Hilbert Scan Research Articles

On-line Signature Matching Based on Hilbert Scanning Patterns

On-line Signature Matching Based on Hilbert Scanning Patterns

Information Hiding Method Based on Block DWT Sub-Band Feature Encoding

For realizing of long text information hiding and covert communication, a binary watermark sequence was obtained firstly from a text file and encoded by a redundant encoding method. Then, two neighboring blocks were selected at each time from the Hilbert scanning sequence of carrier image blocks, and transformed by 1-level discrete wavelet transformation (DWT). And then the double block based JNDs (just noticeable difference) were calculated with a visual model. According to the different codes of each two watermark bits, the average values of two corresponding detail sub-bands were modified by using one of JNDs to hide information into carrier image. The experimental results show that the hidden information is invisible to human eyes, and the algorithm is robust to some common image processing operations. The conclusion is that the algorithm is effective and practical.

A Two-Stage Point Pattern Matching Algorithm Using Ellipse Fitting and Dual Hilbert Scans

Point Pattern Matching (PPM) is an essential problem in many image analysis and computer vision tasks. This paper presents a two-stage algorithm for PPM problem using ellipse fitting and dual Hilbert scans. In the first matching stage, transformation parameters are coarsely estimated by using four node points of ellipses which are fitted by Weighted Least Square Fitting (WLSF). Then, Hilbert scans are used in two aspects of the second matching stage: it is applied to the similarity measure and it is also used for search space reduction. The similarity measure named Hilbert Scanning Distance (HSD) can be computed fast by converting the 2-D coordinates of 2-D points into 1-D space information using Hilbert scan. On the other hand, the N-D search space can be converted to a 1-D search space sequence by N-D Hilbert Scan and an efficient search strategy is proposed on the 1-D search space sequence. In the experiments, we use both simulated point set data and real fingerprint images to evaluate the performance of our algorithm, and our algorithm gives satisfying results both in accuracy and efficiency.

An N-Dimensional Pseudo-Hilbert Scan for Arbitrarily-Sized Hypercuboids

The N-dimensional (N-D) Hilbert curve is a one-to-one mapping between N-D space and one-dimensional (1-D) space. It is studied actively in the area of digital image processing as a scan technique (Hilbert scan) because of its property of preserving the spatial relationship of the N-D patterns. Currently there exist several Hilbert scan algorithms. However, these algorithms have two strict restrictions in implementation. First, recursive functions are used to generate a Hilbert curve, which makes the algorithms complex and computationally expensive. Second, all the sides of the scanned region must have the same size and the length must be a power of two, which limits the application of the Hilbert scan greatly. Thus in order to remove these constraints and improve the Hilbert scan for general application, a nonrecursive N-D Pseudo-Hilbert scan algorithm based on two look-up tables is proposed in this paper. The merit of the proposed algorithm is that implementation is much easier than the original one while preserving the original characteristics. The experimental results indicate that the Pseudo-Hilbert scan can preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points, and it also shows the competitive performance of the Pseudo-Hilbert scan in comparison with other common scan techniques. We believe that this novel scan technique undoubtedly leads to many new applications in those areas can benefit from reducing the dimensionality of the problem.

A Pseudo-Hilbert Scan for Arbitrarily-Sized Arrays

The 2-dimensional (2-D) Hilbert curve is a one-to-one mapping between 2-D space and one-dimensional (1-D) space. It is studied actively in the area of digital image processing as a scan technique (Hilbert scan) because of its property of preserving the spacial relationship of the 2-D patterns. Currently there exist several Hilbert scan algorithms. However, these algorithms have two strict restrictions in implementation. First, recursive functions are used to generate a Hilbert curve, which makes the algorithms complex and computationally expensive. Second, both sides of the scanned rectangle must have same size and each size must be a power of two, which limits the application of the Hilbert scan greatly. In this paper, a Pseudo-Hilbert scan algorithm based on two look-up tables is proposed. The proposed method improves the Hilbert scan to be suitable for real-time processing and general application. The simulation indicates that the Pseudo-Hilbert scan can preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points. It also shows competitive performance of the Pseudo-Hilbert scan in comparison with other scan techniques.

Mesh-Based Video Coding For Low Bit-rate Communications

In this paper, a new method for low bit-rate content-adaptive mesh-based video coding is proposed. Intra-frame coding of this method employs feature map extraction for node distribution at specific threshold levels to achieve higher density placement of initial nodes for regions that contain high frequency features and conversely sparse placement of initial nodes for smooth regions. Insignificant nodes are largely removed using a subsequent node elimination scheme. The Hilbert scan is then applied before quantization and entropy coding to reduce amount of transmitted information. For moving images, both node position and color parameters of only a subset of nodes may change from frame to frame. It is sufficient to transmit only these changed parameters. The proposed method is well-suited for video coding at very low bit rates, as processing results demonstrate that it provides good subjective and objective image quality at a lower number of required bits.

A Fast and Accurate Algorithm for Matching Images Using Hilbert Scanning Distance with Threshold Elimination Function

To find the best transformation between a model point set and an point set is the main purpose of point pattern matching. The similarity measure plays a pivotal role and is used to determine the degree of resemblance between two objects. Although some well-known Hausdorff distance measures work well for this task, they are very computationally expensive and suffer from the noise points. In this paper, we propose a novel similarity measure using the Hilbert curve named Hilbert scanning distance (HSD) to resolve the problems. This method computes the distance measure in the one-dimensional (1-D) sequence instead of in the two-dimensional (2-D) space, which greatly reduces the computational complexity. By applying a threshold elimination function, large distance values caused by noise and position errors (e.g. those that occur with feature or edge extraction) are removed. The proposed algorithm has been applied to the task of matching edge maps with noise. The experimental results show that HSD can provide sufficient information for image matching within low computational complexity. We believe this sets a new direction for the research of point pattern recognition.

One-dimensional B–B polynomial and Hilbert scan for graylevel image coding

Effectiveness of one-dimensional Bezier–Bernstein polynomial has been studied for compression of graylevel images. Both raster and Hilbert scan have been used for this purpose. Two different algorithms for one-dimensional approximation and encoding of Hilbert images provide evidence of better compression ratio compared to that for raster scanned images. Comparison with the result of an existing algorithm has also been performed to examine the effectiveness of our methods.

Adaptive partial distortion search for block motion estimation

Block motion estimation using the exhaustive full search is computationally intensive. Fast search algorithms offered in the past tend to reduce the amount of computation by limiting the number of locations to be searched. All of these algorithms produce some quality degradation of the predicted image. To reduce the computational complexity of the full search algorithm without introducing any loss in the predicted image, we propose an adaptive partial distortion search algorithm (APDS) by selecting the most representative pixels with high activities, such as edges and texture which contribute most to the matching criterion. The APDS algorithm groups the representative pixels based on the pixel activities in the Hilbert scan. By using the grouped information and computing the accumulated partial distortion of the representative pixels before that of the other pixels, impossible candidates can be rejected sooner and the remaining computation involved in the matching criterion can be reduced remarkably. Simulation results show that the proposed APDS algorithm has a significant computational speed-up for all kinds of sequences and is the fastest when compared to the conventional partial distortion search algorithms.

Segmentation based compression for graylevel images

This paper presents a segmentation based lossy image compression (SLIC) algorithm. The segmentation scheme (Biswas and Pal, Pattern Recog. Lett. 21 (2000)), entropy based and hierarchical in nature, provides sub-images of homogeneous regions. The compression algorithm encodes a graylevel image through global approximations of sub-images by 2-d Bezier–Bernstein polynomial along with corrections, if needed, over regions in sub-images by local approximation; contours by 1-d Bezier–Bernstein polynomial and texture, if present, by Huffman coding scheme using Hilbert scan on texture blocks. Order of the 2-d polynomials has been computed with the help of an image quality index (IQI). The proposed compression algorithm also examines the compression result by encoding contours through their approximation based on stretching of discrete circular arcs. Stretching is done by affine transformation. Compression results in both the cases have been compared with JPEG results. Attempts have been made to evaluate the quality of reconstructed images through a fidelity vector whose components are different objective measures.

Region-based image coding with multiple algorithms

The wide usage of small satellite imagery, especially its commercialization, makes data-based onboard compression not only meaningful but also necessary in order to solve the bottleneck between the huge volume of data generated onboard and the very limited downlink bandwidth. The authors propose a method that encodes different regions with different algorithms. The authors use three shape-adaptive image compression algorithms as the candidates. The first one is a JPEG-based algorithm, the second one is based on the object-based wavelet transform method proposed by Katata et al. (1997), and the third adopts Hilbert scanning of the regions of interest followed by one-dimensional (1-D) wavelet transform. The three algorithms are also applied to the full image so that one can compare their performance on a whole rectangular image. The authors use eight Landsat TM multispectral images and another 12 small satellite single-band images as their data set. The results show that these compression algorithms have significantly different performance for different regions.

An analysis of some common scanning techniques for lossless image coding

Though most image coding techniques use a raster scan to order pixels prior to coding, Hilbert and other scans have been proposed as having better performance due to their superior locality preserving properties. However, a general understanding of the merits of various scans has been lacking. This paper develops an approach for quantitatively analyzing the effect of pixel scan order for context-based, predictive lossless image compression and uses it to compare raster, Hilbert, random and hierarchical scans. Specifically, for a quantized-Gaussian image model and a given scan order, it shows how the encoding rate can be estimated from the frequencies with which various pixel configurations are available as previously scanned contexts, and from the corresponding conditional differential entropies. Formulas are derived for such context frequencies and entropies. Assuming an isotropic image model and contexts consisting of previously scanned adjacent pixels, it is found that the raster scan is better than the Hilbert scan which is often used in compression applications due to its locality preserving properties. The hierarchical scan is better still, though it is based on nonadjacent contexts. The random scan is the worst of the four considered. Extensions and implications of the results to lossy coding are also discussed.

2-9 ヒルベルト走査に基づくN次元超直方体領域に対する一走査法

2-9 ヒルベルト走査に基づくN次元超直方体領域に対する一走査法

A new algorithm for N-dimensional Hilbert scanning

There have been many applications of the Hilbert curve, such as image processing, image compression, computer hologram, etc. The Hilbert curve is a one-to-one mapping between N-dimensional space and one-dimensional (l-D) space which preserves point neighborhoods as much as possible. There are several algorithms for N-dimensional Hilbert scanning, such as the Butz algorithm and the Quinqueton algorithm. The Butz algorithm is a mapping function using several bit operations such as shifting, exclusive OR, etc. On the other hand, the Quinqueton algorithm computes all addresses of this curve using recursive functions, but takes time to compute a one to-one mapping correspondence. Both algorithms are complex to compute and both are difficult to implement in hardware. In this paper, we propose a new, simple, nonrecursive algorithm for N-dimensional Hilbert scanning using look-up tables. The merit of our algorithm is that the computation is fast and the implementation is much easier than previous ones.

Hilbert scanning search algorithm for motion estimation

Block-matching algorithms, such as TSS and DSWA/IS, are widely used for motion estimation in low-bit-rate video coding. The assumption behind these algorithms is that when the matching block moves away from the optimal block, the difference between them increases monotonically. Unfortunately, this assumption is often invalid, and therefore leads to a high possibility for the result to be trapped to local minima. In this research, we propose a new multiple-candidate search scheme, Hilbert scanning search algorithm (HSSA), in which the assumption of global monotonicity is not necessary and the local monotonicity can be effectively explored with binary search around each candidate. In HSSA, the number of initial candidates and a threshold to control the selection of candidates from one stage to the next can be adjusted to meet the required search accuracy and/or speed. With properly chosen parameters, the HSSA converges to their optimal results faster and with better accuracy than the conventional block-matching algorithms.