0.000 160 colour samples % fluct. 0.000 0.000 0.000 0.000 mean ∆E*ab min ∆E*ab max ∆E*ab stddev ∆E*ab Random 1 5.886 2.241 13.962 3.414 Random 2 5.886 2.241 13.962 3.414 Random 3 5.886 2.241 13.962 3.414 Random 4 5.886 2.241 13.962 3.414 Random 5 5.886 2.241 13.962 3.414 mean 5.886 2.241 13.962 3.414 std. dev. 0.000 0.000 0.000 0.000 166 colour samples % fluct. 0.000 0.000 0.000 0.000 Appendix 2 Fluctuations of system’s performance depending on the number of samples of the training set Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 254 Table A2.2 (1) Colorimetric Configuration: mean, minimum, maximum and standard deviation of RMSE values obtained using the five different training sets selected from an initial randomly selected colour sample for all sizes considered, and using the CCCR chart as test set. mean RMSE min RMSE max RMSE stddev RMSE mean RMSE min RMSE max RMSE stddev RMSE Random 1 5.777E-02 3.174E-02 1.708E-01 3.003E-02 Random 1 5.762E-02 3.455E-02 1.733E-01 2.945E-02 Random 2 5.638E-02 3.420E-02 1.692E-01 2.740E-02 Random 2 5.625E-02 3.395E-02 1.687E-01 2.732E-02 Random 3 6.288E-02 3.263E-02 1.684E-01 3.093E-02 Random 3 5.861E-02 3.533E-02 1.724E-01 2.871E-02 Random 4 5.811E-02 3.299E-02 1.739E-01 3.098E-02 Random 4 5.706E-02 3.235E-02 1.696E-01 2.791E-02 Random 5 6.491E-02 2.899E-02 1.563E-01 3.344E-02 Random 5 5.671E-02 3.275E-02 1.697E-01 2.797E-02 mean 6.001E-02 3.211E-02 1.677E-01 3.056E-02 mean 5.725E-02 3.379E-02 1.707E-01 2.827E-02 std. dev. 3.676E-03 1.955E-03 6.722E-03 2.172E-03 std. dev. 9.102E-04 1.238E-03 1.991E-03 8.228E-04 10 colour samples % fluct. 6.126 6.088 4.008 7.109 20 colour samples % fluct. 1.590 3.664 1.166 2.910 mean RMSE min RMSE max RMSE stddev RMSE mean RMSE min RMSE max RMSE stddev RMSE Random 1 5.612E-02 3.434E-02 1.701E-01 2.824E-02 Random 1 5.828E-02 3.584E-02 1.748E-01 3.026E-02 Random 2 5.786E-02 3.523E-02 1.749E-01 3.073E-02 Random 2 5.851E-02 3.610E-02 1.749E-01 3.033E-02 Random 3 5.604E-02 3.454E-02 1.699E-01 2.829E-02 Random 3 5.856E-02 3.609E-02 1.751E-01 3.040E-02 Random 4 5.600E-02 3.427E-02 1.694E-01 2.799E-02 Random 4 5.851E-02 3.610E-02 1.749E-01 3.033E-02 Random 5 5.643E-02 3.454E-02 1.694E-01 2.782E-02 Random 5 5.777E-02 3.566E-02 1.743E-01 3.002E-02 mean 5.649E-02 3.458E-02 1.707E-01 2.861E-02 mean 5.833E-02 3.596E-02 1.748E-01 3.027E-02 std. dev. 7.842E-04 3.806E-04 2.346E-03 1.198E-03 std. dev. 3.293E-04 2.003E-04 3.000E-04 1.472E-04 30 colour samples % fluct. 1.388 1.100 1.374 4.187 40 colour samples % fluct. 0.565 0.557 0.172 0.486 mean RMSE min RMSE max RMSE stddev RMSE mean RMSE min RMSE max RMSE stddev RMSE Random 1 5.694E-02 2.783E-02 1.739E-01 3.056E-02 Random 1 5.617E-02 2.890E-02 1.733E-01 3.008E-02 Random 2 5.723E-02 3.136E-02 1.738E-01 3.022E-02 Random 2 5.615E-02 3.031E-02 1.732E-01 2.995E-02 Random 3 5.729E-02 3.084E-02 1.738E-01 3.024E-02 Random 3 5.617E-02 2.890E-02 1.733E-01 3.008E-02 Random 4 5.729E-02 3.084E-02 1.738E-01 3.024E-02 Random 4 5.627E-02 3.052E-02 1.732E-01 2.997E-02 Random 5 5.672E-02 2.812E-02 1.730E-01 3.002E-02 Random 5 5.627E-02 3.052E-02 1.732E-01 2.997E-02 mean 5.709E-02 2.980E-02 1.737E-01 3.026E-02 mean 5.621E-02 2.983E-02 1.732E-01 3.001E-02 std. dev. 2.544E-04 1.681E-03 3.715E-04 1.936E-04 std. dev. 5.899E-05 8.533E-04 5.477E-05 6.442E-05 50 colour samples % fluct. 0.446 5.641 0.214 0.640 60 colour samples % fluct. 0.105 2.861 0.032 0.215 Appendix 2 Fluctuations of system’s performance depending on the number of samples of the training set Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 261 Table A2.4 (2) Multispectral Configuration: mean, minimum, maximum and standard deviation of RMSE values obtained using the five different training sets selected from an initial randomly selected colour sample for all sizes considered, and using the CCCR chart as test set. mean RMSE min RMSE max RMSE stddev RMSE mean RMSE min RMSE max RMSE stddev RMSE Random 1 4.863E-02 2.228E-02 7.735E-02 1.535E-02 Random 1 4.937E-02 1.795E-02 9.562E-02 1.802E-02 Random 2 4.906E-02 2.008E-02 8.802E-02 1.669E-02 Random 2 4.857E-02 2.125E-02 8.004E-02 1.567E-02 Random 3 4.928E-02 2.119E-02 8.698E-02 1.659E-02 Random 3 4.918E-02 1.942E-02 8.912E-02 1.728E-02 Random 4 5.073E-02 2.083E-02 8.581E-02 1.773E-02 Random 4 4.929E-02 1.952E-02 8.847E-02 1.720E-02 Random 5 4.908E-02 2.004E-02 8.900E-02 1.678E-02 Random 5 4.925E-02 2.090E-02 8.910E-02 1.684E-02 mean 4.936E-02 2.088E-02 8.543E-02 1.663E-02 mean 4.913E-02 1.981E-02 8.847E-02 1.700E-02 std. dev. 8.038E-04 9.225E-04 4.671E-03 8.480E-04 std. dev. 3.216E-04 1.319E-03 5.545E-03 8.593E-04 70 colour samples % fluct. 1.629 4.417 5.468 5.100 80 colour samples % fluct. 0.655 6.658 6.268 5.054 mean RMSE min RMSE max RMSE stddev RMSE mean RMSE min RMSE max RMSE stddev RMSE Random 1 4.890E-02 2.099E-02 8.267E-02 1.569E-02 Random 1 4.834E-02 2.300E-02 7.217E-02 1.468E-02 Random 2 4.867E-02 2.248E-02 7.671E-02 1.484E-02 Random 2 4.861E-02 2.245E-02 7.640E-02 1.485E-02 Random 3 4.890E-02 2.099E-02 8.267E-02 1.569E-02 Random 3 4.830E-02 2.285E-02 7.199E-02 1.468E-02 Random 4 4.867E-02 2.076E-02 8.248E-02 1.568E-02 Random 4 4.830E-02 2.285E-02 7.199E-02 1.468E-02 Random 5 4.890E-02 2.099E-02 8.267E-02 1.569E-02 Random 5 4.853E-02 2.211E-02 7.750E-02 1.503E-02 mean 4.881E-02 2.124E-02 8.144E-02 1.552E-02 mean 4.842E-02 2.265E-02 7.401E-02 1.478E-02 std. dev. 1.260E-04 6.992E-04 2.645E-03 3.790E-04 std. dev. 1.443E-04 3.654E-04 2.713E-03 1.560E-04 90 colour samples % fluct. 0.258 3.292 3.248 2.443 100 colour samples % fluct. 0.298 1.613 3.666 1.055 mean RMSE min RMSE max RMSE stddev RMSE mean RMSE min RMSE max RMSE stddev RMSE Random 1 4.699E-02 2.420E-02 6.972E-02 1.375E-02 Random 1 4.679E-02 2.383E-02 7.254E-02 1.401E-02 Random 2 4.742E-02 2.400E-02 7.233E-02 1.389E-02 Random 2 4.692E-02 2.363E-02 7.215E-02 1.407E-02 Random 3 4.740E-02 2.468E-02 7.172E-02 1.383E-02 Random 3 4.693E-02 2.375E-02 7.213E-02 1.400E-02 Random 4 4.705E-02 2.431E-02 6.927E-02 1.364E-02 Random 4 4.695E-02 2.378E-02 7.224E-02 1.402E-02 Random 5 4.750E-02 2.397E-02 7.257E-02 1.386E-02 Random 5 4.695E-02 2.378E-02 7.224E-02 1.402E-02 mean 4.727E-02 2.423E-02 7.112E-02 1.379E-02 mean 4.691E-02 2.375E-02 7.226E-02 1.402E-02 std. dev. 2.340E-04 2.873E-04 1.526E-03 1.006E-04 std. dev. 6.723E-05 7.503E-05 1.645E-04 2.702E-05 110 colour samples % fluct. 0.495 1.186 2.145 0.730 120 colour samples % fluct. 0.143 0.316 0.228 0.193 Appendix 2 Fluctuations of system’s performance depending on the number of samples of the training set Thorough Characterization and Analysis of a Multispectral Imaging System Developed for Colour Measurement 262 Table A2.4 (3) Multispectral Configuration: mean, minimum, maximum and standard deviation of RMSE values obtained using the five different training sets selected from an initial randomly selected colour sample for all sizes considered, and using the CCCR chart as test set. mean RMSE min RMSE max RMSE stddev RMSE mean RMSE min RMSE max RMSE stddev RMSE Random 1 4.760E-02 2.414E-02 7.272E-02 1.369E-02 Random 1 4.814E-02 2.454E-02 7.450E-02 1.401E-02 Random 2 4.753E-02 2.420E-02 7.266E-02 1.377E-02 Random 2 4.822E-02 2.469E-02 7.459E-02 1.396E-02 Random 3 4.755E-02 2.423E-02 7.285E-02 1.378E-02 Random 3 4.814E-02 2.454E-02 7.450E-02 1.401E-02 Random 4 4.755E-02 2.423E-02 7.285E-02 1.378E-02 Random 4 4.816E-02 2.447E-02 7.483E-02 1.404E-02 Random 5 4.760E-02 2.414E-02 7.272E-02 1.369E-02 Random 5 4.822E-02 2.469E-02 7.459E-02 1.396E-02 mean 4.757E-02 2.419E-02 7.276E-02 1.374E-02 mean 4.818E-02 2.459E-02 7.460E-02 1.400E-02 std. dev. 3.209E-05 4.550E-05 8.573E-05 4.764E-05 std. dev. 4.099E-05 9.915E-05 1.352E-04 3.507E-05 130 colour samples % fluct. 0.067 0.188 0.118 0.347 140 colour samples % fluct. 0.085 0.403 0.181 0.251 mean RMSE min RMSE max RMSE stddev RMSE mean RMSE min RMSE max RMSE stddev RMSE Random 1 4.852E-02 2.430E-02 7.593E-02 1.410E-02 Random 1 4.851E-02 2.380E-02 7.729E-02 1.443E-02 Random 2 4.852E-02 2.430E-02 7.593E-02 1.410E-02 Random 2 4.851E-02 2.380E-02 7.729E-02 1.443E-02 Random 3 4.852E-02 2.430E-02 7.593E-02 1.410E-02 Random 3 4.851E-02 2.380E-02 7.729E-02 1.443E-02 Random 4 4.852E-02 2.430E-02 7.593E-02 1.410E-02 Random 4 4.851E-02 2.380E-02 7.729E-02 1.443E-02 Random 5 4.852E-02 2.430E-02 7.593E-02 1.410E-02 Random 5 4.851E-02 2.380E-02 7.729E-02 1.443E-02 mean 4.852E-02 2.430E-02 7.593E-02 1.410E-02 mean 4.851E-02 2.380E-02 7.729E-02 1.443E-02 std. dev. 0.000E+00 0.000E+00 0.000E+00 2.328E-10 std. dev. 0.000E+00 0.000E+00 1.317E-09 0.000E+00 150 colour samples % fluct. 0.000 0.000 0.000 0.000 160 colour samples % fluct. 0.000 0.000 0.000 0.000 mean RMSE min RMSE max RMSE stddev RMSE Random 1 4.835E-02 2.380E-02 7.873E-02 1.457E-02 Random 2 4.835E-02 2.380E-02 7.873E-02 1.457E-02 Random 3 4.835E-02 2.380E-02 7.873E-02 1.457E-02 Random 4 4.835E-02 2.380E-02 7.873E-02 1.457E-02 Random 5 4.835E-02 2.380E-02 7.873E-02 1.457E-02 mean 4.835E-02 2.380E-02 7.873E-02 1.457E-02 std. dev. 0.000E+00 0.000E+00 9.313E-10 0.000E+00 166 colour samples % fluct. 0.000 0.000 0.000 0.000