Two-dimensional Binary Arrays Research Articles

The merit factor of binary arrays derived from the quadratic character

We calculate the asymptotic merit factor, under all cyclic rotations of rows and columns, of two families of binary two-dimensional arrays derived from the quadratic character. The arrays in these families have size $p\times q$, where $p$ and $q$ are not necessarily distinct odd primes, and can be considered as two-dimensional generalisations of a Legendre sequence. The asymptotic values of the merit factor of the two families are generally different, although the maximum asymptotic merit factor, taken over all cyclic rotations of rows and columns, equals $36/13$ for both families. These are the first non-trivial theoretical results for the asymptotic merit factor of families of truly two-dimensional binary arrays.

Subjective randomness and natural scene statistics

Accounts of subjective randomness suggest that people consider a stimulus random when they cannot detect any regularities characterizing the structure of that stimulus. We explored the possibility that the regularities people detect are shaped by the statistics of their natural environment. We did this by testing the hypothesis that people's perception of randomness in two-dimensional binary arrays (images with two levels of intensity) is inversely related to the probability with which the array's pattern would be encountered in nature. We estimated natural scene probabilities for small binary arrays by tabulating the frequencies with which each pattern of cell values appears. We then conducted an experiment in which we collected human randomness judgments. The results show an inverse relationship between people's perceived randomness of an array pattern and the probability of the pattern appearing in nature.

Friendly progressive visual secret sharing using generalized random grids

A random grid is a two-dimensional binary array in which entries, 0 or 1, are determined in 50% to 50%. A generalized random grid is also a 2-D binary array in which entries are determined but not necessarily 50% to 50%. Using generalized random grids for visual secret sharing, friendly meaningful transparencies, also called shares, can be generated, and the size of each share is the same with the secret image size. In the decoding phase, stacking at least two friendly meaningful shares together, the content of the secret image can be revealed without any computation, and the more shares stacked, the clearer the result. The proposed method can also be implemented for gray and color images.

Zero/Positive Capacities of Two-Dimensional Runlength-Constrained Arrays

A binary sequence satisfies a one-dimensional (d, k) runlength constraint if every run of zeroes has length at least d and at most k. A binary sequence satisfies a one-dimensional (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/) runlength constraint if every run of zeroes has length at least d/sub 1/ and at most k/sub 2/ and every run of ones has length at least d/sub 2/ and at most k/sub 2/. A two-dimensional binary array is said to satisfy a (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/; d/sub 3/, d/sub 4/, k/sub 4/) runlength constraint if it satisfies the one-dimensional (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/) runlength constraint horizontally (i.e. on every row) and the one-dimensional (d/sub 3/, k/sub 3/, d/sub 4/, k/sub 4/) runlength constraint vertically (i.e. on every column). For convenience, we will say that a binary array satisfies the (d,k) runlength constraint if each row and each column satisfy the (d,k) runlength constraint and that a binary array satisfies the (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/) runlength constraint if it is (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/) runlength constrained both horizontally and vertically. We say that a binary array satisfies the (d/sub 1/, k/sub 1/; d/sub 3/, k/sub 3/) runlength constraint if each row satisfies the (d/sub 1/, k/sub 1/, d/sub 1/, k/sub 1/) runlength constraint and each column satisfies the (d/sub 3/, k/sub 3/, d/sub 3/, k/sub 3/) runlength constraint. Finally, we always allow violation of the smallest runlength constraint at the beginning and the end sequences and at the edges of arrays. In this work we examine the following basic question: for which values of d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/, d/sub 3/, k/sub 3/, d/sub 4/, k/sub 4/, is C(d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/; d/sub 3/, k/sub 3/, d/sub 4/, k/sub 4/) positive and for which values is it equal to zero?.

Probabilistic quadtrees for variable-resolution mapping of large environments

Probabilistic occupancy grids are a common and well-proven spatial representation used in robot mapping. However, representing very large environments with high resolution can still impose prohibitive memory requirements. A quadtree is a well-known data structure able to achieve compact representations of large two-dimensional binary arrays. We extend this idea and presentprobabilistic quadtrees for efficient representation and storage of probabilistic occupancy maps. We also discuss the implementation of probabilistic quadtrees and their integration into our robotic middleware system Miro.

Efficient code constructions for certain two-dimensional constraints

Efficient encoding algorithms are presented for two types of constraints on two-dimensional binary arrays. The first constraint considered is that of t-conservative arrays, where each row and each column has at least t transitions of the form '0'/spl rarr/'1' or '1'/spl rarr/'0.' The second constraint is that of two-dimensional DC-free arrays, where in each row and each column the number of '0's equals the number of '1's.

Invertible operations on a Cellular Neural Network Universal Machine

This paper is concerned with the invertibility of parallel operations definable on two-dimensional binary arrays by means of a local Boolean function. In this way, it contributes to the theory of cellular automata and may open new potentialities to cellular neural network applications. We provide a theoretically new approach to the invertibility of two-dimensional additive maps which can be used to obtain detailed information on the behaviour of these operations. Other ways to make invertible operations are also investigated, including local maps which are additive in only one of the terms, and second-order cellular automata. The discussed techniques yield a rich variety of invertible operations on infinite and/or finite two-dimensional binary arrays. When implemented on CNN Universal Chips, all of these operations, performed by TeraOPS speed, become subroutines of a 2D analogic algorithm. These operations can be used in 2D cryptography. © 1998 John Wiley & Sons, Ltd.

Two-dimensional perfect binary arrays with 64 elements

Perfect binary arrays can exist for numbers of elements that are even square numbers. Two-dimensional (2-D) perfect binary arrays are 4, 16, 36, and 144 elements are known. Perfect binary arrays with 64 elements can be constructed for three or more dimensions. Here, two-dimensional binary arrays with 64 elements are examined. The results of computer search for symmetric binary arrays with 64 elements are presented in the form of two 2-D perfect binary arrays with sizes 8*8 and 4*16. Applications of these perfect binary arrays are in 2-D synchronization, time-frequency coding, and coding loudspeaker fields.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Perfect binary arrays with 36 elements

The letter presents a new two-dimensional binary array with a perfect periodic autocorrelation function (PACF). Four decompositions of the new array in two-, three- and four-dimensional arrays with the same property are shown. These can be applied, for example, in time-frequency coding, two-dimensional synchronisation and image coding.

Two-dimensional binary arrays with good autocorrelation

Calabro and Wolf (1968) Inform. Contr. 11 ) investigate the autocorrelation properties of certain periodic two-dimensional arrays. This note points out a relationship between periodic p × q -arrays with two-level autocorrelation and difference sets in the group C ( p ) × C ( q ), where C ( n ) denote the cyclic group of order n . This observation enables us to construct several families of such arrays, some of which are perfect.

Two-Dimensional Binary Arrays

A method of converting certain types of analog signals to digital form is described. The signals considered are those describing movement in a plane and are digitized by reference to a rectangular array of 1's and 0's.