Recently, Dr. Andy Rowlands, a lecturer at the School of Engineering and Computing of SBC, published an article titled “Analytic model for the autocorrelation matrix based on piecewise-functional spectra, and its application in camera characterization” in Optics Express (JCR-Q2). Dr. Rowlands is the first and corresponding author.
The paper introduces the concept of piecewise-functional (PF) spectra as a novel tool for modeling autocorrelation statistics in the context of reflectance and color-signal spectra. Significantly, such spectra can be generated numerically for a given statistical model, and an infinite number of them can be analytically integrated over to directly obtain the autocorrelation matrix in closed form. The model contains only a single tuning parameter that enables the degree of correlation to be adjusted, offering a flexible and computationally efficient alternative to traditional measured spectral datasets, which are unavoidably small.
The first application of this work centers on the statistical (computational) method for camera color characterization. The PF reflectance spectra were used to generate autocorrelation matrices that closely matched those of widely used real-world measured reflectance datasets. Even though the PF autocorrelation matrices were trained upon (optimized for) an infinite number of spectra, the characterization performance was found to be almost as good as when using autocorrelation matrices optimized for the real-world datasets.
Due to the simplicity and flexibility of the model, the authors anticipate its application both as a closed-form representation of autocorrelation and as an investigative tool in color and image processing.
Related figure
Related: https://doi.org/10.1364/OE.579609
