Abstract: The described implementations relate to enhancing images. One system includes a lens configured to focus an image on an image sensor. The image sensor is configured to capture the image. The model of the lens can be known to the system. The system can also include an image enhancement component configured to receive the captured image and to utilize a simulated blur kernel of the known model to produce an enhanced image.

Abstract: An efficient symbolic differentiation method and system that automatically computes one or more derivatives of a function using a computing device. A derivative graph is used to graphically represent the derivative of a function. Repeated factorization of the derivative graph yields a factored derivative graph. The derivative is computed by summing the products along all product paths in the factored derivative graph. The efficient symbolic differentiation method and system operates on both single input/single output and multiple input/multiple output functions. For a single input/single output function, the order of the factoring does not matter. However, for a multiple input/multiple output function, the factoring order is such that the factor subgraph appearing most frequently in the derivative graph is factored first. The method and system also use a product pairs priority queue to avoid the re-computing of sub-strings that are common between product paths.

Abstract: A control system is described for controlling the operation of a target system, such as a data center. The control system uses a prediction module to predict demand for resources of the target system for future time steps. The control system then uses a transition determination module to determine state transitions within the target system to address the predicted demand. Each state transition describes a number of units to be advanced from a first state, at a first time step, to a second state, at a second time step. The control system then commences those state transitions which begin in the current step, and then repeats the predicting and determining for a next time step. The transition determination module can determine the state transitions by operating on an objective function that includes a demand difference component and a cost component, as subject to a set of conservation equations.

Abstract: Compact and accurate piecewise parametric representations of implicit curves may be achieved by iteratively selecting ranges of parameterizing regions and testing each for satisfying an intervalized super convergence test. In one aspect, the implicit curves is represented as a compact form of one or more representations of such convergence regions. For memory and bandwidth constrained applications, starting points of convergence regions may not be stored but instead calculated at runtime prior to rendering a point on the implicit curve. Furthermore, not all endpoints relevant convergence regions of a selected implicit curve need be stored. Instead, based on at least one endpoint, the other endpoints can be derived via Newton iterations. To further reduce memory and bandwidth costs, coordinates can be stored in a quantized format and the points reflecting floating point accuracy can be derived at runtime again by Newton iteration.

Abstract: In the described embodiment, methods and systems for processing facial image data for use in animation are described. In one embodiment, a system is provided that illuminates a face with illumination that is sufficient to enable the simultaneous capture of both structure data, e.g. a range or depth map, and reflectance properties, e.g. the diffuse reflectance of a subject's face. This captured information can then be used for various facial animation operations, among which are included expression recognition and expression transformation.

Abstract: The illustrated and described embodiments describe techniques for capturing data that describes 3-dimensional (3-D) aspects of a face, transforming facial motion from one individual to another in a realistic manner, and modeling skin reflectance.

Abstract: In the described embodiment, methods and systems for processing facial image data for use in animation are described. In one embodiment, a system is provided that illuminates a face with illumination that is sufficient to enable the simultaneous capture of both structure data, e.g. a range or depth map, and reflectance properties, e.g. the diffuse reflectance of a subject's face. This captured information can then be used for various facial animation operations, among which are included expression recognition and expression transformation.

Abstract: Compact and accurate piecewise parametric representations of implicit functions may be achieved by iteratively selecting ranges of parameterizing regions and testing each for satisfying an intervalized super convergence test. In one aspect, the implicit function is represented as a compact form of one or more representations of such convergence regions. In yet another aspect, iteration is begun with applying the intervalized convergence test to an entire pameterization region. In yet another aspect, the range being tested for super convergence is iteratively sub-divided to generate other ranges for testing. In one aspect, such sub-dividing comprises dividing the selected ranges by half. In one further aspect, Newton iterate steps are applied to selected ranges to change such ranges for further testing of super convergence of such ranges.

Abstract: An efficient symbolic differentiation method and system that automatically computes one or more derivatives of a function using a computing device. A derivative graph is used to graphically represent the derivative of a function. Repeated factorization of the derivative graph yields a factored derivative graph. The derivative is computed by summing the products along all product paths in the factored derivative graph. The efficient symbolic differentiation method and system operates on both single input/single output and multiple input/multiple output functions. For a single input/single output function, the order of the factoring does not matter. However, for a multiple input/multiple output function, the factoring order is such that the factor subgraph appearing most frequently in the derivative graph is factored first. The method and system also use a product pairs priority queue to avoid the re-computing of sub-strings that are common between product paths.

Abstract: A complex procedural surface can be expressed based on some constructive solid geometry operations performed on primitive procedural surfaces. The domain based representation of the complex procedural surface includes implicit curves of intersection. During pre-processing, the parts of the domain based representation to be triangulated are first sub-divided into simple triangles not bound on any side by an edge related to the parameterized regions of the implicit curve and curve visibility triangles. The coarse pre-processed triangulated mesh is later refined during runtime by further sub-dividing the coarse mesh to add triangles with curve based edges and non-curve based edges to generate a mesh of sampling triangles. The more refined sampling triangle mesh is further refined by applying geometry instancing to map appropriate instance meshes into the appropriate sampling triangles to create an even more refined triangulated mesh at runtime for rendering.

Abstract: In the described embodiment, methods and systems for processing facial image data for use in animation are described. In one embodiment, a system is provided that illuminates a face with illumination that is sufficient to enable the simultaneous capture of both structure data, e.g. a range or depth map, and reflectance properties, e.g. the diffuse reflectance of a subject's face. This captured information can then be used for various facial animation operations, among which are included expression recognition and expression transformation.

Abstract: In the described embodiment, methods and systems for processing facial image data for use in animation are described. In one embodiment, a system is provided that illuminates a face with illumination that is sufficient to enable the simultaneous capture of both structure data, e.g. a range or depth map, and reflectance properties, e.g. the diffuse reflectance of a subject's face. This captured information can then be used for various facial animation operations, among which are included expression recognition and expression transformation.

Abstract: In the described embodiment, methods and systems for processing facial image data for use in animation are described. In one embodiment, a system is provided that illuminates a face with illumination that is sufficient to enable the simultaneous capture of both structure data, e.g. a range or depth map, and reflectance properties, e.g. the diffuse reflectance of a subject's face. This captured information can then be used for various facial animation operations, among which are included expression recognition and expression transformation.

Abstract: The illustrated and described embodiments describe techniques for capturing data that describes 3-dimensional (3-D) aspects of a face, transforming facial motion from one individual to another in a realistic manner, and modeling skin reflectance.

Abstract: In the described embodiment, methods and systems for processing facial image data for use in animation are described. In one embodiment, a system is provided that illuminates a face with illumination that is sufficient to enable the simultaneous capture of both structure data, e.g. a range or depth map, and reflectance properties, e.g. the diffuse reflectance of a subject's face. This captured information can then be used for various facial animation operations, among which are included expression recognition and expression transformation.

Abstract: The illustrated and described embodiments describe techniques for capturing data that describes 3-dimensional (3-D) aspects of a face, transforming facial motion from one individual to another in a realistic manner, and modeling skin reflectance.

Abstract: Methods and systems for animating facial features and transforming facial expressions are described. In one embodiment, a code book contains data that defines a set of facial expressions of a first person. A training set of facial expressions from a second person and corresponding expressions from the code book are used to derive a transformation function that is then applied to all of the expressions of the code book. In this manner, expressions from the first person can be realistically transformed into expressions of a second person and vice versa. Particularly advantageous aspects of the described embodiments provide a single common generic face model that is used as the basis for a fitting operation for many different faces. Use of the single common generic face model and certain user-defined constraints provide a mechanism by which correspondences between the different faces can be established.

Abstract: In the described embodiment, methods and systems for processing facial image data for use in animation are described. In one embodiment, a system is provided that illuminates a face with illumination that is sufficient to enable the simultaneous capture of both structure data, e.g. a range or depth map, and reflectance properties, e.g. the diffuse reflectance of a subject's face. This captured information can then be used for various facial animation operations, among which are included expression recognition and expression transformation.

Abstract: The illustrated and described embodiments describe techniques for capturing data that describes 3-dimensional (3-D) aspects of a face, transforming facial motion from one individual to another in a realistic manner, and modeling skin reflectance.

Abstract: In the described embodiment, methods and systems for processing facial image data for use in animation are described. In one embodiment, a system is provided that illuminates a face with illumination that is sufficient to enable the simultaneous capture of both structure data, e.g. a range or depth map, and reflectance properties, e.g. the diffuse reflectance of a subject's face. This captured information can then be used for various facial animation operations, among which are included expression recognition and expression transformation.