Abstract: This invention presents a method for data modeling in multivariate regression models and neural networks. It replaces the vertical distance of data points from a hyperplane with the normal distance, ensuring finite values even when the vertical distance becomes infinite, provided the data points have a finite magnitude. In the context of neural networks, a hidden output coordinate dimension is utilized on a per hyperplane basis, allowing the introduction of any desired surface as a hidden surface. The invention also includes methods to limit the unbounded growth of weight components, addressing issues of numerical instability in machine learning models.

Abstract: The present invention provides a method, system, and apparatus for solving the stereo vision matching problem. The invention implements a method for solving image correspondence problems so that each front region between consecutive extremal pixels in one image is matched to a corresponding front region between consecutive extremal pixels in another image.

Abstract: The present invention relates to an apparatus and methods for performing image restoration. More specifically, the present invention relates to an apparatus and methods which are capable of quickly restoring various sizes of selected areas of an image. In one embodiment, a user may select or mark a target region in an image which is to be restored. A source window may then be generated and a pixel from within the target region may be selected for restoration. The intensity distribution of pixels surrounding the selected pixel may be compared with other pixels in the image and a pixel to be used for restoration of the selected pixel may be chosen based on the comparison of the intensity distributions. Once a pixel is chosen for restoration, the selected pixel and its surrounding pixels may be restored using the intensity distribution of the chosen pixel and its surrounding pixels. The method may continue in this manner until all pixels within the target region have been restored.

Abstract: The present invention provides a method, system, and apparatus for solving the stereo vision matching problem. The invention implements a method for solving image correspondence problems so that each front region between consecutive extremal pixels in one image is matched to a corresponding front region between consecutive extremal pixels in another image.

Abstract: The present invention relates to an apparatus and methods for performing image restoration. More specifically, the present invention relates to an apparatus and methods which are capable of quickly restoring various sizes of selected areas of an image. In one embodiment, a user may select or mark a target region in an image which is to be restored. A source window may then be generated and a pixel from within the target region may be selected for restoration. The intensity distribution of pixels surrounding the selected pixel may be compared with other pixels in the image and a pixel to be used for restoration of the selected pixel may be chosen based on the comparison of the intensity distributions. Once a pixel is chosen for restoration, the selected pixel and its surrounding pixels may be restored using the intensity distribution of the chosen pixel and its surrounding pixels. The method may continue in this manner until all pixels within the target region have been restored.

Abstract: Apparatus and methods for estimating the optical flow velocity components using an upwind discretization are presented. In prior art, the knowledge of the signs of the optical flow velocity components is needed for using upwind discretization. But in optical flow computations the velocity components are precisely the unknowns and thus their sign information is not available. This invention discloses apparatus and methods in which upwinding is done based on the sign of the local time derivative instead of the signs of the optical flow velocity components.

Abstract: An apparatus and method for estimating optical flow use equations derived by setting the deformation tensor to zero.