Abstract: A method executed by a computer system that transmits a multimedia content through a negative-base number. The method includes generating a binary sequence for the multimedia content, converting the binary sequence into a negative-base number, receiving the negative-base number, retrieving a negative base of the negative base number, calculating the binary sequence based on the negative-base number and the negative base, and obtaining the multimedia content based on the binary sequence.

Abstract: A method improves information security by generating a key with which a first multimedia content is encrypted into a second multimedia content. The method generates a first representation for the first multimedia content and a second representation for the second multimedia content on a complex plane, and improves the information security by generating the key by determining a relationship between the first representation and the second representation on the complex plane such that the first multimedia content is encrypted into the second multimedia content with the relationship as the key.

Abstract: Example embodiments include a method that improves calculations of surface roughness that map a planetary surface. The method includes calculating a V-system matrix with a size of ?×? in an interval [0,1]; transforming the V-system matrix into an orthogonal matrix; improving calculations of the surface roughness of the planetary surface by calculating the surface roughness of a digital elevation model generated from data captured from the planetary surface; and generating a map of the planetary surface based on the surface roughness.

Abstract: Example embodiments include a method that improves calculations of surface roughness that map a planetary surface. The method includes calculating a V-system matrix with a size of ?×? in an interval [0,1]; transforming the V-system matrix into an orthogonal matrix; improving calculations of the surface roughness of the planetary surface by calculating the surface roughness of a digital elevation model generated from data captured from the planetary surface; and generating a map of the planetary surface based on the surface roughness.

Abstract: One embodiment is a method that improves computations of correlation values between a surface roughness and terrain parameters of a terrain surface. The method includes applying the terrain parameters as an input of a Back Propagation Neural Network (BPNN) and the surface roughness as an output of the BPNN; implementing a nonlinear mapping from the input to the output of the BPNN; generating a weight matrix (?1) and a weight matrix (?2); and improving computations of the correlation values by calculating a correlation matrix by ?2×?1, calculating a unit weight which is a sum of absolute values in the correlation matrix, and dividing each value in the correlation matrix by the unit weight.

Abstract: A method executed by a computer system that transmits a multimedia content through a negative-base number. The method includes generating a binary sequence for the multimedia content, converting the binary sequence into a negative-base number, receiving the negative-base number, retrieving a negative base of the negative base number, calculating the binary sequence based on the negative-base number and the negative base, and obtaining the multimedia content based on the binary sequence.

Abstract: A method executed by a computer system to construct an omnidirectional roughness (OR) map of a lunar crater based on a data set of a digital elevation model (DEM) of surface textures of the lunar crater is provided. The method includes setting a center and a first point of the data set, selecting a moving window, utilizing a one point-to-point step when the moving window slides over the DEM, calculating a morphological surface roughness (MSR) that detects a vertical roughness of the lunar crater, calculating a topographic frequency coefficient (TFC) that detects a horizontal roughness of the lunar crater, constructing the OR map, and displaying the OR map to show a surface roughness of the lunar crater.

Abstract: A computer system executes hierarchical MK splines approximation for lunar brightness temperature (TB) data approximation. The computer system constructs a TB model map by generating a final approximation function for constructing an interpolated surface that approximates the TB data set obtained by lunar probe. The method includes executing MK splines approximation to the TB data set with a hierarchy of control lattice from coarsest lattice to densest lattice to iteratively obtain approximation functions. The TB model map is constructed by generating a final approximation function to construct the interpolated surface.

Abstract: A method constructs an image with improved peak signal-to-noise ratio (PSNR) from a scattered pixel set. The method generates an approximation function that is a linear combination of a plurality of Many-Knot (MK) spline basis functions, and constructs the image with improved PSNR by conducting a least squares treatment on the approximation function to minimize a residual of each pixel value in the scattered pixel set from the approximation function.

Abstract: A method embeds a watermark image into a host image with adaptive rectangular partition and Lower Upper (LU) decomposition such that a watermarked image is generated with improved computational complexity. The method divides a host image into an Red (R) component, a Green (G) component, and a Blue (B) component, and divides each component of the R, G, and B components into a plurality of M×M size blocks, and partitions each of the plurality of M×M size blocks into a plurality of non-overlapping blocks with adaptive rectangular partition. The method selects a plurality of embedding blocks from the plurality of M×M size blocks for each component of the R, G, and B components of the host image to embed watermark information such that the watermarked image is generated.

Abstract: A method improves information security by generating a key with which a first multimedia content is encrypted into a second multimedia content. The method generates a first representation for the first multimedia content and a second representation for the second multimedia content on a complex plane, and improves the information security by generating the key by determining a relationship between the first representation and the second representation on the complex plane such that the first multimedia content is encrypted into the second multimedia content with the relationship as the key.

Abstract: A method constructs an image with improved peak signal-to-noise ratio (PSNR) from a scattered pixel set. The method generates an approximation function that is a linear combination of a plurality of Many-Knot (MK) spline basis functions, and constructs the image with improved PSNR by conducting a least squares treatment on the approximation function to minimize a residual of each pixel value in the scattered pixel set from the approximation function.

Abstract: Example embodiments include a method that reduces consumption of computer resources in a computer system to reconstruct a shape of a multi-object image using finite terms. The method includes computing an initial function by performing V-system of degree 0 and functions of curves by performing hierarchical V-system. Norms of the functions of curves are compared with a predetermined threshold. A reconstruction function of the shape of the multi-object image is generated by summing the initial function and the functions of curves.

Abstract: A method embeds a watermark image into a host image with adaptive rectangular partition and Lower Upper (LU) decomposition such that a watermarked image is generated with improved computational complexity. The method divides a host image into an Red (R) component, a Green (G) component, and a Blue (B) component, and divides each component of the R, G, and B components into a plurality of M×M size blocks, and partitions each of the plurality of M×M size blocks into a plurality of non-overlapping blocks with adaptive rectangular partition. The method selects a plurality of embedding blocks from the plurality of M×M size blocks for each component of the R, G, and B components of the host image to embed watermark information such that the watermarked image is generated.

Abstract: One example embodiment is a method to embed a watermark image into a host image such that a watermarked image is generated. The method divides a host image into an Red (R) component, a Green (G) component, and a Blue (B) component, and partitions each component of the R, G, and B components into non-overlapping blocks from which embedding blocks are selected to embed watermark information such that a watermarked image is generated.

Abstract: A method executed by a computer system to construct an omnidirectional roughness (OR) map of a lunar crater based on a data set of a digital elevation model (DEM) of surface textures of the lunar crater is provided. The method includes setting a center and a first point of the data set, selecting a moving window, utilizing a one point-to-point step when the moving window slides over the DEM, calculating a morphological surface roughness (MSR) that detects a vertical roughness of the lunar crater, calculating a topographic frequency coefficient (TFC) that detects a horizontal roughness of the lunar crater, constructing the OR map, and displaying the OR map to show a surface roughness of the lunar crater.

Abstract: A computer system that execute a method to stitch satellite images into a wide-angle image. The method includes dividing each of the satellite images into plural subimages, determining whether the subimages include an overlap area that overlaps with adjacent subimages, obtaining cropped subimages by removing the overlap area from the subimages, generating preprocessed satellite images each including the cropped subimages, selecting a reference image and a target image from the preprocessed satellite images, determining plural correspondent pairs in an overlap region between the reference and target images based on a feature matching algorithm, obtaining a transformation matrix by a least-squares algorithm and based on coordinates of the correspondent pairs, obtaining calibrated coordinates for each pixel of the target image by applying the transformation matrix, and stitching the target images into the wide-angle image based on the calibrated coordinates of the target image.

Abstract: A computer system executes hierarchical MK splines for scattered data approximation. The computer system constructs an image by generating a final approximation function that approximates a scattered data set with a hierarchy of control lattice from coarsest to densest. The method includes executing MK splines approximation to the scattered data set with the hierarchy of control lattice to iteratively obtain approximation functions. The image is constructed by generating the final approximation function to construct an interpolated surface.

Abstract: A computer system executes hierarchical MK splines approximation for lunar brightness temperature (TB) data approximation. The computer system constructs a TB model map by generating a final approximation function for constructing an interpolated surface that approximates the TB data set obtained by lunar probe. The method includes executing MK splines approximation to the TB data set with a hierarchy of control lattice from coarsest lattice to densest lattice to iteratively obtain approximation functions. The TB model map is constructed by generating a final approximation function to construct the interpolated surface.

Abstract: One example embodiment is a method to embed a watermark image into a host image such that a watermarked image is generated. The method divides a host image into an Red (R) component, a Green (G) component, and a Blue (B) component, and partitions each component of the R, G, and B components into non-overlapping blocks from which embedding blocks are selected to embed watermark information such that a watermarked image is generated.