Matrix Differential Calculus with Applications in Statistics and Econometrics

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Linear And Nonlinear Programming

When I began to study lighting engineering, my professor told me I was about to enter a magnificent community of about 3000 people distributed around the world, and in just five years from then I w...

Human Factors in Lighting

The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating the discrete cosine transform, we propose a generalized discrete cosine transform with three parameters, and prove its orthogonality for some new cases. A new type of discrete cosine transform is proposed and its orthogonality is proved. Finally, we propose a generalized discrete W transform with three parameters, and prove its orthogonality for some new cases. Keywords: Discrete Fourier transform, discrete sine transform, discrete cosine transform, discrete W transform Nigerian Journal of Technological Research , vol7(1) 2012

On discrete cosine transform

An improved spectral reflectance estimation method is developed to transform raw camera RGB responses to spectral reflectance. The novelty of our method is to apply a local weighted linear regression model for spectral reflectance estimation and construct the weighting matrix using a Gaussian function in CIELAB uniform color space. The proposed method was tested using both a standard color chart and a set of textile samples, with a digital RGB camera and by ten times ten-fold cross-validation. The results demonstrate that our method gives the best accuracy in estimating both the spectral reflectance and the colorimetric values in comparison with existing methods.

Spectra estimation from raw camera responses based on adaptive local-weighted linear regression.

A improved spectral reflectance reconstruction method is developed to transform camera RGB to spectral reflectance for skin images. Rather than using conventional direct or two-step processes, we transform camera RGB to skin reflectance directly using a principal component analysis (PCA) approach. The novelty in our direct method (RGB to spectra) is the use of a skin-specific colour characterisation chart with spectra closer to human skin spectra, and a new database of skin reflectances to derive the PCA bases. The experimental results using the facial images of 17 subjects demonstrate that our new direct method gives a significantly better performance than conventional, two-step methods and direct methods with traditional characterization charts. This new spectral reconstruction algorithm is sufficiently precise to reconstruct spectral properites relating to chromophores and its performance is within the acceptable range for maxillofacial soft tissue prostheses (error < 3 ΔE*ab units).

Improved method for skin reflectance reconstruction from camera images.

The idea of placing a coloured filter in front of a camera to make it more colorimetric has been previously proposed. However, this prior art approach sought to increase the dimensionality of the capture — i.e. to take an image with and without a filter — rather than to change the spectral characteristics of the sensor itself. In this paper, we set out a new method for finding the filter that, in a least-squares sense best achieves the Luther condition. That is, the filter multiplied by the camera spectral sensitivities is ‘almost’ a linear combination from the colour matching functions of the human visual system. We show that for a given sensor set the best filter and best linear mapping can be found together by solving an alternating least-squares problem. Experiments demonstrate that placing an optimal filter in front of a camera can result in a dramatic improvement in its ability to see the world colorimetrically.

/pdf/using-a-simple-colour-pre-filter-to-make-cameras-more-2y9gqb7tki.pdf

Using a Simple Colour Pre-filter to Make Cameras More Colorimetric

Recently, an iterative optimization method was proposed that determines the spectral transmittance of a color filter which, when placed in front of a camera, makes the camera more colorimetric [1]. However, the performance of this method depends strongly on the filter (guess) that initializes the optimization. In this paper, we develop a simple extension to the optimization where we systematically sample the set of possible initial filters and for each initialization solve for the best refinement. Experiments demonstrate that improving the initialization step can result in the effective ‘camera+filter’ imaging system being much more colorimetric. Moreover, the filters we design are smoother than previously reported (which makes them easier to manufacture).

/pdf/an-improved-optimization-method-for-finding-a-color-filter-1w68v2bz7h.pdf

An improved optimization method for finding a color filter to make a camera more colorimetric

When we place a colored filter in front of a camera the effective camera response functions are equal to the given camera spectral sensitivities multiplied by the filter spectral transmittance. In this article, we solve for the filter which returns the modified sensitivities as close to being a linear transformation from the color matching functions of the human visual system as possible. When this linearity condition - sometimes called the Luther condition - is approximately met, the ‘camera+filter’ system can be used for accurate color measurement. Then, we reformulate our filter design optimisation for making the sensor responses as close to the CIEXYZ tristimulus values as possible given the knowledge of real measured surfaces and illuminants spectra data. This data-driven method in turn is extended to incorporate constraints on the filter (smoothness and bounded transmission). Also, because how the optimisation is initialised is shown to impact on the performance of the solved-for filters, a multi-initialisation optimisation is developed. Experiments demonstrate that, by taking pictures through our optimised color filters, we can make cameras significantly more colorimetric.

Designing Color Filters That Make Cameras More Colorimetric

The Luther condition states that a camera is colorimetric if its spectral sensitivities are a linear transform from the XYZ colour matching functions. Recently, a method has been proposed for finding the optimal coloured filter that when placed in front of a camera, results in effective sensitivities that satisfy the Luther condition. The advantage of this method is that it finds the best filter for all possible physical capture conditions. The disadvantage is that the statistical information of typical scenes are not taken into account.

Yuteng Zhu

Papers

Improved method for skin reflectance reconstruction from camera images.

Using a Simple Colour Pre-filter to Make Cameras More Colorimetric

An improved optimization method for finding a color filter to make a camera more colorimetric

Designing Color Filters That Make Cameras More Colorimetric

Finding a Colour Filter to Make a Camera Colorimetric by Optimisation