Sketch interpretation using multiscale stochastic models of temporal patterns

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 102-114).Sketching is a natural mode of interaction used in a variety of settings. For example, people sketch during early design and brainstorming sessions to guide the thought process; when we communicate certain ideas, we use sketching as an additional modality to convey ideas that can not be put in words. The emergence of hardware such as PDAs and Tablet PCs has enabled capturing freehand sketches, enabling the routine use of sketching as an additional human-computer interaction modality. But despite the availability of pen based information capture hardware, relatively little effort has been put into developing software capable of understanding and reasoning about sketches. To date, most approaches to sketch recognition have treated sketches as images (i.e., static finished products) and have applied vision algorithms for recognition. However, unlike images, sketches are produced incrementally and interactively, one stroke at a time and their processing should take advantage of this. This thesis explores ways of doing sketch recognition by extracting as much information as possible from temporal patterns that appear during sketching.(cont.) We present a sketch recognition framework based on hierarchical statistical models of temporal patterns. We show that in certain domains, stroke orderings used in the course of drawing individual objects contain temporal patterns that can aid recognition. We build on this work to show how sketch recognition systems can use knowledge of both common stroke orderings and common object orderings. We describe a statistical framework based on Dynamic Bayesian Networks that can learn temporal models of object-level and stroke-level patterns for recognition. Our framework supports multi-object strokes, multi-stroke objects, and allows interspersed drawing of objects - relaxing the assumption that objects are drawn one at a time. Our system also supports real-valued feature representations using a numerically stable recognition algorithm. We present recognition results for hand-drawn electronic circuit diagrams. The results show that modeling temporal patterns at multiple scales provides a significant increase in correct recognition rates, with no added computational penalties.by Tevfik Metin Sezgin.Ph.D

The Role of Data in Model Building and Prediction: A Survey Through Examples

The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of quantitative sciences, mean abstract mathematical or algorithmical representations. This short review discusses a few key examples from Physics, taken from dynamical systems theory, biophysics, and statistical mechanics, representing three paradigmatic procedures to build models and predictions from available data. In the case of dynamical systems we show how predictions can be obtained in a virtually model-free framework using the methods of analogues, and we briefly discuss other approaches based on machine learning methods. In cases where the complexity of systems is challenging, like in biophysics, we stress the necessity to include part of the empirical knowledge in the models to gain the minimal amount of realism. Finally, we consider many body systems where many (temporal or spatial) scales are at play and show how to derive from data a dimensional reduction in terms of a Langevin dynamics for their slow components

The role of data in model building and prediction: a survey through examples

The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of quantitative sciences, mean abstract mathematical or algorithmical representations. This short review discusses a few key examples from Physics, taken from dynamical systems theory, biophysics, and statistical mechanics, representing three paradigmatic procedures to build models and predictions from available data. In the case of dynamical systems we show how predictions can be obtained in a virtually model-free framework using the methods of analogues, and we briefly discuss other approaches based on machine learning methods. In cases where the complexity of systems is challenging, like in biophysics, we stress the necessity to include part of the empirical knowledge in the models to gain the minimal amount of realism. Finally, we consider many body systems where many (temporal or spatial) scales are at play-and show how to derive from data a dimensional reduction in terms of a Langevin dynamics for their slow components

Additive noise effects in active nonlinear spatially extended systems

We examine the effects of pure additive noise on spatially extended systems with quadratic nonlinearities. We develop a general multiscale theory for such systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We first focus on a regime close to the instability onset (primary bifurcation), where the system can be described by a single dominant mode. We show analytically that the resulting noise in the equation describing the amplitude of the dominant mode largely depends on the nature of the stochastic forcing. For a highly degenerate noise, in the sense that it is acting on the first stable mode only, the amplitude equation is dominated by a pure multiplicative noise, which in turn induces the dominant mode to undergo several critical state transitions and complex phenomena, including intermittency and stabilisation, as the noise strength is increased. The intermittent behaviour is characterised by a power-law probability density and the corresponding critical exponent is calculated rigorously by making use of the first-passage properties of the amplitude equation. On the other hand, when the noise is acting on the whole subspace of stable modes, the multiplicative noise is corrected by an additive-like term, with the eventual loss of any stabilised state. We also show that the stochastic forcing has no effect on the dominant mode dynamics when it is acting on the second stable mode. Finally, in a regime which is relatively far from the instability onset, so that there are two unstable modes, we observe numerically that when the noise is acting on the first stable mode, both dominant modes show noise-induced complex phenomena similar to the single-mode case

Intensification of tilted atmospheric vortices by asymmetric diabatic heating

P\"aschke et al. (JFM, 701, 137--170 (2012)) studied the nonlinear dynamics of strongly tilted vortices subject to asymmetric diabatic heating by asymptotic methods. They found, i.a., that an azimuthal Fourier mode 1 heating pattern can intensify or attenuate such a vortex depending on the relative orientation of tilt and heating asymmetries. The theory originally addressed the gradient wind regime which, asymptotically speaking, corresponds to vortex Rossby numbers of order O(1) in the limit. Formally, this restricts the appicability of the theory to rather weak vortices in the near equatorial region. It is shown below that said theory is, in contrast, uniformly valid for vanishing Coriolis parameter and thus applicable to vortices up to hurricane strength. The paper's main contribution is a series of three-dimensional numerical simulations which fully support the analytical predictions.Comment: 22 pages, 11 figure