Abstract: A watermarking system uses distinct bit patterns to identify a logic 0, a logic 1, and a marker bit, which demarcates segments of logic bit information. Marker bits, which are printed on both foreground and background areas of an image, outline message blocks. In message extraction, a preprocessing step removes any white boarders, identifies the best defined corner of a message block, crops the image, and rotates the image to place the identified corner at the top-left corner. Message extraction scans the rotated image in window segments of increasing size during multiple cycles. During each cycle, if a bit pattern cannot be identified as a data bit, then the size of the examined bit area is increased and rechecked to see it specifically is a marker bit. If no bit information can be definitively identified, then it is assigned a logic bit value based on a 50% random assignment.

Abstract: A watermarking system uses distinct bit patterns to identify a logic 0, a logic 1, and a marker bit, which demarcates segments of logic bit information. Marker bits, which are printed on both foreground and background areas of an image, outline message blocks. In message extraction, a preprocessing step removes any white boarders, identifies the best defined corner of a message block, crops the image, and rotates the image to place the identified corner at the top-left corner. Message extraction scans the rotated image in window segments of increasing size during multiple cycles. During each cycle, if a bit pattern cannot be identified as a data bit, then the size of the examined bit area is increased and rechecked to see it specifically is a marker bit. If no bit information can be definitively identified, then it is assigned a logic bit value based on a 50% random assignment.

Abstract: A watermarking system uses distinct bit patterns to identify a logic 0, a logic 1, and a marker bit, which demarcates segments of logic bit information. Marker bits, which are printed on both foreground and background areas of an image, outline message blocks. In message extraction, a preprocessing step removes any white boarders, identifies the best defined corner of a message block, crops the image, and rotates the image to place the identified corner at the top-left corner. Message extraction scans the rotated image in window segments of increasing size during multiple cycles. During each cycle, if a bit pattern cannot be identified as a data bit, then the size of the examined bit area is increased and rechecked to see it specifically is a marker bit. If no bit information can be definitively identified, then it is assigned a logic bit value based on a 50% random assignment.

Abstract: Similarities between simplex projection with upper bounds and L1 projection are explored. Criteria for a-priori determination of sequence in which various constraints become active are derived, and this sequence is used to develop efficient algorithms for projecting a vector onto the L1-ball while observing box constraints. Three projection methods are presented. The first projection method performs exact projection in O(n2) worst case complexity, where n is the space dimension. Using a novel criteria for ordering constraints, the second projection method has a worst case complexity of O(n log n). The third projection method is a worst case linear time algorithm having O(n) complexity. The upper bounds defined for the projected entries guide the L1-ball projection to more meaningful predictions.

Abstract: Non-negative matrix factorization, NMF, is combined with identification of a maximum margin classifier by minimizing a cost function that contains a generative component and the discriminative component. The relative weighting between the generative component and the discriminative component are adjusting during subsequent iterations such that initially, when confidence is low, the generative model is favored. But as the iterations proceed, confidence increases and the weight of the discriminative component is steadily increased until it is of equal weight as the generative model. Preferably, the cost function to be minimized is: min F , G ? 0 ? ? X - FG ? 2 + ? ? ( ? w ? 2 + C ? ? i = 1 n ? L ? ( y i , w · g i + b ) ) .