The McCollough Effect is an orientation specific colored aftereffect. That is, following prolonged viewing of a vertical grid on orange ground alternated with a horizontal grid on blue ground, a yellow-orange hue is perceived on an achromatic horizontal grid, and a bluish hue on a vertical grid. McCollough suggested that the colored aftereffect may depend upon color adaptation of a population of neural elements specific to colored edges of a particular orientation. Accordingly vertical edge detectors sensitive to orange adapt during inspection such that when vertical edges are presented on an achromatic ground only those non-adapted color-line detectors respond creating the perception of blue. Similarly, horizontal edge detectors specific to blue adapt such that response to achromatic edges creates the perception of yellow-orange. In a subsequent study McCollough and Clark used left and right diagonal inspection patterns and observed that the aftereffect of orange and right diagonal was influenced by the left diagonal color that was alternated with it. The aftereffect of orange right diagonal tended toward blue when the orange stimulus was alternated with a blue left diagonal stimulus pattern and tended toward green when the orange stimulus was alternated with a green left diagonal pattern. On the basis of the color coded edge detector theory McCollough and Clark suggested the effect was induced by wavelength adaptation of wavelength sensitive edge detectors which may influence the hue of the• aftereffect on the orthogonal test pattern. A test of McCollough's model of color coded edge detectors was made by presenting a colored field (no lines) to S before the presentation of the color-line stimulus. If wavelength and edge stimuli were processed by a population of neural elements sensitive to both, then the aftereffect would not be affected by the presentation of an unlined color field. If color and line stimuli were processed separately, then the "effective" color component of the lined stimulus pattern would be that portion of the spectrum not stimulated by the preceeding color field. The color of the aftereffect would be approximately complementary to the non-adapted population of color receptors stimulated by the lined inspection pattern. In the experiment 28 college juniors observed two inspection conditions. In condition 1 orange vertical alternated with blue horizontal and the aftereffect created was measured via a colorimeter. The same stimulus patterns were employed in condition 2 where each was preceeded by a plain color field that stimulated a portion of the spectrum illuminated by the following lined stimulus. The aftereffect observed was compared with the aftereffect on condition 1. Color matches were measured by three photometer readings indicating percent transmittance of red, blue, and green in each match. These readings were translated into CIE x, y coordinates and the means plotted on a chromaticity diagram. Statistical analysis of the data indicated that the color matches in condition I and condition 2 were significantly different and varied as predicted. While McCollough and Clark attributed the variation in the hue of the colored aftereffect to the relative spectral properties of the lined inspection patterns employed in their experiment, the present study shows that the results may be due to the state of color adaptation resulting from the preceeding stimulus pattern. The adapting color stimulus is not necessarily a lined color pattern. It may indeed be a plain color field. The results suggest that the colored line-contingent aftereffect is created by at least two levels in the visual system: color receptors independent of slope analysers. The color coded edge detector model is not adequate to account for the McCollough Effect.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

The detectivity and resolution of single aperture and multiple aperture optical imaging systems are compared for single point sources in optically background limited environments. The single aperture system assumes a single large diameter lens with a detector array at the focal plane. The multiple aperture system assumes an independent detector array at the focal plane of each of the apertures of the multiaperture system. The multiaperture lenses are arranged in a rectangularly symmetric pattern within the perimeter that a single large aperture would occupy. Due to the presence of a constant signal plus an optical noise field whose amplitude is Rayleigh distributed, Rician squared statistics are used to model the detector voltage random variable. The detectivity is analyzed assuming a detector optical amplitude threshold is chosen such that the signal is considered present when the optical amplitude exceeds threshold and considered absent when the optical amplitude falls below threshold. The optimum threshold is found to be given by Io(AT/n2 ∝ EXP [A2/(2n2)] where (A2/n2) is the signal to noise power ratio, T is the optical amplitude threshold, and IO is the modified Bessel function of order zero. Detector size is found to be the predominant factor in resolution, due to the minute size of an Airy disc image from a point source. The resolution angle ( γ resolution) can be approximated by γresolution = (Ae/f) where Ae is the distance between detector centers and f is the imaging system focal length. Single aperture and multiple aperture systems are found to be equal in detectivity performance when optically background limited. For equal detector sizes and spacings, and equal imaging system focal lengths, multiple aperture systems are found to provide resolution improvement over single aperture systems. This resolution improvement depends on the overlap of the field of view between the detector arrays of the individual apertures in the multiple aperture system.

Étant donné une matrice ou un opérateur, comprendre comment se comportent ses puissances et plus généralement le calcul fonctionnel, est un problème qui intervient dans de nombreux domaines. Pour les opérateurs normaux, le spectre fournit de précieuses informations sur la norme du calcul fonctionnel. Cependant, la situation est très différente pour les opérateurs non normaux. Dans cette thèse, nous étudions donc plusieurs alternatives au spectre pour contrôler la norme des puissances ou fonctions de matrices ou d'opérateurs non normaux. Dans un premier temps, on s'intéresse à l'image numérique, aux ensembles K-spectraux et plus précisément à la conjecture de Crouzeix. Posée par Crouzeix en 2004, celle-ci stipule que l'image numérique pourrait être un ensemble 2-spectral. Récemment, Crouzeix et Palencia ont montré que c'est un ensemble (1+√2)-spectral. En s'inspirant de leur résultat, nous proposons une approche abstraite de la conjecture de Crouzeix en commençant par une version abstraite de leur résultat. On montre que si A est une algèbre uniforme et θ : A → Mₙ(ℂ) est un morphisme d'algèbre continu, s'il existe une contraction antilinéaire α : A → A telle que ∥θ(f) + θ(α(f))*∥ ≤ 2∥f∥ (f ∈ A), alors ∥θ∥ ≤ 1 + √2. Sous ces conditions 1 + √2 est optimale mais si on suppose en plus que α(1) = 1, alors il se pourrait que ∥θ∥ ≤ 2. Enfin, on montre deux cas particuliers pour lesquels on a réussi à prouver cette conjecture. Dans un second temps nous étudions le théorème de Kreiss et ses généralisations. Ce théorème permet de contrôler le supremum de la norme des puissances d'une matrice à l'aide de sa résolvante. Il a été généralisé aux polynômes et sur des domaines généraux par Toh et Trefethen puis pour les fonctions holomorphes sur le disque par Vitse. On étudie leurs résultats et on montre une inégalité de type Kreiss pour les fonctions rationnelles bornées sur des domaines généraux : pour un domaine Ω dont la frontière est une courbe de Jordan C², il existe une constante C > 0 telle que pour toute fonction rationnelle f bornée sur Ω et pour tout opérateur T ∈ B(X) tel que σ(T) ⊂ Ω[barre au-dessus], on a ∥f(T)∥ ≤ C(deg(f) + 1)∥f∥ [indice Ω] sup [z∉Ω[barre au-dessus] en-dessous] [dist(z, Ω)∥(zI - T)⁻¹∥]. Enfin, nous nous intéressons aux matrices ayant des pseudospectres identiques. Il est connu que les pseudospectres permettent de contrôler les normes des matrices à un facteur multiplicatif 2 près. Mais l'histoire est vraiment différente pour les puissances supérieures comme le montre un résultat de Ransford. Celui-ci a pour conséquence que, pour tout M > 0, il existe des matrices A, B ∈ M[indice N](ℂ) ayant des pseudospectres identiques telles que ∥Aⁿ∥ > M∥Bⁿ∥ pour tout 2 ≤ n ≤ (N - 3)/2. Quelques années plus tard, Ransford et Raouafi ont montré que pour tout M > 0 et n ≥ 2, il existe deux matrices A, B ∈ M₆(ℂ) ayant des pseudospectres identiques mais tels que ∥Aⁿ∥ > M∥Bⁿ∥ en montrant ce résultat plus généralement pour des fonctions holomorphes qui ne sont pas des transformations de Möbius. On obtient un résultat similaire pour deux puissances. Plus précisément, on montre qu'étant donné M > 0 et n, m ≥ 2, il existe deux matrices A et B de taille 10 x 10 ayant des pseudospectres identiques telles que ∥Aⁿ∥ > M∥Bⁿ∥ et ∥Aᵐ∥ > M∥Bᵐ∥ et que ce résultat tient pour deux fonctions holomorphes moyennant une condition technique.

<div>Steganalysis is the study of detecting secret information hidden in objects such as images, videos, texts, time series and games via steganography. Among those objects, the image is the most widely used object to hide secret messages. Detection of possible secret information hidden in images has attracted a lot of attention over the past ten years. People may conduct covert communications by exchanging images in which secret messages may be embedded in bits. One of main advantages of steganography over cryptography is that the former makes this communication insensible for human beings. So statistical methods or tools are needed to help distinguish cover images from stego images. <br></div><div><br></div><div>In this thesis, we start with a discussion of image steganography. Different kinds of embedding schemes for hiding secret information in images are investigated. We also propose a hiding scheme using a reference matrix to lower the distortion caused by embedding. As a result, we obtain Peak Signal-to-Noise Ratios (PSNRs) of stego images that are higher than those given by a Sudoku-based embedding scheme. Next, we consider statistical steganalysis of images in two different frameworks. We first study staganalysis in the framework of statistical hypothesis testing. That is, we cast a cover/stego image detection problem as a hypothesis testing problem. For this purpose, we employ different statistical models for cover images and simulate the effects caused by secret information embedding operations on cover images. Then the staganalysis can be characterized by a hypothesis testing problem in terms of the embedding rate. Rao’s score statistic is used to help make a decision. The main advantage of using Rao’s score test for this problem is that it eliminates an assumption used in the previous work where approximated log likelihood ratio (LR) statistics were commonly employed for the hypothesis testing problems.<br></div><div><br></div><div>We also investigate steganalysis using the deep learning framework. Motivated by neural network architectures applied in computer vision and other tasks, we propose a carefully designed a deep convolutional neural network architecture to classify the cover and stego images. We empirically show the proposed neural network outperforms the state-of-the-art ensemble classifier using a rich model, and is also comparable to other convolutional neural network architectures used for steganalysis.<br></div><div><br></div>The image databases used in the thesis are available on websites cited in the thesis. The stego images are generated from the image databases using source code from the website. <a href="http://dde.binghamton.edu/download/">http://dde.binghamton.edu/download/</a>