39 results about "Automatic differentiation" patented technology

A method for automatically or semi-automatically constructing a digital 3D model of a scene from photographic data and photogrammetry data includes defining an initial rough model as a solution estimate. A reverse rendering step includes a second-order solution method that employs automatic differentiation techniques to accurately compute derivatives of an error function. In an embodiment of the method, at least one camera is placed within the scene being constructed, and photographic data from this camera is used in the solution process.

The invention relates to a method and a device for automatically differentiating bones or other calcium-containing materials and contrast agent in soft tissue of an object area. In at least one embodiment of the method, two image data records of two computed tomography pictures of the object are provided that have been recorded in the context of a different spectral distribution of the X-radiation. For voxels of at least one interesting slice, there is calculated from the two image data records a ratio r that is yielded from measured or averaged X-ray attenuation values of the respective voxel or its environment in the context of the different spectral distributions of the X-radiation and prescribed X-ray attenuation values of soft tissue in the context of the different spectral distributions of the X-radiation according to a prescribed calculation rule. Upon overshooting of a threshold value for the ratio r the respective voxel is assigned either contrast agent or calcium-containing material as a function of the magnitude of r. The proposed method and / or the associated device enable a reliable automatic differentiation of bones or other calcium-containing materials and contrast agent in computed tomography pictures.

The disclosed system provides a transformation-based implementation of forward-mode and reverse-mode automatic differentiation as a built-in, first-class function in a functional programming language. Each of these constructs imposes only a small constant factor of the computational burden (time) of the function itself, and the forward construct has the same properties in terms of space. The functions can be applied to any function, including those involving derivatives and nested closures.

The method for rendering using symplectic ray tracing is comprised the step of fixing the location of observation, fixing view screen of observation, practicing the symplectic ray tracing, acquiring the information of the color where the light rays cross the surface of the objects, rendering the objects according to the information of the color acquired.The symplectic ray tracing of the present invention forms the Hamilton's canonical equation by applying the fast automatic differentiation techniques with the Hamiltonian H of the objects, and practices the symplectic integration by applying the symplectic Euler method to the formed Hamilton's canonical equation. The present invention can provide the apparatus and method for rendering which can visualize the phenomena in non-homogeneously transparent object or the four-dimensional black hole space time.