Abstract: A method for scaling a signal sample rate includes interpolating between at least two scaling ratios to calculate an arbitrary scaling ratio, using a predetermined interpolation algorithm, and scaling a sample rate for a first portion of the signal using a first scaling ratio, and scaling a sample rate for a second portion of the signal using a second scaling ratio, to form a scaled signal having an average scaling ratio equal to the arbitrary scaling ratio.

Abstract: A one-dimensional algorithm for perform the merging of complementary portions from two independent overlapped images on the same 8×8 grid without the computational expense of conversion to and from the real domain is extended to a two-dimensional procedure. The merging process is performed exclusively in the frequency domain. The extension to two dimensions is done by shifting and/or merging rows of side-by-side two-dimensional transformed data blocks using the one-dimensional algorithm. Then a vertical shifting and/or merging can be performed on the horizontally shifted and/or merged blocks again using the one-dimensional algorithm with an independent shift/merge parameter.

Abstract: A one-dimensional (1D) Inverse Discrete Cosine Transform (IDCT) is applied to an input two-dimensional (2D) transform block along the axis to be modified. Since the one-dimensional IDCT is not performed on the other axis, each block is left in a one-dimensional transform space (called hybrid space). For a shift (merge), the appropriate “m” elements are picked up from one block and the “8−m” elements are picked up from the other block and are used as input to the one-dimensional forward DCT (FDCT) along that same axis. For two-dimensional shifts or merges, the results of the first one-dimensional IDCT and FDCT can be stored with extra precision to be used as input to a second one-dimensional IDCT and FDCT along the other axis. The execution time worst case conditions are approximately constant for all shift/merger amounts. Taking advantage of fast paths can improve the execution times for typical blocks.

Abstract: A method of transform domain processing of transformed data is applied to image processing in various applications. A one-dimensional algorithm allows for the selection of an arbitrary contiguous eight component DCT sub-block from two adjacent DCT blocks that foregoes the expense of image manipulation in the real domain. Due to the fact that non-zero DCT coefficients are generally sparse, this algorithm lends itself nicely to the development of special cases which are faster than methods in use today. The de-quantization and re-quantization can be combined at execution time with the constants.

Abstract: Spinal modeling is based on a concept called spinal energy which assumes that the spine assumes a shape to minimize spinal energy. Spinal energy depends on parameters called stiffness coefficients. These parameters can be determined from human data which, by hypothesis, are universal for a large class of humans. The method adapts Newton's method to the manifold SO(3)n to find a solution of model of the human spine. Where basins of attraction are small in Newton's method, homotopy methods are introduced to move from known solutions to unknown solutions. By setting the gradient of the spinal energy to zero, Newton's method is used to solve the inverse problem of finding stiffness coefficients from human data. A new approach to improving deformed spines uses the modeling method based on spinal energy. This approach preserves maximally the range of motion of the spine. The technique used is vertebraplasty; i.e.

Abstract: A method and apparatus for halftoning digital images renders color data subject to constraints on the number of colorants which can be deposited on a single pixel and constraints on consecutive pixels rendered with the same color. The color data to be rendered is mapped into a second data set in an achievable color gamut space. Then, using a digital halftoning method in the achievable color gamut space, the second data set is rendered, so that the constraints are satisfied.

Abstract: A system and method for detecting parallel marketing of an item, include forming at least one of a coating and a code on the item, interrogating the at least one of the coating and said code, and determining from the interrogating whether the item has been transferred from an authorized merchant to an unauthorized merchant.

Abstract: An apparatus and method allow to deposit ordinary checks from home or office. A special scanner is used to scan an endorsed check for deposit. The check may have printed thereon encryptions in at least selected locations. Scanning the endorsed check with the scanner to generates a digitized version of the check. The scanner virtually partitions the digitized version of the check into a plurality of regions. These regions may be stripes or zones. Each region is successively examined to extract from the digitized version of the check information from that region. The information extracted from a region is encrypted and transmitted to a bank. Upon acknowledgment from the bank, at least some of the regions of the plurality of regions voided by a form of indelible but non-invasive (e.g. allowing reading after voiding) marking such as punched holes, burned areas, overprinting of a pattern. The processing by the scanner continues until all regions have been processed.

Abstract: A method (and apparatus) for guaranteeing authenticity of an object, includes providing a sample of material obtainable only by at least one of chemical and physical processes such that the sample is random and not reproducible, associating a number reproducibly to the sample by using a specific reader, and forming at least one coded version of the number. The at least one coded version is obtained by a public key encryption, and the version is recorded into an area of the object.

Abstract: An apparatus and method allow to deposit ordinary checks from home or office. A special scanner is used to scan an endorsed check for deposit. The check may have printed thereon encryptions in at least selected locations. Scanning the endorsed check with the scanner to generates a digitized version of the check. The scanner virtually partitions the digitized version of the check into a plurality of regions. These regions may be stripes or zones. Each region is successively examined to extract from the digitized version of the check information from that region. The information extracted from a region is encrypted and transmitted to a bank. Upon acknowledgment from the bank, at least some of the regions of the plurality of regions voided by a form of indelible but non-invasive (e.g. allowing reading after voiding) marking such as punched holes, burned areas, overprinting of a pattern. The processing by the scanner continues until all regions have been processed.

Abstract: A form of paper checks, and the apparatus and method to handle them, allows deposit from home or office. The apparatus can be implemented with a Personal Computer (PC) having a secure cryptography generator (SCG) installed. The process of depositing paper checks begins by the payee endorsing a check having printed thereon encryptions in at least selected locations where information is written by a payer. The act of writing by the payee obscuring some of the encryptions. The payee then scans the endorsed check with a scanner to generate a digitized version of the check. The computer extracts from the digitized version of the check a concatenated branch number, account number and check number and a corresponding digital signature. The payee then transmits the extracted information together with the digitized version of the check for deposit. The checks a specially designed to prevent fraud such alteration of the payee, amount and multiple deposits.