Quadtree Blocks Research Articles

Depth Estimation Using a Self-Supervised Network Based on Cross-Layer Feature Fusion and the Quadtree Constraint

Depth estimation from a camera is an important task for 3D perception. Recently, without using the labeled ground truth of depth map, a self-supervised deep learning network can use relative pose to synthesize the target image from the reference image, and the photometric error between synthesized reference image and real one is used as self-supervisory signal. In this paper, we propose a novel self-supervised depth estimation network, which takes advantage of the quadtree constraint to optimize the depth estimation network. Based on the quadtree constraint, the photometric loss and depth loss of quadtree are proposed. In order to solve the problem that multiple depth values in repeated structures and uniform texture regions can cause relatively low photometric loss, we use quadtree-based photometric loss, which calculates the averaged photometric loss in quadtree blocks instead of the pixel-wise loss. For the problem of imbalanced depth distribution, we use quadtree depth loss, which constrains the depth inconsistency within quadtree blocks. The depth estimation network is composed of deep fusion module and cross-layer feature fusion module, which can better extract the feature information of RGB image and sparse keypoints depths, and makes full use of the detail information of the shallow feature map and the semantic information of the deep feature map to enrich the feature information extraction. Experimental results demonstrate that our method outperforms the state-of-the-art approaches of depth estimation.

Fuzzy split and merge for shadow detection

Presence of shadow in an image often causes problems in computer vision applications such as object recognition and image segmentation. This paper proposes a method to detect the shadow from a single image using fuzzy split and merge approach. Split and merge is a classical algorithm used in image segmentation. Predicate function in the classical approach is replaced by a Fuzzy predicate in the proposed approach. The method follows a top down approach of recursively splitting an image into homogeneous quadtree blocks, followed by a bottom up approach by merging adjacent unique regions. The method has been compared with previous approaches and found to be better in performance in terms of accuracy.

Multi-Scale Seamless Visualization of the Global Terrain Based on DQG

Real-time and seamless visualization of the Earth terrain based on Global Discrete Grids is a subject of considerable current attention. In this paper a multi-scales visualization model of the global terrain based on DQG (Degenerate Quadtree Grid) is approached. Our approach starts with a partition method, called Degenerate Quadtree Grid (DQG) and an encoding scheme of the corresponding grids is introduced briefly. Next, a multiple level of detail model related to viewpoint is presented. In this model, a criterion of terrain model simplification based on viewpoint and roughness of the degenerate quadtree node is developed. Then, making full use of the characteristics of quadtree structure, the cracks within quadtree blocks are induced by simplification. Thus, the cracks splicing are all seamless. In the end, the experiment and analysis are made with the global terrain data, GTOPO30. The results illustrate that: (1) the global terrain based on the DQG is seamless, hierarchical, and regular over the whole Earth; (2) the quantity of global DEM data can be reduced significantly; (3) the visual effect of the global multi-scale terrain is seamless by the model simplification ensuring the accuracy and efficiency of the terrain display.

An Optimal Algorithm for Searching the Optimal Translation of Query Windows in Quadtree Decomposition

One of the efficient methods to build the index of continuous window queries over moving objects is by means of region quadtree index. In this paper, we present an optimal algorithm to search for the optimal position translation of query windows, where the total number of decomposed quadtree blocks for those windows in quadtree representation is minimal. We exploit the branch-and-bound concept to prune the particular paths of recursions in the search space. Evaluation proves that our optimal algorithm reduces search time greatly and the quadtree index based on optimal position translation works efficiently for continuous window queries. To the best of our knowledge, the algorithms and experiments reported in this paper are novel.

Efficient algorithms for coding Hilbert curve of arbitrary-sized image and application to window query

Previously, several efficient Hilbert scan-based operations were presented, but they all suffer from the constraint that the image size must be 2 r × 2 r . Considering an image with arbitrary size I 1 × I 2, this paper first presents an efficient snake scan-based algorithm for coding the Hilbert curve of the given image. The proposed coding algorithm takes O ( k + log U ) time to code the Hilbert order of one pixel where k denotes the number of the quadrants and U = min ( I 1 , I 2 ) . Next, a memory-saving Hilbert curve representation called HCGL is presented for representing the encoded Hilbert curve and it can be constructed in O ( L 2 log L ) time where L = max ( I 1 , I 2 ) . Based on the HCGL representation of arbitrary-sized image, an application to window query is presented and the proposed window query algorithm takes O ( M log L + P ) time where M denotes the number of generated maximal quadtree blocks and P denotes the number of output codes. Under the same PSNR (Peak Signal to Noise Ratio), experimental results demonstrate that our proposed HCGL representation outperforms some existing related algorithms in terms of execution-time and BPP (Bit Per Pixel). In addition, our proposed window query algorithm has been justified in the GIS (Geographical Information System) application.

An exact closed-form formula for d-dimensional quadtree decomposition of arbitrary hyperrectangles

In this paper, we solve the classic problem of computing the average number of decomposed quadtree blocks (quadrants, nodes, or pieces) in quadtree decomposition for an arbitrary hyperrectangle aligned with the axes. We derive a closed-form formula for general cases. The previously known state-of-the-art solution provided a closed-form solution for special cases and utilized these formulas to derive linearly interpolated formulas for general cases individually. However, there is no exact and uniform closed-form formula that fits all cases. Contrary to the top-down counting approach used by most prior solutions, we employ a bottom-up enumeration approach to transform the problem into one that involves the Cartesian product of d multisets of successive 2's powers. Classic combinatorial enumeration techniques are applied to obtain an exact and uniform closed-form formula. The result is of theoretical interest since it is the first exact closed-form formula for arbitrary cases. Practically, it is nice to have a uniform formula for estimating the average number since a simple program can be conveniently constructed taking side lengths as inputs.

Texture discrimination of volcanic ashes from different fragmentation mechanisms: A case study, Mount Nemrut stratovolcano, eastern Turkey

Multicondition-driven mechanisms may produce pyroclastic deposits varying in fundamental properties such as dispersal, grain size, vesicularity and morphology of juvenile clasts, and the abundance of lithic or “wall rock” ejecta (xenoliths). Volcanic ash particles from different fragmentation mechanisms have different surface textures and morphologies. The analysis of the volcanic clast shape remained largely qualitative. A new method for ash particle characterization based on quadtree decomposition and surface gradient analysis is introduced. The approach is applied for assessing fragmentation mechanisms operating during eruptions. The surface descriptor variables like the number of quadtree blocks (nQT), the mean block size (mQT), the standard deviation of block sizes (sQT) and the surface descriptors derived from gradient analysis seem to be suitable for quantifying the structural changes of the ash surface due to variable explosion conditions. These parameters are presented in volcanology as distinctive key parameters for different eruption types. This may enrich our capabilities for effective prediction for the basis of planning to overcome the impending danger of eruptions.

Examination of a constant-area quadrilateral grid in representation of global digital elevation models

The WGS84 ellipsoid is tessellated using quadrilaterals of roughly the same size. This tiling is of general interest to global geographical information systems, but it has special relevance to global digital elevation models based on block averages. The simple relation between the tiling presented and the latitude/longitude reference system makes the tiling easy to implement, and the quadrilateral property of the cells offers regular subdivision like quadtrees. An error analysis gives a strict bound on the difference between cell averages calculated in plane and ellipsoidal coordinates. The mathematical results from this investigation are general and can be applied in error analysis related to other types of quadrilateral meshes. The grid can be easily subdivided into quadtree blocks. The error estimate makes it possible to combine the quadtree structure with standard two-dimensional wavelet representations.

A strip-splitting-based optimal algorithm for decomposing a query window into maximal quadtree blocks

Decomposing a query window into maximal quadtree blocks is a fundamental problem in quadtree-based spatial database. Recently, Proietti presented the first optimal algorithm for solving this problem. Given a query window of size n/sub 1//spl times/n/sub 2/, Proietti's algorithm takes O(n/sub 1/) time, where n/sub 1/=max(n/sub 1/, n/sub 2/). Based on a strip-splitting approach, we present a new optimal algorithm for solving the same problem. Experimental results reveal that our proposed algorithm is quite competitive with Proietti's algorithm.

Window Query Processing in Linear Quadtrees

The linear quadtree is a spatial access method that is built by decomposing the spatial objects in a database into quadtree blocks and storing these quadtree blocks in a B-tree. The linear quadtree is very useful for geographic information systems because it provides good query performance while using existing B-tree implementations. An algorithm and a cost model are presented for processing window queries in linear quadtrees. The algorithm can handle query windows of any shape in the general case of spatial databases with overlapping objects. The algorithm recursively decomposes the space into quadtree blocks, and uses the quadtree blocks overlapping the query window to search the B-tree. The cost model estimates the I/O cost of processing window queries using the algorithm. The cost model is also based on a recursive decomposition of the space, and it uses very simple parameters that can easily be maintained in the database catalog. Experiments with real and synthetic data sets verify the accuracy of the cost model.

An optimal algorithm for decomposing a window into maximal quadtree blocks

Decomposing a two-dimensional window (i.e., the region specified by the cross product of two closed intervals over a given two-dimensional space) into its maximal quadtree blocks means to find the set of black quadrants that would be obtained by representing the region covered by the window using a quadtree. In this paper we propose an optimal O(n) time algorithm for decomposing a square window of size \(n \times n\) embedded in an image space of \(T \times T\) pixel elements, thus improving the O(n log log T) time algorithm of Aref and Samet [2]. As a direct consequence of this new faster algorithm, classical window operations on main memory quadtree based data structures can be solved more efficiently. In particular, we show that the exist and report queries on the incomplete pyramid [1] and on the up-down pyramid [8] can be solved in O(n) time, which is optimal.

Efficient Window Block Retrieval in Quadtree-Based Spatial Databases

An algorithm is presented to answer window queries in a quadtree-based spatial database environment by retrieving all of the quadtree blocks in the underlying spatial database that cover the quadtree blocks that comprise the window. It works by decomposing the window operation into sub-operations over smaller window partitions. These partitions are the quadtree blocks corresponding to the window. Although a block b in the underlying spatial database may cover several of the smaller window partitions, b is only retrieved once rather than multiple times. This is achieved by using an auxiliary main memory data structure called the active border which requires O\left(n\right) additional storage for a window query of size n\times n . As a result, the algorithm generates an optimal number of disk I/O requests to answer a window query (i.e., one request per covering quadtree block). A proof of correctness and an analysis of the algorithm’s execution time and space requirements are given, as are some experimental results.

Using topological sweep to extract the boundaries of regions in maps represented by region quadtrees

A variant of the plane-sweep paradigm known as topological sweep is adapted to solve geometric problems involving two-dimensional regions when the underlying representation is a region quadtree. The utility of this technique is illustrated by showing how it can be used to extract the boundaries of a map inO(M) space andO(Mα(M)) time, whereM is the number of quadtree blocks in the map, andα(·) is the (extremely slowly growing) inverse of Ackerman's function. The algorithm works for maps that contain multiple regions as well as holes. The algorithm makes use of active objects (in the form of regions) and an active border. It keeps track of the current position in the active border so that at each step no search is necessary. The algorithm represents a considerable improvement over a previous approach whose worst-case execution time is proportional to the product of the number of blocks in the map and the resolution of the quadtree (i.e., the maximum level of decomposition). The algorithm works for many different quadtree representations including those where the quadtree is stored in external storage.

Using Topological Sweep to Extract the Boundaries of Regions in Maps Represented by Region Quadtrees

A variant of the plane-sweep paradigm known as topological sweep is adapted to solve geometric problems involving two-dimensional regions when the underlying representation is a region quadtree. The utility of this technique is illustrated by showing how it can be used to extract the boundaries of a map inO(M) space andO(Mα(M)) time, whereM is the number of quadtree blocks in the map, andα(·) is the (extremely slowly growing) inverse of Ackerman's function. The algorithm works for maps that contain multiple regions as well as holes. The algorithm makes use of active objects (in the form of regions) and an active border. It keeps track of the current position in the active border so that at each step no search is necessary. The algorithm represents a considerable improvement over a previous approach whose worst-case execution time is proportional to the product of the number of blocks in the map and the resolution of the quadtree (i.e., the maximum level of decomposition). The algorithm works for many different quadtree representations including those where the quadtree is stored in external storage.

Decomposing a window into maximal quadtree blocks

Window operations serve as the basis of a number of queries that can be posed in a spatial database. Examples of window-based queries include the exist query (i.e., determining whether or not a spatial feature exists inside a window), the report query (i.e., report the identity of all the features that exist inside a window), and the select query (i.e., determine the locations covered by a given feature inside a window). Often spatial databases make use of a quadtree decomposition, which yields a set of maximal blocks, to enable the features to be accessed quickly without having to search the entire database. One way to perform a window query is to decompose the window into its maximal quadtree blocks. An algorithm is described for decomposing a two-dimensional window into its maximal quadtree blocks inO(nlog logT) time for a window of sizen×n in a feature space (e.g., an image) of sizeT×T (e.g., pixel elements).