Cross-diffusion systems for image processing: II. The nonlinear case

In this paper the use of nonlinear cross-diffu\-sion systems to model image restoration is investigated, theoretically and numerically. In the first case, well-posedness, scale-space properties and long time behaviour are analyzed. From a numerical point of view, a computational study of the performance of the models is carried out, suggesting their diversity and potentialities to treat image filtering problems. The present paper is a continuation of a previous work of the same authors, devoted to linear cross-diffusion models. \keywords{Cross-diffusion \and Complex diffusion \and Image restoration

The ring of differential Fourier expansions

For a fixed prime we prove structure theorems for the kernel and the image of the map that attaches to any differential modular function its differential Fourier expansion. The image of this map, which is the ring of differential Fourier expansions, plays the role of ring of functions on a "differential Igusa curve". Our constructions are then used to perform an analytic continuation between isogeny covariant differential modular forms on the differential Igusa curves belonging to different primes

Notes on the Margins of Metadata; Concerning the Undecidability of the Digital Image

This paper considers the significance of metadata in relation to the image economy of the web. Social practices such as keywording, tagging, rating and viewing increasingly influence the modes of navigation and hence the utility of images in online environments. To a user faced with an avalanche of images, metadata promises to make photographs machine-readable in order to mobilize new knowledge, in a continuation of the archival paradigm. At the same time, metadata enables new topologies of the image, new temporalities and multiplicities which present a challenge to historical models of representation. As photography becomes an encoded discourse, we suggest that the turning away from the visual towards the mathematical and the algorithmic establishes undecidability as a key property of the networked image

Kinematics at the intersection of the Garlock and Death Valley fault zones, California: Integration of TM data and field studies

The Garlock and Death Valley fault zones in SE California are two active strike-slip faults coming together on the east side of the Avawatz Mtns. The kinematics of this intersection, and the possible continuation of either fault zone, are being investigated using a combination of field mapping, and processing and interpretation of remotely sensed image data. Regional and local relationships are derivable from Thematic Mapper data (30 m resolution), including discrimination and relative age dating of alluvial fans, bedrock mapping, and fault mapping. Aircraft data provide higher spatial resolution over more limited areas. Hypotheses being considered are: (1) the Garlock fault extends east of the intersection; (2) the Garlock fault terminates at the intersection and the Death Valley fault continues southeastward; and (3) the Garlock fault has been offset right laterally by the Death Valley fault which continues to the southeast. Preliminary work indicates that the first hypothesis is invalid. From kinematic considerations, image analysis, and field work the third hypothesis is favored. The projected continuation of the Death Valley zone defines the boundary between the Mojave crustal block and the Basin and Range block