966 resultados para Invariant integrals


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The important basis for the children to study chinese character is the Chinese character awareness, which means the understanding and extracting of the Chinese character combinatorial rule. The perceptual learning intrinsically is the direct perceive to the invariant rules. As the important mechanism to extract the abstract rule, the perceptual learning is the important mechanism of the development of the Chinese character awareness also. 4-6-year-old children's Chinese character awareness are tested by the degree of acceptance to the graphic words, inlaying words and pseudowords. The perceptual disintegration are tested by the perceptual learning experiment. Moreover, the development of the ability to finely-identify the Chinese character under the different level of attention condition is explored. The result suggests the quality to the development of the children's Chinese character awareness: The Chinese character awareness to 4-year-old children is in the rudiment stage, and it have different qualities as the change of the age. As the mechanism of the Chinese character awareness, the perceptual learning have an complex correlation to the awareness. The result indicates the following effects of the children perceptual disintegration: the level of the perceptual disintegration is transitive from three-dimension confusion to one-dimension falsity. It have correlation with the ability to finely-identify the Chinese character to a certain degree. The result also shows: the developmental specialties of the ability to finely-identify the Chinese character are different in the different age. The ability to finely-identify the Chinese character under the different level of attention condition have very similar processes.

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Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

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How can one compute qualitative properties of the optical flow, such as expansion or rotation, in a way which is robust and invariant to the position of the focus of expansion or the center of rotation? We suggest a particularly simple algorithm, well-suited to VLSI implementations, that exploits well-known relations between the integral and differential properties of vector fields and their linear behaviour near singularities.

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Different approaches to visual object recognition can be divided into two general classes: model-based vs. non model-based schemes. In this paper we establish some limitation on the class of non model-based recognition schemes. We show that every function that is invariant to viewing position of all objects is the trivial (constant) function. It follows that every consistent recognition scheme for recognizing all 3-D objects must in general be model based. The result is extended to recognition schemes that are imperfect (allowed to make mistakes) or restricted to certain classes of objects.

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How does the brain recognize three-dimensional objects? We trained monkeys to recognize computer rendered objects presented from an arbitrarily chosen training view, and subsequently tested their ability to generalize recognition for other views. Our results provide additional evidence in favor of with a recognition model that accomplishes view-invariant performance by storing a limited number of object views or templates together with the capacity to interpolate between the templates (Poggio and Edelman, 1990).

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We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call "relative affine structure". Via a number of corollaries of our main results we show that our framework unifies previous work --- including Euclidean, projective and affine --- in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.

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The inferior temporal cortex (IT) of monkeys is thought to play an essential role in visual object recognition. Inferotemporal neurons are known to respond to complex visual stimuli, including patterns like faces, hands, or other body parts. What is the role of such neurons in object recognition? The present study examines this question in combined psychophysical and electrophysiological experiments, in which monkeys learned to classify and recognize novel visual 3D objects. A population of neurons in IT were found to respond selectively to such objects that the monkeys had recently learned to recognize. A large majority of these cells discharged maximally for one view of the object, while their response fell off gradually as the object was rotated away from the neuron"s preferred view. Most neurons exhibited orientation-dependent responses also during view-plane rotations. Some neurons were found tuned around two views of the same object, while a very small number of cells responded in a view- invariant manner. For five different objects that were extensively used during the training of the animals, and for which behavioral performance became view-independent, multiple cells were found that were tuned around different views of the same object. No selective responses were ever encountered for views that the animal systematically failed to recognize. The results of our experiments suggest that neurons in this area can develop a complex receptive field organization as a consequence of extensive training in the discrimination and recognition of objects. Simple geometric features did not appear to account for the neurons" selective responses. These findings support the idea that a population of neurons -- each tuned to a different object aspect, and each showing a certain degree of invariance to image transformations -- may, as an assembly, encode complex 3D objects. In such a system, several neurons may be active for any given vantage point, with a single unit acting like a blurred template for a limited neighborhood of a single view.

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If we are provided a face database with only one example view per person, is it possible to recognize new views of them under a variety of different poses, especially views rotated in depth from the original example view? We investigate using prior knowledge about faces plus each single example view to generate virtual views of each person, or views of the face as seen from different poses. Prior knowledge of faces is represented in an example-based way, using 2D views of a prototype face seen rotating in depth. The synthesized virtual views are evaluated as example views in a view-based approach to pose-invariant face recognition. They are shown to improve the recognition rate over the scenario where only the single real view is used.

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The problem of detecting intensity changes in images is canonical in vision. Edge detection operators are typically designed to optimally estimate first or second derivative over some (usually small) support. Other criteria such as output signal to noise ratio or bandwidth have also been argued for. This thesis is an attempt to formulate a set of edge detection criteria that capture as directly as possible the desirable properties of an edge operator. Variational techniques are used to find a solution over the space of all linear shift invariant operators. The first criterion is that the detector have low probability of error i.e. failing to mark edges or falsely marking non-edges. The second is that the marked points should be as close as possible to the centre of the true edge. The third criterion is that there should be low probability of more than one response to a single edge. The technique is used to find optimal operators for step edges and for extended impulse profiles (ridges or valleys in two dimensions). The extension of the one dimensional operators to two dimentions is then discussed. The result is a set of operators of varying width, length and orientation. The problem of combining these outputs into a single description is discussed, and a set of heuristics for the integration are given.

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The equivalence of two ways for the calculation of overlap integrals, i.e. the Sharp Rosenstock generating function method and the Doktorov coherent state method, has been proved. On the basis of the generating function of the overlap integrals, a new closed form expression for the Franck - Condon integrals for overlap multidimensional harmonic oscillators has been exactly derived. In addition, some useful analytical expressions for the calculations of the multimode Franck - Condon factors have been given.

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One of the major challenges encountered in earthquake geotechnical physical modelling is to determine the effects induced by the artificial boundaries of the soil container on the dynamic response of the soil deposit. Over the past years, the use of absorbing material for minimising boundaries effects has become an increasing alternative solution, yet little systematic research has been carried out to quantify the dynamic performance of the absorbing material and the amount of energy dissipated by it. This paper aims to examine the effects induced by the absorbing material on the dynamic response of the soil, and estimate the amount of energy reduced by the absorbing boundaries. The absorbent material consisted of panels made of commercially available foams, which were placed on both inner sides of end-walls of the soil container. These walls are perpendicular to the shaking direction. Three types of foam with different mechanical properties were used in this study. The results were obtained from tests carried out using a shaking table and Redhill 110 sand for the soil deposit. It was found that a considerably amount of energy was dissipated, in particular within the frequency range close to the resonance of the soil deposit. This feature suggests that the presence of foams provides a significant influence to the dynamic response of the soil. The energy absorbed by the boundaries was also quantified from integrals of the Power Spectral Density of the accelerations. It was found that the absorbed energy ranged between a minimum of 41% to a maximum of 92% of the input levels, depending mainly on the foam used in the test. The effects provided by the acceleration levels and depth at which the energy was evaluated were practically negligible. Finally, practical guidelines for the selection of the absorbing material are provided.

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Morgan, Huw, Habbal, S.R., Woo, R., (2006) 'The Depiction of Coronal Structure in White-Light Images', Solar Physics 236(2) pp.263-272 RAE2008

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Hill, Joe M., Lloyd, Noel G., Pearson, Jane M., 'Centres and limit cycles for an extended Kukles system', Electronic Journal of Differential Equations, Vol. 2007(2007), No. 119, pp. 1-23.

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Gohm, Rolf; Dey, S., 'Characteristic function for ergodic tuples', Integral Equations and Operator Theory 58(1) pp.43-63 RAE2008

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A framework for the simultaneous localization and recognition of dynamic hand gestures is proposed. At the core of this framework is a dynamic space-time warping (DSTW) algorithm, that aligns a pair of query and model gestures in both space and time. For every frame of the query sequence, feature detectors generate multiple hand region candidates. Dynamic programming is then used to compute both a global matching cost, which is used to recognize the query gesture, and a warping path, which aligns the query and model sequences in time, and also finds the best hand candidate region in every query frame. The proposed framework includes translation invariant recognition of gestures, a desirable property for many HCI systems. The performance of the approach is evaluated on a dataset of hand signed digits gestured by people wearing short sleeve shirts, in front of a background containing other non-hand skin-colored objects. The algorithm simultaneously localizes the gesturing hand and recognizes the hand-signed digit. Although DSTW is illustrated in a gesture recognition setting, the proposed algorithm is a general method for matching time series, that allows for multiple candidate feature vectors to be extracted at each time step.