Robust and efficient detection of salient convex groups

Segmentation is a very critical stage in the character recognition process as the performance of any character recognition system depends heavily on the accuracy of segmentation. Although segmentation is a well-researched area, segmentation of handwritten text is still difficult owing to several factors like skewed and overlapping lines, the presence of touching, broken and degraded characters, and variations in writing styles. Therefore, researchers in this area are working continuously to develop new techniques for the efficient segmentation and recognition of characters. In the character recognition process, segmentation can be implemented at the line, word, and character level. Text line segmentation is the first step in the text/character recognition process. The line segmentation methods used in the character recognition of handwritten documents are presented in this paper. The various levels of segmentation which include line, word, and character segmentation are discussed with a focus on line segmentation.KeywordsSegmentationOCRPattern recognitionLine segmentationWord segmentationCharacter segmentationTouching lines segmentationOverlapping lines segmentation

The straight line segment is the basic graphic element, and its generation algorithm has a great influence on the generation speed of complex graphics. In the past, the efficiency of integer operation is higher than that of floating-point operation, and the complexity of DDA algorithm is mainly floating-point addition and rounding operation, and the complexity of Bresenham algorithm is mainly integer operation through further improvement. Therefore, it is clearly explained in the existing computer graphics textbooks that the efficiency of Bresenham algorithm is higher than that of DDA algorithm. Through experiments, endpoints of 1,000 to 10,000 straight line segments are randomly generated, and the runtime of Bresenham algorithm and DDA algorithm is compared. It is found that the efficiency of DDA algorithm is higher than that of Bresenham algorithm. Then, by combining the comparison of the efficiency of modern CPU for addition, multiplication and division of integer and floating point with the improvement of floating-point computing hardware and instruction set in modern CPU, the computer's floating-point computing capabilities have been greatly improved, thus making the DDA algorithm more efficient than the Bresenham algorithm.

Solving all-pairs shortest path by single-source computations: Theory and practice

A method for the efficient encoding and decoding of a shape with application to edge map image compression is proposed. The method relies on the modeling of the manifold of a shape by line segments. Then, encoding is performed by collecting the characteristic features of each line segment, namely the starting and ending points and the number of points contributing to the computation of the corresponding segment. The reconstruction of the shape may be obtained by uniform sampling of points from each line segment computed in the encoding process. Experimental analysis demonstrates that in case of employing a robust and efficient line segment detection algorithm, the proposed encoding/decoding scheme exhibits high compression rates, compared to widely used lossless compression methods, while providing low distortion values.

Given a collection of line segments in the plane we would like to connect the segments by their endpoints to construct a simple circuit. (A simple circuit is the boundary of a simple polygon). However, there are collections of line segments where this cannot be done. In this note it is proved that deciding whether a set of line segments admits a simple circuit is NP-complete. Deciding whether a set of horizontal line segments can be connected with horizontal and vertical line segments to construct an orthogonal simple circuit is also shown to be NP-complete.

We present an algorithm to find a set of all optimal solutions for a channel placement problem. A channel consists of two rows of horizontal line segments (representing components). Each line segment contains some terminals with fixed positions. Sets of terminals, called nets, are to be connected. The relative ordering of line segments in each row is fixed. The line segments can be shifted left or right, which will affect the width needed for routing and the length of the channel. We want to find the tradeoff between channel length and routing width. Since the channel routing problem is NP-complete, we use a lower bound on routing width, called density. The density of a placement is the maximum number of nets crossing each vertical cut. We can increase the total length to minimize the channel density, or minimize the total length by increasing the channel density. The pair (density, total length) is called the shape of a placement. A shape is minimal if a decrease in density would cause an increase in total length, and vice versa. Our algorithm computes all the minimal shapes in O (N 4 ) time, where N is the number of nets. This is the first known algorithm for this problem whose running time is polynomial in the number of nets and independent of the length of the channel.

The size of five trie-based methods of sorting large collections of line segments in a spatial database is investigated analytically using a random lines image model and geometric probability techniques. The methods are based on sorting the line segments with respect to the space that they occupy. Since the space is two-dimensional, the trie is formed by interleaving the bits corresponding to the binary representation of the x and y coordinates of the underlying space and then testing two bits at each iteration. The result of this formulation yields a class of representations that are referred to as quadtrie variants, although they have been traditionally referred to as quadtree variants. The analysis differs from prior work in that it uses a detailed explicit model of the image instead of relying on modeling the branching process represented by the tree and leaving the underlying image unspecified. The analysis provides analytic expressions and bounds on the expected size of these quadtree variants. This enables the prediction of storage required by the representations and of the associated performance of algorithms that rely on them. The results are useful in the following two ways: They reveal the properties of the various representations and permit their comparison using analytic, nonexperimental criteria. Some of the results confirm previous analyses (e.g., that the storage requirement of the MX quadtree is proportional to the total lengths of the line segments). An important new result is that for a PMR and Bucket PMR quadtree with sufficiently high values of the splitting threshold (i.e., $\geq 4$) the number of nodes is proportional to the number of line segments and is independent of the maximum depth of the tree. This provides a theoretical justification for the good behavior and use of the PMR quadtree, which so far has been only of an empirical nature.The random lines model was found to be general enough to approximate real data in the sense that the properties of the trie representations, when used to store real data (e.g., maps), are similar to their properties when storing random lines data. Therefore, by specifying an equivalent random lines model for a real map, the proposed analytical expressions can be applied to predict the storage required for real data. Specifying the equivalent random lines model requires only an estimate of the effective number of random lines in it. Several such estimates are derived for real images, and the accuracy of the implied predictions is demonstrated on a real collection of maps. The agreement between the predictions and real data suggests that they could serve as the basis of a cost model that can be used by a query optimizer to generate an appropriate query evaluation plan.

In this paper, we propose a new model for text line segmentation and classification, which consists of convolutional and two-layer bi-directional long short-term memory (BiLSTM) networks. Trained on the synthetic text dataset, it performs excellently when predicting the real data. Without labelling every line on the real data, a generalized standard for evaluating the accuracy is proposed. We also propose a simplified IoU loss to improve the execution speed greatly. In the experiments, it achieves 98.1% line segmentation accuracy and 99.5% classification accuracy on the English fiction Pride and Prejudice by Jane Austen, and achieves 98.5% line segmentation accuracy and 99.7% classification accuracy on the The Secret Of Plato's Atlantis by John Arundell, outperforming the traditional methods. Furthermore, for 1024 × 724 input samples, it gets 2.95 FPS speed when using a Tesla K80 GPU. Index Terms—Text line segmentation, Text classification, Synthetic text, BiLSTM, Convolutional network.

Planar graphs are known to allow subexponential algorithms running in time \(2^{O(\sqrt{n})}\) or \(2^{O(\sqrt{n} \log n)}\) for most of the paradigmatic problems, while the brute-force time \(2^{\varTheta (n)}\) is very likely to be asymptotically best on general graphs. Intrigued by an algorithm packing curves in \(2^{O(n^{2/3}\log n)}\) by Fox and Pach [SODA’11], we investigate which problems have subexponential algorithms on the intersection graphs of curves (string graphs) or segments (segment intersection graphs) and which problems have no such algorithms under the ETH (Exponential Time Hypothesis). Among our results, we show that, quite surprisingly, 3-Coloring can also be solved in time \(2^{O(n^{2/3}\log ^{O(1)}n)}\) on string graphs while an algorithm running in time \(2^{o(n)}\) for 4-Coloring even on axis-parallel segments (of unbounded length) would disprove the ETH. For 4-Coloring of unit segments, we show a weaker lower bound, excluding a \(2^{o(n^{2/3})}\) algorithm (under the ETH). The construction exploits the celebrated Erdős-Szekeres theorem. The subexponential running time also carries over to Min Feedback Vertex Set, but not to Min Dominating Set and Min Independent Dominating Set.

Performance improvement of character recognition in industrial applications using prior knowledge for more reliable segmentation

In this study, a simple and efficient airport detection method is presented. The method is performed uses both the geometric and texture features. The method that use RASAT satellite images is carried out in two stages as coarse and fine stage. In the first stage, line segments are detected with line segment detector (LSD) and the short length of lines are filtered. Remaining line segments are grouped using breadth first search (BFS) to extract airport candidate locations. In the second stage, texture features are calculated using texture around line segments and parallel density feature that is extracted from line segment groups are merged. Finally merged features are classified with support vector machine (SVM) to make detection airport.

An upper dominating set is a minimal dominating set in a graph. In the Upper Dominating Set problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for Upper Dominating Set, as well as its sub-exponential approximation. First, we prove that, under ETH, k -Upper Dominating Set cannot be solved in time \(O(n^{o(k)})\) (improving on \(O(n^{o(\sqrt{k})})\)), and in the same time we show under the same complexity assumption that for any constant ratio r and any \(\varepsilon > 0\), there is no r-approximation algorithm running in time \(O(n^{k^{1-\varepsilon }})\). Then, we settle the problem’s complexity parameterized by pathwidth by giving an algorithm running in time \(O^*(6^{pw})\) (improving the current best \(O^*(7^{pw})\)), and a lower bound showing that our algorithm is the best we can get under the SETH. Furthermore, we obtain a simple sub-exponential approximation algorithm for this problem: an algorithm that produces an r-approximation in time \(n^{O(n/r)}\), for any desired approximation ratio \(r 1\) and \(\varepsilon > 0\), no algorithm can output an r-approximation in time \(n^{(n/r)^{1-\varepsilon }}\). Hence, we completely characterize the approximability of the problem in sub-exponential time.

The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponential-sized space of TSP tours, each of which is a 2-approximation to the exact solution. We consider the problem of minimum-weight double-tree shortcutting, for which Burkard et al. gave an algorithm running in time O(2dn3) and memory O(2dn2), where d is the maximum node degree in the rooted minimum spanning tree (e.g. in the non-degenerate planar Euclidean case, d ≤ 4). We give an improved algorithm running in time O(4dn2) and memory O(4dn), which allows one to solve the problem on much larger instances. Our computational experiments suggest that the minimum-weight double-tree shortcutting method provides one of the best known tour-constructing heuristics.

Bridging gap between standard and differential polynomial approximation: The case of bin-packing

Consider a graph G. A subset of vertices, F, is called a vertex cover \(P_t\) (\(VCP_t\)) set if every path of order t contains at least one vertex in F. Finding a minimum \(VCP_t\) set in a graph is is NP-hard for any integer \(t\ge 2\) and is called the \(MVCP_3\) problem. In this paper, we study the parameterized algorithms for the \(MVCP_3\) problem when the underlying graph G is parameterized by the treewidth. Given an n-vertex graph together with its tree decomposition of width at most p, we present an algorithm running in time \(4^{p}\cdot n^{O(1)}\) for the \(MVCP_3\) problem. Moreover, we show that for the \(MVCP_3\) problem on planar graphs, there is a subexponential parameterized algorithm running in time \(2^{O(\sqrt{k})}\cdot n^{O(1)}\) where k is the size of the optimal solution.