3.7. Multivariate statistical methods for image and VNIRS analysis
3.7.2. Typical multivariate statistical methods
Although there are many statistical methods used for analyzing the data obtained from machine vision, VNIRS and hyperspectral image, the most common and efficient methods used in image processing are principle component analysis (PCA), partial least square (PLS) and artificial neural network (ANN).
3.7.2.1. Principle Component Analysis (PCA)
Principle component analysis is a multivariate statistical method to reduce the large number of original variables into some linear combinations of transformed variables. These transformed variables represent the constituents from the spectral information and further used for data analysis and processing. For example, considering the variations in the spectra due to change in amount of water and sugar content of the samples. A set of variation spectra (principle components) were calculated to represent the changes in absorbance related to the concentration of internal components of samples, at all wavelengths of the spectra. These principle components or factors are formed by multiplying the eigen vectors representing the variance structure by a constant called eigen values or scores and adding the values. The principle components represent the largest variations among the values of the spectral data.
Pettersson and Aberg (2003) investigated the use of near infrared transmittance instrumentation in the wavelength range of 570 - 1100 nm for finding out the mycotoxin deoxynivalenol in wheat kernel. Principal component analysis and partial least square regression calculations were used to formulate the best models. The wavelength range 670–1100 nm gave the best regression model with a slope of 0.949 having a correlation coefficient of 0.984 with a standard error of 381 àg microtoxin deoxynivalenol per kg of wheat.
3.7.2.2. Partial Least Square (PLS)
Partial least square regression is a multivariate statistical method for establishing models between the spectra and known chemical values to analyze the unknown samples.
PLS regression combines the features of principle component analysis and multiple regression. The decomposition of data is similar to the principle component analysis with an additional advantage of data reduction on both spectral and concentration data. When the spectral data is processed using the PLS algorithm two eigen vectors are formed representing variation in spectral data and changes in spectra due to variations in concentration.
Musleh et al. (2005) used NIRS with a wavelength range of 400 and 1100 nm for estimating water and protein content in surimi. Partial least squares (PLS) regression was used to develop predictive equations. The feasibility of an NIR hyperspectral imaging spectrometer application for the quality analysis of single maize kernel was tested by Cogdill et al. (2004). Hyperspectral transmittance of Maize kernels was collected in the range of 750 to 1090 nm. Partial least squares (PLS) regression and principal components regression (PCR) was used to develop predictive calibrations for moisture and oil
content. Viljoen et al. (2005) used NIRS to predict the chemical composition of freeze–
dried ostrich meat samples such as ash, dry matter (DM), crude protein (CP) and fat content. The samples were scanned in the wavelength range of 1100–2500 nm and PLS regression was used to predict the chemical composition. The calibrations were most accurate for crude protein and fat content with regression values for the validation set and the standard error of performance of 0.97, 0.64% and 0.99, 0.18% respectively.
Downey et al. (2005) predicted the maturity and sensory attributes of Cheddar cheese using NIRS in the wavelength range of 750–2498 nm. The sensory attributes like crumbliness, fragmentability, firmness, rubber ness, gritty, grainy, moist, chewy, mouth coating, greasy/oily, melting and mass forming were assessed by trained persons and developed predictive models by PLS regression. The second derivation produced most accurate models and suggested for industrial application.
3.7.2.3. Artificial Neural Network (ANN)
An Artificial Neural network is an information processing concept constructed by a large number of individual, locally connected processing element or units called as neurons similar to biological nervous system or human brain. These neurons in the network sum up the results of the respective input connections, weigh them and transform the weighted sum by a non-linear function of variables. ANN is applied in many complex real-world problems like pattern recognition, forecasting and data classification. The use of ANN in the field of image processing and analysis is increasing rapidly because of the ability of ANN to handle large volume of complex data for processing and classification.
Any ANN is supplied with a training data set obtained from images from which the network can learn about the pattern and also the target output for the pattern. After successful training, the neural network can be used to produce the predictions.