Objects reflecting lights, which invoke the identical responses of the photoreceptors, are called metameric. Metameric objects match each other in color. Assuming all the reflecting objects equiprobable, the probability density distribution on the set of all the classes of mutually metameric objects is evaluated. Metamerism depends on illumination. Objects metameric under one illumination might produce different photoreceptor responses (i.e., mismatch each other) under the other illumination. In particular, objects mapping to a single point in the photoreceptor response space under one illumination map to a volume (referred to as the metamer mismatch volume) in the photoreceptor response space under the second illumination. The probability density distribution in the metamer mismatch volume is also evaluated. Its center is expressed as a function of the photoreceptor spectral sensitivities and the spectral power distributions of the illuminants. Potential application of the obtained results to color management is discussed.

Postreconstructed and postregistered medical images are typically treated as the raw data, implicitly assuming that those operations are error free. We question this assumption and explore how the precision of reconstruction and affine registration can be assessed by the image covariance matrix and confidence interval, called the confidence eigenimage, using a statistical model-based approach. Various hypotheses may be tested after image reconstruction and registration using classical statistical hypothesis testing vehicles: Is there a statistically significant difference between images? Does the intensity at a specific location or area of interest belong to the "normal" range? Is there a tumor? Does the image require rigid registration? We illustrate statistical hypothesis testing with three examples: breast computed tomography, breast near infrared linear reconstruction, and brain magnetic resonance imaging.

This paper is built upon the assumption that in electrical impedance tomography, vectors of voltages and currents are linearly dependent through a resistance matrix. This linear relationship was confirmed experimentally and may be derived analytically under certain assumptions regarding electrodes (Isaacson, 1991). Given measurement data consisting of voltages and currents, we treat this relationship as a linear statistical model. Thus, our goal is not to reconstruct the image but directly estimate its electromagnetic properties reflected in the resistance and/or conductance matrix using electrical impedance tomography (EIT) measurements of voltages and currents on the periphery of the body. Since no inverse problem is involved the algorithm for estimation merely reduces to one matrix inversion. We estimate the impedance resistance matrix using well established statistical inference techniques for linear regression models. We provide a comprehensive treatment for a two-dimensional homogeneous body of a circular shape, by which many concepts of electrical impedance tomography, such as width of electrodes, the difference between voltage-current and current-voltage systems are illustrated. Our theory may be applied to various tests including EIT hardware calibration and whether the medium is homogeneous. These tests are illustrated on phantom agar data.

This paper extends basic concepts of statistical hypothesis testing and confidence intervals to images generated by a new procedure for near infrared spectroscopic tomography being developed for use in breast cancer diagnosis. By estimating the covariance matrix of the pixels of an image from data used in the image reconstruction process, confidence maps for statistical tests on individual pixels and confidence intervals for entire images are displayed as an aid to research and clinical personnel interpreting possibly noisy images. The methods are applied to simulated and phantom-based images.