Spatial filtering in tone reproduction and vision

This thesis is concerned with spatial filtering. What is its utility in tone reproduction? Does it exist in vision, and if so, what constraints does it impose on the nervous system?

Tone reproduction is just the art and science of taking a picture and then displaying it. The sensors available to capture an image have a greater dynamic range than the media that may be used to display it. Conventionally, spatial filtering is used to boost contrast; it ameliorates the loss of contrast that results when the sensor signal range is scaled down to fit the display range. In this thesis, a type of nonlinear spatial filtering is discussed that results in direct range reduction without range scaling. This filtering process is instantiated in a real-time image processor built using analog CMOS VLSI.

Spatial filtering must be applied with care in both artificial and natural vision systems. It is argued that the nervous system does not simply filter linearly across an image. Rather, the way that we see things implies that the nervous system filters nonlinearly. Further, many models for color vision include a high-pass filtering step in which the DC information is lost. A real-time study of filtering in color space leads to the conclusion that the nervous system is not that simple, and that it maintains DC information by referencing to white.

Controlling wave propagation through nonlinear engineered granular systems

We study the fundamental dynamic behavior of a special class of ordered granular systems in order to design new, structured materials with unique physical properties. The dynamic properties of granular systems are dictated by the nonlinear, Hertzian, potential in compression and zero tensile strength resulting from the discrete material structure. Engineering the underlying particle arrangement of granular systems allows for unique dynamic properties, not observed in natural, disordered granular media. While extensive studies on 1D granular crystals have suggested their usefulness for a variety of engineering applications, considerably less attention has been given to higher-dimensional systems. The extension of these studies in higher dimensions could enable the discovery of richer physical phenomena not possible in 1D, such as spatial redirection and anisotropic energy trapping. We present experiments, numerical simulation (based on a discrete particle model), and in some cases theoretical predictions for several engineered granular systems, studying the effects of particle arrangement on the highly nonlinear transient wave propagation to develop means for controlling the wave propagation pathways. The first component of this thesis studies the stress wave propagation resulting from a localized impulsive loading for three different 2D particle lattice structures: square, centered square, and hexagonal granular crystals. By varying the lattice structure, we observe a wide range of properties for the propagating stress waves: quasi-1D solitary wave propagation, fully 2D wave propagation with tunable wave front shapes, and 2D pulsed wave propagation. Additionally the effects of weak disorder, inevitably present in real granular systems, are investigated. The second half of this thesis studies the solitary wave propagation through 2D and 3D ordered networks of granular chains, reducing the effective density compared to granular crystals by selectively placing wave guiding chains to control the acoustic wave transmission. The rapid wave front amplitude decay exhibited by these granular networks makes them highly attractive for impact mitigation applications. The agreement between experiments, numerical simulations, and applicable theoretical predictions validates the wave guiding capabilities of these engineered granular crystals and networks and opens a wide range of possibilities for the realization of increasingly complex granular material design.

Experimental and theoretical studies of Notch signaling-mediated spatial pattern

Notch signaling acts in many diverse developmental spatial patterning processes. To better understand why this particular pathway is employed where it is and how downstream feedbacks interact with the signaling system to drive patterning, we have pursued three aims: (i) to quantitatively measure the Notch system's signal input/output (I/O) relationship in cell culture, (ii) to use the quantitative I/O relationship to computationally predict patterning outcomes of downstream feedbacks, and (iii) to reconstitute a Notch-mediated lateral induction feedback (in which Notch signaling upregulates the expression of Delta) in cell culture. The quantitative Notch I/O relationship revealed that in addition to the trans-activation between Notch and Delta on neighboring cells there is also a strong, mutual cis-inactivation between Notch and Delta on the same cell. This feature tends to amplify small differences between cells. Incorporating our improved understanding of the signaling system into simulations of different types of downstream feedbacks and boundary conditions lent us several insights into their function. The Notch system converts a shallow gradient of Delta expression into a sharp band of Notch signaling without any sort of feedback at all, in a system motivated by the Drosophila wing vein. It also improves the robustness of lateral inhibition patterning, where signal downregulates ligand expression, by removing the requirement for explicit cooperativity in the feedback and permitting an exceptionally simple mechanism for the pattern. When coupled to a downstream lateral induction feedback, the Notch system supports the propagation of a signaling front across a tissue to convert a large area from one state to another with only a local source of initial stimulation. It is also capable of converting a slowly-varying gradient in parameters into a sharp delineation between high- and low-ligand populations of cells, a pattern reminiscent of smooth muscle specification around artery walls. Finally, by implementing a version of the lateral induction feedback architecture modified with the addition of an autoregulatory positive feedback loop, we were able to generate cells that produce enough cis ligand when stimulated by trans ligand to themselves transmit signal to neighboring cells, which is the hallmark of lateral induction.