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Abstract The emerging technology of reversible circuits offers a potential solution to the synthesis of ultra low‐power quantum computing systems. A reversible circuit can be envisaged as a cascade of reversible gates only, such as Toffoli gate, which has two components: k control bits and a target bit (k‐CNOT), k ≥ 1. While analysing testability issues in a reversible circuit, the missing‐gate fault model is often used for modelling physical defects in k‐CNOT gates. A new design‐for‐testability (DFT) technique is proposed for reversible circuits that deploys bit‐swapping using Fredkin reversible gates. It is shown that in an (n × n) circuit implemented with k‐CNOT gates, addition of only two extra inputs along with a few Fredkin gates yields easy testability in the circuit. The modified design admits a universal test set of maximum size 2n + 1 that detects all detectable missing gate faults in the original circuit, where n is the number of input/output lines in the circuit. The DFT overhead in terms of quantum cost is much less compared to that of previous approaches. The method is more advantageous for large circuits.

This thesis reports several methods for automated analysis and interpretation of bone X-ray images. Automatic segmentation of the bone part in a digital X-ray image is a challenging problem because of its low contrast against the surrounding flesh. In this thesis, we propose a fully automated X-ray image segmentation technique, which is based on a variant of entropy measure of the image. We have also analyzed the geometric information embedded in the long-bone contour image to identify the presence of abnormalities in the bone and perform fracture detection, fracture classification, and bone cancer diagnosis.

A novel technique on shape coding of an object in a binary digital image, based on the tight isotheticpolygonal covers of the object in a multiresolution background, is proposed. This technique would be useful in various analyses and applications related with digital images. To demonstrate the power and usefulness of such shape codes, we have also proposed an image retrieval scheme based on shape codes. The elegance of the scheme on shape codes lies in capturing the shape of the object(s) present in an image from its gross appearance to its finer details by a set of isothetic polygons, in a hierarchical manner. The inherent tolerance present in such a cast of isothetic polygonal shape enables the shape codes of two objects resemble closely as the grid resolution becomes finer and finer, provided the objects are of similar shapes. The method is very fast because it does not involve any complex computations, and requires only integer-based comparisons and additions. Experimental results demonstrate the strength and efficiency of the proposed scheme.

Since the inception of successful rasterization of curves and objects in the digital space, several algorithms have been proposed for approximating a given digital curve. All these algorithms, however, resort to thinning as preprocessing before approximating a digital curve with changing thickness. Described in this paper is a novel thinning-free algorithm for polygonal approximation of an arbitrarily thick digital curve, using the concept of “cellular envelope”, which is newly introduced in this paper. The cellular envelope, defined as the smallest set of cells containing the given curve, and hence bounded by two tightest (inner and outer) isothetic polygons, is constructed using a combinatorial technique. This envelope, in turn, is analyzed to determine a polygonal approximation of the curve as a sequence of cells using certain attributes of digital straightness. Since a real-world curve=curve-shaped object with varying thickness, unexpected disconnectedness, noisy information, etc., is unsuitable for the existing algorithms on polygonal approximation, the curve is encapsulated by the cellular envelope to enable the polygonal approximation. Owing to the implicit Euclidean-free metrics and combinatorial properties prevailing in the cellular plane, implementation of the proposed algorithm involves primitive integer operations only, leading to fast execution of the algorithm. Experimental results that include output polygons for different values of the approximation parameter corresponding to several real-world digital curves, a couple of measures on the quality of approximation, comparative results related with two other well-referred algorithms, and CPU times, have been presented to demonstrate the elegance and efficacy of the proposed algorithm.