Moustafa M. Fahmy

Binary text image compression using overlapping rectangular partitioning

Abstract In this paper a new lossless binary text image coding technique based on overlapping partitioning is presented. In this technique, the black regions in the image are first partitioned into a number of overlapping and nonoverlapping rectangles. This partitioning algorithm gives, in general, fewer rectangles than those obtained using nonoverlapping partitioning. After partitioning, the two opposite vertices of each rectangle are compressed using a simple encoding technique. For binary text images (of different languages and fonts) the overlapping partitioning proposed here yields compression ratios better than the nonoverlapping partitioning. In addition, the proposed scheme is suitable for texts consisting of different languages, fonts and sizes.

NMR signal enhancement via a new time-frequency transform

In this paper, a reliable method to reduce the noise from nuclear magnetic resonance (NMR) signals using a recently developed linear critically sampled time-frequency transform is proposed. In addition to its low computational requirements, this transform has many theoretical advantages that make it a good candidate for NMR signal enhancement. NMR signals in the transform domain are concentrated in a few coefficients while the noise is well distributed. Performing a thresholding technique in the transform domain, therefore, significantly enhances the signal. A comparison with other signal enhancement techniques shows that this technique has a superior performance, thus confirming the theoretical expectations.

Stable critically-sampled Gabor transform with localized biorthogonal function

In this paper, a new critically-sampled Gabor transform is presented. This transform, unlike all currently available critically-sampled Gabor transforms, leads to a stable transform. In addition, the resulting biorthogonal function, which is unique in the critical sampling case, is well localized in both time and frequency. It thus overcomes the main two problems of previous transforms.

An improved wavelet-based corner detection technique

An improved, wavelet-based technique for corner detection, in 2-D planar curves, is presented. This boundary based technique is simple to implement and computationally efficient and exploits wavelet transform modulus maxima (WTMM) to detect corners. The proposed algorithm is robust with respect to object geometry. We also report results under additive white Gaussian noise (AWGN).

Critically sampled Gabor transform with localized biorthogonal function

A new implementation of the critically sampled nonperiodic real Gabor transform (GT) is presented for non-separable time-frequency (TF) plane sampling. In the propsed implementation, the quincunx sampling is used to sample the TF plane. This leads to a well localized biorthogonal function in both time and frequency. It thus overcomes the main problem of the previous implementations, which is the non-localization of the resultant biorthogonal function. A fast algorithm to compute the derived biorthogonal function is proposed.

An efficient ℓ p optimization technique for the design of 2-D linear phase FIR digital filters

An iterative optimization technique, based on the method of parallel tangents coupled with an efficient line searching technique, is proposed for the design of two-dimensional linear phase FIR digital filters. The performance index for the optimization procedure is shown to be convex and hence this technique will always converge towards the global minimum. An important feature is that the design time increases slowly as the number of filter coefficients increases. To illustrate the technique several circular lowpass filters were designed. These filters compare favourably to filters designed using the minimax technique that was developed by Harris. The technique can also be used for the design of one-dimensional and multi-dimensional linear phase FIR digital filters.

A new compression technique for binary text images

In this paper a new lossless binary text image coding technique based on overlapping partitioning is presented. In this technique, the black regions in the image are first partitioned into a number of fully overlapping and nonoverlapping rectangles. After partitioning, the two opposite vertices of each rectangle are compressed using a simple encoding technique. It has been demonstrated that the compression ratios obtained for different text images are better than the nonoverlapping partitioning.

Symmetry in two-dimensional rectangularly-sampled digital filters

It is well known that exploiting the quadrantal, diagonal or octagonal symmetry existing in the 2-D filter frequency response results in a reduction in the design and implementation complexities. This paper introduces new symmetries that could possibly exist in the 2-D filter frequency response. The symmetries are presented in a general framework that encompasses all previously known and newly discovered symmetries. The commonly found cases such as displacement, rotation and reflection symmetries are discussed in some detail to present their geometric properties in the frequency-plane. An example is solved at the end to illustrate the significant savings resulting from exploiting those previously unknown symmetries.

2-D separable digital filters

A known method to design 2-D filters is to transform the design problem from the 2-D to the 1-D domain by decomposing the 2-D specification into a sum of separable specification components. The filter used for the approximation is taken in the form of a sum of separable 2-D filters (i.e. a separable denominator filter). In this paper a framework that encompasses the available decomposition techniques is presented. Other techniques with desirable characteristics are proposed. The definition of separability is also extended to include filters with general impulse response support.

Spatial-domain design of two-dimensional recursive digital filters

An optimization technique is proposed to design stable two-dimensional recursive digital filters with prescribed impulse or step response. The performance measure used is the weighted l p -norm of the error function. The optimization is carried out using the Davidon-Fletcher and Powell algorithm. Throughout the paper, the local state space model is used to represent the filter. The matrix derivative linear operator is used to calculate the performance measure gradient vector. A design for an asymmetric-half-plane filter is solved to illustrate the proposed technique.