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 watermarking method involves mostly invisible artifacts and is sensitive to any modification of the picture at the level of precision rendered by the compressed version of the image. The image is compressed according to a known compression standard, such as the JPEG standard, and with a fixed quality setting. Using the JPEG standard, the original image is cut into blocks to which the Discrete Cosine Transform (DCT) is applied and the DCT coefficients quantized. The watermark according to the invention is applied to the quantized DCT coefficients. This is done using an encryption function, such as a secret key/public key algorithm. The JPEG compression is then completed using a lossless compression scheme, such as Huffman coding, to produce the compressed and watermarked image. Authentication of the compressed and watermarked image begins with a lossless decompression scheme to obtain the set of quantized DCT coefficients. The coefficients are authenticated, and the DCT output of each block is dequantized.

Abstract: Method and apparatus is described for encoding and decoding a stream of randomly distributed binary bits representing digital data, including an encoder for encoding the bit stream to achieve a run length limited, partial response coding of the stream; a recording medium for recording the encoded stream; and a decoding system for recovering timing signals and a stream of data signals separately from the recorded stream using a first channel for decoding the recorded stream to recover a timing signal stream; therefrom; and a second channel for decoding the recorded stream to recover a stream of data signals therefrom.

Abstract: An algorithm and the hardware embodiment for producing a run length limited code useful in magnetic recording channels are described. The system described produces sequences which have a minimum of 2 zeros and a maximum of 7 zeros between adjacent 1's. The code is generated by a sequential scheme that maps 1 bit of unconstrained into 2 bits of constrained data. The encoder is a finite state machine whose internal state description requires 3 bits. It possesses the attractive feature of reset data blocks which reset it to a fixed state. The decoder requires a lookahead of three future channel symbols (6 bits) and its operation is channel state independent. The error propagation due to a random error is 3 bits. The hardware implementation is extremely simple and can operate at very high data speeds.

Abstract: An algorithm and the hardware embodiment for producing a run length limited code useful in magnetic recording channels are described. The system described produces sequences which have a minimum of 1 zero and a maximum of 7 zeros between adjacent 1's. The code is generated by a sequential scheme that map 2 bits of unconstrained into 3 bits of constrained data. The encoder is a finite state machine whose internal state description requires 3 bits. It possesses the attractive feature of reset data blocks which reset it to a fixed state. The decoder requires a lookahead of two future channel symbols (6 bits) and its operation is channel state independent. The error propagation due to a random error is 5 bits. The hardware implementation is extremely simple and can operate at very high data speeds.

Abstract: A cryptographic system for encrypting a block of binary data under the control of a key consisting of a set of binary symbols. The cryptographic system may be utilized within a data processing environment to ensure complete privacy of data and information that is stored or processed within a computing system. All authorized subscribers who are permitted access to data within the network are assigned a unique key consisting of a combination of binary symbols. The central processing unit within the computing network contains a complete listing of all distributed authorized subscriber keys. All communications transmitted from terminal input are encrypted into a block cipher by use of the cryptographic system operating under the control of the subscriber key which is inputed to the terminal device. At the receiving station or central processing unit, an identical subscriber key which is obtained from internal tables stored within the computing system is used to decipher all received ciphered communications.