Generally, two problems of bag-of-features in image retrieval are still considered unsolved: one is that spatial information about descriptors is not employed well, which affects the accuracy of retrieval; the other is that the trade-off between vocabulary size and good precision, which decides the storage and retrieval performance. In this paper, we propose a novel approach called Hilbert scan based bag-of-features (HS-BoF) for image retrieval. Firstly, Hilbert scan based tree representation (HSBT) is studied, which is built based on the local descriptors while spatial relationships are added into the nodes by a novel grouping rule, resulting of a tree structure for each image. Further, we give two ways of codebook production based on HSBT: multi-layer codebook and multi-size codebook. Owing to the properties of Hilbert scanning and the merits of our grouping method, sub-regions of the tree are not only flexible to the distribution of local patches but also have hierarchical relations. Extensive experiments on caltech-256, 13-scene and 1 million ImageNet images show that HS-BoF obtains higher accuracy with less memory usage.

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.

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.

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.

To find the best transformation between a "model" point set and an "image" 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.

This paper presents a novel approach to pixel decimation for motion estimation in video coding. Early techniques of pixel decimation use regular pixel patterns to evaluate matching criterion. Recent techniques use adaptive pixel patterns and have achieved better efficiency. However, these adaptive techniques require an initial division of a block into a set of uniform regions and therefore are only locally-adaptive in essence. In this paper, we present a globally-adaptive scheme for pixel decimation, in which no regions are fixed at the beginning and pixels are selected only if they have features important to the determination of a match. The experiment results show that when no more than 40 pixels are selected out of a 1616 block, this approach achieves a better search accuracy by 13-22% than the previous locally-adaptive methods which also use features.

Conventional fast block-matching algorithms, such as TSS and DSWA/IS, are widely used for motion estimation in the low-bit-rate video coding. These algorithms are based on the assumption that when searching in the previous frame for the block that best matches a block in the current frame, the difference between them increases monotonically when a matching block moves away from the optimal solution. Unfortunately, this assumption of global monotonicity is often not valid, which can lead to a high possibility for the matching block to be trapped to local minima. On the other hand, monotonicity does exist in localized areas. In this paper, we proposed a new algorithm called Peano-Hilbert scanning search algorithm (PHSSA). With the Peano-Hilbert image representation, the assumption of global monotonicity is not necessary, while local monotonicity can be effectively explored with binary search. PHSSA selects multiple winners at each search stage, minimizing the possibility of the result being trapped to local minima. The algorithm allows selection of three parameters to meet different search accuracy and process speed: (1) the number of initial candidate intervals, (2) a threshold to remove the unpromising candidate intervals at each stage, and (3) a threshold to control when interval subdivision stops. With proper parameters, the multiple-candidate PHSSA converges to the optimal result faster and with better accuracy than the conventional block matching algorithms.

The Hilbert curve is one of the simplest curves which pass through all points in a space. Many researchers have worked on this curve from the engineering point of view, such as for an expression of two-dimensional patterns, for data compression in an image or in color space, for pseudo color image displays, etc. A computation algorithm of this curve is usually based on a look-up table instead of a recursive algorithm. In such algorithm, a large memory is required for the path look-up table, and the memory size becomes proportional to the image size. In this paper, we present an implementation of a fast sequential algorithm that requires little memory for two and three dimensional Hilbert curves. Our method is based on some rules of quad-tree traversal in two dimensional space, and octtree traversal in three dimensional space. The two dimensional Hilbert curve is similar to the scanning of a DF (Depth First) expression, which is a quad-tree expression of an image. The important feature is that it scans continuously from one quadrant, which is obtained by quad tree splitting, to the next adjacent one in two dimensional space. From this point, if we consider run-lengths of black and white pixels during the scan, the run-lengths of the Hilbert scan tend to be longer than those of the raster scan and the DF expression scanning. We discuss the application to data compression using binary images and three dimensional data.