Timo Eckhard

Evaluating logarithmic kernel for spectral reflectance estimation—effects on model parametrization, training set size, and number of sensor spectral channels

In this work, we evaluate the conditionally positive definite logarithmic kernel in kernel-based estimation of reflectance spectra. Reflectance spectra are estimated from responses of a 12-channel multispectral imaging system. We demonstrate the performance of the logarithmic kernel in comparison with the linear and Gaussian kernel using simulated and measured camera responses for the Pantone and HKS color charts. Especially, we focus on the estimation model evaluations in case the selection of model parameters is optimized using a cross-validation technique. In experiments, it was found that the Gaussian and logarithmic kernel outperformed the linear kernel in almost all evaluation cases (training set size, response channel number) for both sets. Furthermore, the spectral and color estimation accuracies of the Gaussian and logarithmic kernel were found to be similar in several evaluation cases for real and simulated responses. However, results suggest that for a relatively small training set size, the accuracy of the logarithmic kernel can be markedly lower when compared to the Gaussian kernel. Further it was found from our data that the parameter of the logarithmic kernel could be fixed, which simplified the use of this kernel when compared with the Gaussian kernel.

Improved estimation of reflectance spectra by utilizing prior knowledge.

Estimating spectral reflectance has attracted extensive research efforts in color science and machine learning, motivated through a wide range of applications. In many practical situations, prior knowledge is available that ought to be used. Here, we have developed a general Bayesian method that allows the incorporation of prior knowledge from previous monochromator and spectrophotometer measurements. The approach yields analytical expressions for fast and efficient estimation of spectral reflectance. In addition to point estimates, probability distributions are also obtained, which completely characterize the uncertainty associated with the reconstructed spectrum. We demonstrate that, through the incorporation of prior knowledge, our approach yields improved reconstruction results compared with methods that resort to training data only. Our method is particularly useful when the spectral reflectance to be recovered resides beyond the scope of the training data.

Adaptive global training set selection for spectral estimation of printed inks using reflectance modeling.

The performance of learning-based spectral estimation is greatly influenced by the set of training samples selected to create the reconstruction model. Training sample selection schemes can be categorized into global and local approaches. Most of the previously proposed global training schemes aim to reduce the number of training samples, or a selection of representative samples, to maintain the generality of the training dataset. This work relates to printed ink reflectance estimation for quality assessment in in-line print inspection. We propose what we believe is a novel global training scheme that models a large population of realistic printable ink reflectances. Based on this dataset, we used a recursive top-down algorithm to reject clusters of training samples that do not enhance the performance of a linear least-square regression (pseudoinverse-based estimation) process. A set of experiments with real camera response data of a 12-channel multispectral camera system illustrate the advantages of this selection scheme over some other state-of-the-art algorithms. For our data, our method of global training sample selection outperforms other methods in terms of estimation quality and, more importantly, can quickly handle large datasets. Furthermore, we show that reflectance modeling is a reasonable, convenient tool to generate large training sets for print inspection applications.

Outdoor scene reflectance measurements using a Bragg-grating-based hyperspectral imager

The acquisition of spectral reflectance factor image data in an outdoor environment is a challenging task, mostly due to nonstatic scene content and illumination. In this work, we propose a work-flow for this task using a commercial Bragg-grating-based hyperspectral imager that can capture the visible and near-infrared part of the light spectrum. To our knowledge, we are the first who use this technology for outdoor spectral reflectance factor imaging. The work-flow involves focus position and exposure time estimation, illumination scaling, and image registration, among other procedures. Most of them generally apply to hyperspectral imaging, while some are specific to a Bragg-grating-based hyperspectral imaging device when dealing with specific challenges in outdoor environments. We have conducted some experiments to evaluate the quality of the acquired image data and discussed some limitations of the technology for spectral imaging of outdoor scenes. Fourteen urban scene spectral images acquired using the proposed approach are already publicly available to the scientific community under a Creative Commons license.

Improved Spectral Density Measurement from Estimated Reflectance Data with Kernel Ridge Regression

Density measurement of printed color samples takes an important role in print quality inspection and process control. When multi-spectral imaging systems are considered for surface reflectance measurement, the possibility of calculating spectral print density over the spatial image domain arises. A drawback in using multi-spectral imaging systems is that some spectral reconstruction algorithms can produce estimated reflectances which contain negative values that are physically not meaningful. When spectral density calculations are considered, the results are erroneous and calculations might even fail in the worst case. We demonstrate how this problem can be avoided by using kernel ridge regression with additional link functions to constrain the estimates to positive values.

Nonrigid registration with free-form deformation model of multilevel uniform cubic B-splines: application to image registration and distortion correction of spectral image cubes

In spectral imaging, spatial and spectral information of an image scene are combined. There exist several technologies that allow the acquisition of this kind of data. Depending on the optical components used in the spectral imaging systems, misalignment between image channels can occur. Further, the projection of some systems deviates from that of a perfect optical lens system enough that a distortion of scene content in the images becomes apparent to the observer. Correcting distortion and misalignment can be complicated for spectral image data if they are different at each image channel. In this work, we propose an image registration and distortion correction scheme for spectral image cubes that is based on a free-form deformation model of uniform cubic B-splines with multilevel grid refinement. This scheme is adaptive with respect to image size, degree of misalignment, and degree of distortion, and in that sense is superior to previous approaches. We support our proposed scheme with empirical data from a Bragg-grating-based hyperspectral imager, for which a registration accuracy of approximately one pixel was achieved.

Multispectral imaging approach for simplified non-invasive in-vivo evaluation of gingival erythema

Erythema is a common visual sign of gingivitis. In this work, a new and simple low-cost image capture and analysis method for erythema assessment is proposed. The method is based on digital still images of gingivae and applied on a pixel-by-pixel basis. Multispectral images are acquired with a conventional digital camera and multiplexed LED illumination panels at 460nm and 630nm peak wavelength. An automatic work-flow segments teeth from gingiva regions in the images and creates a map of local blood oxygenation levels, which relates to the presence of erythema. The map is computed from the ratio of the two spectral images. An advantage of the proposed approach is that the whole process is easy to manage by dental health care professionals in clinical environment.