Treaty between the United States of America and the western bands of Shoshonee Indians.

"Concluded at Ruby valley, in the territory of Nevada."

The bands of Orion,

Mode of access: Internet.

Treaty between the United States of America and the Chippewas of the Mississippi and the Pillager and Lake Winibigoshish bands of Chippewa Indians in Minnesota. Concluded March 11, 1863. Ratification advised with amendments, by Senate, March 13, 1863. Amendments accepted March 14, 1863. Proclaimed March 19, 1863.

"Concluded at ... Washington ... District of Columbia."

World Percussion Bash UW Percussion Ensemble UW Gamelan Ensemble UW Steel Bands May 25, 2016

Concert Program

Mach Bands: multi-scale spatial filtering and co-operative coding of edges and bars

Perception of Mach bands may be explained by spatial filtering ('lateral inhibition') that can be approximated by 2nd derivative computation, and several alternative models have been proposed. To distinguish between them, we used a novel set of ‘generalised Gaussian’ images, in which the sharp ramp-plateau junction of the Mach ramp was replaced by smoother transitions. The images ranged from a slightly blurred Mach ramp to a Gaussian edge and beyond, and also included a sine-wave edge. The probability of seeing Mach Bands increased with the (relative) sharpness of the junction, but was largely independent of absolute spatial scale. These data did not fit the predictions of MIRAGE, nor 2nd derivative computation at a single fine scale. In experiment 2, observers used a cursor to mark features on the same set of images. Data on perceived position of Mach bands did not support the local energy model. Perceived width of Mach bands was poorly explained by a single-scale edge detection model, despite its previous success with Mach edges (Wallis & Georgeson, 2009, Vision Research, 49, 1886-1893). A more successful model used separate (odd and even) scale-space filtering for edges and bars, local peak detection to find candidate features, and the MAX operator to compare odd- and even-filter response maps (Georgeson, VSS 2006, Journal of Vision 6(6), 191a). Mach bands are seen when there is a local peak in the even-filter (bar) response map, AND that peak value exceeds corresponding responses in the odd-filter (edge) maps.

Theoretical study of Talbot-like bands observed using a laser diode below threshold

We report on a theoretical study of an interferometric system in which half of a collimated beam from a broadband optical source is intercepted by a glass slide, the whole beam subsequently being incident on a diffraction grating and the resulting spectrum being viewed using a linear CCD array. Using Fourier theory, we derive the expression of the intensity distribution across the CCD array. This expression is then examined for non-cavity and cavity sources for different cases determined by the direction from which the slide is inserted into the beam and the source bandwidth. The theoretical model shows that the narrower the source linewidth, the higher the deviation of the Talbot bands' visibility (as it is dependent on the path imbalance) from the previously known triangular shape. When the source is a laser diode below threshold, the structure of the CCD signal spectrum is very complex. The number of components present simultaneously increases with the number of grating lines and decreases with the laser cavity length. The model also predicts the appearance of bands in situations not usually associated with Talbot bands.

Talbot-like bands for a laser diode below threshold

We report on the problems encountered when replacing a tungsten filament lamp with a laser diode in a set-up for displaying Talbot bands using a diffraction grating. It is shown that the band pattern is rather complex and strong interference signals may exist in situations where Talbot bands are not normally expected to appear. In these situations, the period of the bands increases with the optical path difference (OPD). The visibility of bands as dependence on path imbalance is obtained by suitably obstructing halfway into the arms of a Michelson interferometer using opaque screens.

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.

Theoretical study of Talbot-like bands observed using a laser diode below threshold

We report on a theoretical study of an interferometric system in which half of a collimated beam from a broadband optical source is intercepted by a glass slide, the whole beam subsequently being incident on a diffraction grating and the resulting spectrum being viewed using a linear CCD array. Using Fourier theory, we derive the expression of the intensity distribution across the CCD array. This expression is then examined for non-cavity and cavity sources for different cases determined by the direction from which the slide is inserted into the beam and the source bandwidth. The theoretical model shows that the narrower the source linewidth, the higher the deviation of the Talbot bands' visibility (as it is dependent on the path imbalance) from the previously known triangular shape. When the source is a laser diode below threshold, the structure of the CCD signal spectrum is very complex. The number of components present simultaneously increases with the number of grating lines and decreases with the laser cavity length. The model also predicts the appearance of bands in situations not usually associated with Talbot bands.