Abstract: In this paper, a near lossless image coding scheme
based on Orthogonal Polynomials Transform (OPT) has been
presented. The polynomial operators and polynomials basis operators
are obtained from set of orthogonal polynomials functions for the
proposed transform coding. The image is partitioned into a number of
distinct square blocks and the proposed transform coding is applied to
each of these individually. After applying the proposed transform
coding, the transformed coefficients are rearranged into a sub-band
structure. The Embedded Zerotree (EZ) coding algorithm is then
employed to quantize the coefficients. The proposed transform is
implemented for various block sizes and the performance is
compared with existing Discrete Cosine Transform (DCT) transform
coding scheme.
Abstract: In this paper, an image adaptive, invisible digital
watermarking algorithm with Orthogonal Polynomials based
Transformation (OPT) is proposed, for copyright protection of digital
images. The proposed algorithm utilizes a visual model to determine
the watermarking strength necessary to invisibly embed the
watermark in the mid frequency AC coefficients of the cover image,
chosen with a secret key. The visual model is designed to generate a
Just Noticeable Distortion mask (JND) by analyzing the low level
image characteristics such as textures, edges and luminance of the
cover image in the orthogonal polynomials based transformation
domain. Since the secret key is required for both embedding and
extraction of watermark, it is not possible for an unauthorized user to
extract the embedded watermark. The proposed scheme is robust to
common image processing distortions like filtering, JPEG
compression and additive noise. Experimental results show that the
quality of OPT domain watermarked images is better than its DCT
counterpart.
Abstract: X-ray mammography is the most effective method for
the early detection of breast diseases. However, the typical diagnostic
signs such as microcalcifications and masses are difficult to detect
because mammograms are of low-contrast and noisy. In this paper, a
new algorithm for image denoising and enhancement in Orthogonal
Polynomials Transformation (OPT) is proposed for radiologists to
screen mammograms. In this method, a set of OPT edge coefficients
are scaled to a new set by a scale factor called OPT scale factor. The
new set of coefficients is then inverse transformed resulting in
contrast improved image. Applications of the proposed method to
mammograms with subtle lesions are shown. To validate the
effectiveness of the proposed method, we compare the results to
those obtained by the Histogram Equalization (HE) and the Unsharp
Masking (UM) methods. Our preliminary results strongly suggest
that the proposed method offers considerably improved enhancement
capability over the HE and UM methods.
Abstract: In this paper, a new algorithm for generating codebook is proposed for vector quantization (VQ) in image coding. The significant features of the training image vectors are extracted by using the proposed Orthogonal Polynomials based transformation. We propose to generate the codebook by partitioning these feature vectors into a binary tree. Each feature vector at a non-terminal node of the binary tree is directed to one of the two descendants by comparing a single feature associated with that node to a threshold. The binary tree codebook is used for encoding and decoding the feature vectors. In the decoding process the feature vectors are subjected to inverse transformation with the help of basis functions of the proposed Orthogonal Polynomials based transformation to get back the approximated input image training vectors. The results of the proposed coding are compared with the VQ using Discrete Cosine Transform (DCT) and Pairwise Nearest Neighbor (PNN) algorithm. The new algorithm results in a considerable reduction in computation time and provides better reconstructed picture quality.
Abstract: The density estimates considered in this paper comprise
a base density and an adjustment component consisting of a linear
combination of orthogonal polynomials. It is shown that, in the
context of density approximation, the coefficients of the linear combination
can be determined either from a moment-matching technique
or a weighted least-squares approach. A kernel representation of
the corresponding density estimates is obtained. Additionally, two
refinements of the Kronmal-Tarter stopping criterion are proposed
for determining the degree of the polynomial adjustment. By way of
illustration, the density estimation methodology advocated herein is
applied to two data sets.