تمثيل الإطار الخارجي للكلمات العربية بكفاءة من خلال الدمج بين نموذج الكنتور النشط وتحديد ونقاط الزوايا

Graphical curves and surfaces fitting are hot areas of research studies and application, such as artistic applications, analysis applications and encoding purposes. Outline capture of digital word images is important in most of the desktop publishing systems. The shapes of the characters are stored in the computer memory in terms of their outlines, and the outlines are expressed as Bezier curves. Existing methods for Arabic font outline description suffer from low fitting accuracy and efficiency. In our research, we developed a new method for outlining shapes using Bezier curves with minimal set of curve points. A distinguishing characteristic of our method is that it combines the active contour method (snake) with corner detection to achieve an initial set of points that is as close to the shape's boundaries as possible. The method links these points (snake + corner) into a compound Bezier curve, and iteratively improves the fitting of the curve over the actual boundaries of the shape. We implemented and tested our method using MATLAB. Test cases included various levels of shape complexity varying from simple, moderate, and high complexity depending on factors, such as: boundary concavities, number of corners. Results show that our method achieved average 86% of accuracy when measured relative to true shape boundary. When compared to other similar methods (Masood & Sarfraz, 2009; Sarfraz & Khan, 2002; Ferdous A Sohel, Karmakar, Dooley, & Bennamoun, 2010), our method performed comparatively well. Keywords: Bezier curves, shape descriptor, curvature, corner points, control points, Active Contour Model.تعتبر المنحنيات والأسطح الرسومية موضوعاً هاماً في الدراسات البحثية وفي التطبيقات البرمجية مثل التطبيقات الفنية، وتطبيقات تحليل وترميز البيانات. ويعتبر تخطيط الحدود الخارجية للكلمات عملية أساسية في غالبية تطبيقات النشر المكتبي. في هذه التطبيقات تخزن أشكال الأحرف في الذاكرة من حيث خطوطها الخارجية، وتمثل الخطوط الخارجية على هيئة منحنيات Bezier. الطرق المستخدمة حالياً لتحديد الخطوط الخارجية للكلمات العربية تنقصها دقة وكفاءة الملاءمة ما بين الحدود الحقيقية والمنحنى الرسومي الذي تقوم بتشكيله. في هذا البحث قمنا بتطوير طريقة جديدة لتخطيط الحدود الخارجية للكلمات تعتمد على منحنيات Bezier بمجموعة أقل من المنحنيات الجزئية. تتميز طريقتنا بخاصية مميزة وهي الدمج بين آلية لاستشعار الزوايا مع آلية نموذج الكنتور النشط (الأفعى). يتم الدمج بين نقاط الزوايا ونقاط الأفعى لتشكيل مجموعة موحدة من النقاط المبدئية قريبة قدر الإمكان من الحدود الحقيقية للشكل المراد تحديده. يتشكل منحنى Bezier من هذه المجموعة المدمجة، وتتم عملية تدريجية على دورات لملاءمة المنحنى على الحدود الحقيقية للشكل. قام الباحث بتنفيذ وتجربة الطريقة الجديدة باستخدام برنامج MATLAB. وتم اختيار أشكال رسومية كعينات اختبار تتصف بمستويات متباينة من التعقيد تتراوح ما بين بسيط إلى متوسط إلى عالي التعقيد على أساس عوامل مثل تقعرات الحدود، عدد نقاط الزوايا، الفتحات الداخلية، إلخ. وقد أظهرت نتائج الاختبار أن طريقتنا الجديدة حققت دقة في الملائمة تصل نسبتها إلى 86% مقارنة بالحدود الحقيقية للشكل المستهدف. وكذلك فقد كان أداء طريقتنا جيداً بالمقارنة مع طرق أخرى مماثلة

Area-Construction Algorithms Using Tangent Circles

Computer aided geometric design employs mathematical and computational methods for describing geometric objects, such as curves, areas in two dimensions (2D) and surfaces, and solids in 3D. An area can be represented using its boundary curves, and a solid can be represented using its boundary surfaces with intersection curves among these boundary surfaces. In addition, other methods, such as the medial-axis transform, can also be used to represent an area. Although most researchers have presented algorithms that find the medial-axis transform from an area, a algorithm using the contrasting approach is proposed; i.e., it finds an area using a medial-axis transform. The medial-axis transform is constructed using discrete points on a curve and referred to as the skeleton of the area. Subsequently, using the aforementioned discrete points, medial-axis circles are generated and referred to as the muscles of the area. Finally, these medial-axis circles are blended and referred to as the blended boundary curves skin of the area; consequently, the boundary of the area generated is smooth

Stroke trajectory generation for a robotic Chinese calligrapher.

Lam, Hiu Man.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 84-89).Abstracts in English and Chinese.Chapter Chapter 1: --- Introduction --- p.1Chapter 1.1. --- Overview on Robotics --- p.1Chapter 1.2. --- Literture Review on Art-Robot --- p.1Chapter 1.3. --- Robot artist for Chinese Calligraphy and Paintings --- p.3Chapter 1.4. --- Motivation and Research Objective --- p.4Chapter 1.5. --- Thesis Outline --- p.5Chapter Chapter 2: --- Intelligent Robotic Art System --- p.6Chapter 2.1. --- Previous Configuration --- p.6Chapter 2.1.1. --- 3 DOF Manipulator --- p.7Chapter 2.1.2. --- Digital Image Input System --- p.7Chapter 2.2. --- Hardware Modification --- p.8Chapter 2.2.1. --- Additional Degree of Freedoms --- p.8Chapter 2.2.2. --- Infra-red Sensing System for Manipulator Positioning --- p.9Chapter 2.2.3. --- Axial-rotary Brush --- p.11Chapter 2.2.4. --- Interface program --- p.13Chapter 2.2.5. --- Vibration Reduction --- p.16Chapter Chapter 3: --- Skeletonization Based on Delaunay Triangulation and Bezier Interpolation --- p.18Chapter 3.1. --- Background Theory --- p.20Chapter 3.1.1. --- Smoothed Local Symmetry --- p.20Chapter 3.1.2. --- Delaunay Triangulation --- p.21Chapter 3.1.3. --- Bezier Curve --- p.23Chapter 3.2. --- Algorithm --- p.24Chapter 3.2.1. --- Edge Sampling --- p.24Chapter 3.2.2. --- Triangle Modification --- p.26Chapter 3.2.3. --- Triangle Filtering and Replacement --- p.28Chapter 3.2.4. --- Internal Edge Refinement --- p.30Chapter 3.2.5. --- Skeletal Interpolation --- p.31Chapter 3.3. --- Experiments --- p.32Chapter 3.4. --- Chapter Summary --- p.36Chapter Chapter 4: --- Stroke Segmentation for Chinese Words --- p.37Chapter 4.1. --- Rule-based Spurious Branches Removal --- p.38Chapter 4.1.1. --- Spurious Branch in Stroke Terminal --- p.40Chapter 4.1.2. --- Spurious Branch Caused by Turning Stroke --- p.42Chapter 4.2. --- Stroke Connectivity Determination --- p.44Chapter 4.2.1. --- Gradient of Medial Axis --- p.45Chapter 4.2.2. --- Gradient of Branch Boundary --- p.47Chapter 4.2.3. --- Branch Width --- p.49Chapter 4.2.4. --- Combined Objective Function --- p.50Chapter 4.3. --- Stroke Generation --- p.51Chapter 4.3.1. --- Stroke Connection between Branches --- p.52Chapter 4.3.2. --- Stroke Generation in Stroke Terminal --- p.53Chapter 4.4. --- Experiment Using Intelligent Robotic Art System --- p.54Chapter 4.5. --- Discussion --- p.59Chapter Chapter 5: --- Experimental Acquisition of Brush Footprints --- p.61Chapter 5.1. --- Brush Footprint Extraction --- p.62Chapter 5.2. --- Graphical Interface for Inputting Sample Points of Brush Footprints --- p.64Chapter 5.3. --- Curve Fitting for Brush Footprint Sample Points --- p.70Chapter 5.3.1. --- Curve Fitting Using Genetic Algorithm --- p.70Chapter 5.3.2. --- Curve Fitting by Least Squares Regression --- p.72Chapter 5.4. --- Discussion --- p.74Chapter Chapter 6: --- Trajectory Generation for Robotic Chinese Calligraphy --- p.75Chapter 6.1. --- Stroke Trajectory Searching with According Stroke Width --- p.75Chapter 6.2. --- Improvement in Stroke Trajectory --- p.77Chapter 6.3. --- Experiment --- p.80Conclusion and Future Work --- p.82References --- p.84Appendix --- p.90Chapter 9.1. --- Segmented Strokes of Bada Shanren's Calligraphy --- p.9

A Bezier curve-based generic shape encoder

Existing Bezier curve based shape description techniques primarily focus upon determining a set of pertinent Control Points (CP) to represent a particular shape contour. While many different approaches have been proposed, none adequately consider domain specific information about the shape contour like its gradualness and sharpness, in the CP generation process which can potentially result in large distortions in the object’s shape representation. This paper introduces a novel Bezier Curve-based Generic Shape Encoder (BCGSE) that partitions an object contour into contiguous segments based upon its cornerity, before generating the CP for each segment using relevant shape curvature information. In addition, while CP encoding has generally been ignored, BCGSE embeds an efficient vertex-based encoding strategy exploiting the latent equidistance between consecutive CP. A nonlinear optimisation technique is also presented to enable the encoder is automatically adapt to bit-rate constraints. The performance of the BCGSE framework has been rigorously tested on a variety of diverse arbitrary shapes from both a distortion and requisite bit-rate perspective, with qualitative and quantitative results corroborating its superiority over existing shape descriptors

A generic shape descriptor using Bezier curves

Bezier curves are robust tool for a wide array of applications ranging from computer-aided design to calligraphic character, outlining and object shape description. In terms of the control point generation process, existing shape descriptor techniques that employ Bezier curves do not distinguish between regions where an object's shape changes rapidly and those where the change is more gradual or flat. This can lead to an erroneous shape description, particularly where there are significantly sharp changes in shape, such as at sharp corners. This paper presents a novel shape description algorithm called a generic shape descriptor using Bezier curves (SDBC), which defines a new strategy for Bezier control point generation by integrating domain specific information about the shape of an object in a particular region. The strategy also includes an improved dynamic fixed length coding scheme for control points. The SDBC framework has been rigorously tested upon a number of arbitrary shapes, and both quantitative and qualitative analyses have confirmed its superior performance in comparison with existing algorithms

A Novel Half-Way Shifting Bezier Curve Model

Bezier curves can cause a considerable gap to occur between the approximation curve and its control polygon, due to considering only the global information of the control points. In order to reduce this error in curve representations, localised information needs to be incorporated, with the main philosophy to narrow down the gap by shifting the Bezier curve points closer to the control polygon. To integrate this idea into the theoretical framework of the classical Bezier curve model, this paper presents a novel Half-way shifting Bezier Curve (HBC) model, which automatically incorporates localised information along with the global Bezier information. Both subjective and objective performance evaluations of the HBC model using upon a number of objects having arbitrary shape confirm its considerable improvement over the classical Bezier curve model without increasing the order of computational complexity

Enhanced Bezier curve models incorporating local information

The Bezier curve is fundamental to many challenging and practical applications, ranging from computer aided geometric design and postscript font representations through to generic object shape descriptors and surface representation. A drawback of the Bezier curve however, is that it only considers global information about the control points, so there is often a large gap between the curve and its control polygon, leading to considerable error in curve representations. To address this issue, this paper presents enhanced Bezier curve (EBC) models which seamlessly incorporate local information. The performance of the models is empirically evaluated upon a number of natural and synthetic objects having arbitrary shape and both qualitative and quantitative results confirm the superiority of both EBC models in comparison with the classical Bezier curve representation, with no increase in the order of computational complexity

The Tangent Medial Circles Inside the Region Defined by Hermite Curve Tangent to Unit Circle

The design of curves, surfaces, and solids are important in computer aided geometric design (CAGD). Images, surround by boundary curves, are also investigated by many researchers. One way to describe an image is using the medial axis transform. Under this consideration, the properties of the boundary curves tangent to circles become important to design for 2D images. In this paper, we want to find the medial axis transform (MAT) for a special class of region, which is bounded by unit circle and the curves whose end points is on a the circle, and endpoints tangent vectors are parallel to the tangent of circle at the end points. During the process, we want find the medial circle tangent to other medial circle, until we reach the medial circle whose center is the center of the osculating circle for the point with local maximum curvature. There are 4 cases, symmetric/non-symmetric region with singular point/local maximum curvature point, and proposed algorithm for these 4 cases. We introduced algorithm for this 4 cases in this paper

Visual-based decision for iterative quality enhancement in robot drawing.

Kwok, Ka Wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 113-116).Abstracts in English and Chinese.ABSTRACT --- p.iChapter 1. --- INTRODUCTION --- p.1Chapter 1.1 --- Artistic robot in western art --- p.1Chapter 1.2 --- Chinese calligraphy robot --- p.2Chapter 1.3 --- Our robot drawing system --- p.3Chapter 1.4 --- Thesis outline --- p.3Chapter 2. --- ROBOT DRAWING SYSTEM --- p.5Chapter 2.1 --- Robot drawing manipulation --- p.5Chapter 2.2 --- Input modes --- p.6Chapter 2.3 --- Visual-feedback system --- p.8Chapter 2.4 --- Footprint study setup --- p.8Chapter 2.5 --- Chapter summary --- p.10Chapter 3. --- LINE STROKE EXTRACTION AND ORDER ASSIGNMENT --- p.11Chapter 3.1 --- Skeleton-based line trajectory generation --- p.12Chapter 3.2 --- Line stroke vectorization --- p.15Chapter 3.3 --- Skeleton tangential slope evaluation using MIC --- p.16Chapter 3.4 --- Skeleton-based vectorization using Bezier curve interpolation --- p.21Chapter 3.5 --- Line stroke extraction --- p.25Chapter 3.6 --- Line stroke order assignment --- p.30Chapter 3.7 --- Chapter summary --- p.33Chapter 4. --- PROJECTIVE RECTIFICATION AND VISION-BASED CORRECTION --- p.34Chapter 4.1 --- Projective rectification --- p.34Chapter 4.2 --- Homography transformation by selected correspondences --- p.35Chapter 4.3 --- Homography transformation using GA --- p.39Chapter 4.4 --- Visual-based iterative correction example --- p.45Chapter 4.5 --- Chapter summary --- p.49Chapter 5. --- ITERATIVE ENHANCEMENT ON OFFSET EFFECT AND BRUSH THICKNESS --- p.52Chapter 5.1 --- Offset painting effect by Chinese brush pen --- p.52Chapter 5.2 --- Iterative robot drawing process --- p.53Chapter 5.3 --- Iterative line drawing experimental results --- p.56Chapter 5.4 --- Chapter summary --- p.67Chapter 6. --- GA-BASED BRUSH STROKE GENERATION --- p.68Chapter 6.1 --- Brush trajectory representation --- p.69Chapter 6.2 --- Brush stroke modeling --- p.70Chapter 6.3 --- Stroke simulation using GA --- p.72Chapter 6.4 --- Evolutionary computing results --- p.77Chapter 6.5 --- Chapter summary --- p.95Chapter 7. --- BRUSH STROKE FOOTPRINT CHARACTERIZATION --- p.96Chapter 7.1 --- Footprint video capturing --- p.97Chapter 7.2 --- Footprint image property --- p.98Chapter 7.3 --- Experimental results --- p.102Chapter 7.4 --- Chapter summary --- p.109Chapter 8. --- CONCLUSIONS AND FUTURE WORKS --- p.111BIBLIOGRAPHY --- p.11