Representation image
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This document discusses various techniques for representing and describing images for image processing and segmentation. It covers chain codes, polygonal approximations using minimum perimeter polygons and merging/splitting techniques, signatures which provide a 1D functional representation of boundaries, boundary segments to extract information from concave parts of objects, and skeletons which reduce regions to graphs by obtaining medial axis transformations. It also provides examples of thinning algorithms used to obtain skeletons by iteratively deleting contour points while ensuring the overall shape is preserved.
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MS University, Tirunelveli Dist, Tamilnadu.
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The document discusses various techniques for representing and describing image regions after segmentation. It describes choosing external or internal representation based on focusing on shape or region properties. Common representation techniques include chain codes, polygonal approximations, signatures, boundary segments, and skeletons. Descriptors are then used to represent regions in a compact, invariant form for further processing and analysis.
Clipping & Rasterization
The document discusses techniques for clipping and rasterization in computer graphics. It covers line segment clipping algorithms like Cohen-Sutherland and Liang-Barsky. It also discusses polygon clipping, including brute force, triangulation, and a black box pipeline approach. Finally, it covers rasterization techniques for points, lines, and polygons, including inside-outside testing methods, fill algorithms like flood fill and scanline fill.
Two Dimensional Shape and Texture Quantification - Medical Image Processing
1. The document discusses various methods for quantifying two-dimensional shapes and textures in medical images, including statistical moments, spatial moments, radial distance measures, chain codes, Fourier descriptors, thinning, and texture measures.
2. Compactness, calculated using perimeter and area, quantifies how close a shape is to a circle. Spatial moments provide quantitative measurements of point distributions and shapes. Radial distance measures analyze boundary curvature. Chain codes represent boundary points.
3. Fourier descriptors and thinning/skeletonization reduce shapes to descriptors and graphs for analysis. Texture is quantified using statistical moments, co-occurrence matrices, spectral measures, and fractal dimensions.
Lec08 fitting
This document discusses techniques for fitting parametric models to sets of image features. It begins by introducing the concept of fitting, where a simple parametric model (like a line or circle) is used to represent multiple detected features. It describes how fitting involves choosing the best model, assigning features to model instances, and determining the number of instances. The document then discusses specific issues that arise, such as noise, outliers, missing data, and model selection. It presents techniques for line fitting, including least squares, total least squares, and robust methods like RANSAC. It also discusses fitting general curves and conics using least squares approaches.
"Mesh of Periodic Minimal Surfaces in CGAL."
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The document provides information about computer graphics concepts including:
1. Summarizing questions and answers about 3D triangles, rotation matrices, vector operations, splines, and computer graphics techniques like environment mapping and anti-aliasing.
2. Explaining modifications made to the active edge list algorithm to enable scan conversion of different triangle types like smoothly shaded, textured, and environment mapped triangles.
3. Deriving the 4x4 projection matrix that maps a 3D object point to its shadow point on a plane, to create planar shadows.
Computer Graphics Unit 1
The document describes various computer graphics output primitives and algorithms for drawing them, including lines, circles, and filled areas. It discusses line drawing algorithms like DDA, Bresenham's, and midpoint circle algorithms. These algorithms use incremental integer calculations to efficiently rasterize primitives by determining the next pixel coordinates without performing floating point calculations at each step. The midpoint circle algorithm in particular uses a "circle function" and incremental updates to its value to determine whether the next pixel is inside or outside the circle boundary.
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This document discusses distance measures and scales of measurement that are important for k-nearest neighbor classification. It covers two major classes of distance measures - Euclidean and non-Euclidean. It also describes three major scales of measurement for data - nominal, ordinal, and interval scales. It provides examples of different distance functions like Euclidean, Manhattan, cosine, and edit distances. It discusses how the choice of distance measure depends on the type of data and its scale of measurement.
ImageSegmentation.ppt
Image segmentation involves partitioning an image into regions, linear structures, or shapes. There are several main methods of region segmentation including region growing, clustering, and split and merge. Region growing starts with seed pixels and grows regions by adding similar neighboring pixels. Clustering groups pixels into clusters to minimize differences within clusters. Common clustering algorithms include K-means, ISODATA, and histogram-based clustering. Edge detection finds boundaries between regions by looking for changes in intensity values. Popular edge detectors include Sobel, Canny, and zero-crossing operators. Line and curve segments can be found from edge images using tracking or the Hough transform, which accumulates votes for parameter values of lines and curves in an image.
ImageSegmentation.ppt
Image segmentation involves partitioning an image into regions, linear structures (line segments, curve segments), or 2D shapes (circles, ellipses). Common region segmentation methods include region growing, clustering, and split-merge. Region growing starts with seed pixels and grows regions based on similarity. Clustering groups pixels into clusters to minimize dissimilarity within clusters. The Hough transform detects lines or curves by accumulating votes in a parameter space based on edge pixels.
ImageSegmentation (1).ppt
Image segmentation is a computer vision task that involves dividing an image into multiple segments or regions, where each segment corresponds to a distinct object, region, or feature within the image. The goal of image segmentation is to simplify and analyze an image by partitioning it into meaningful and semantically relevant parts. This is a crucial step in various applications, including object recognition, medical imaging, autonomous driving, and more.
Key points about image segmentation:
Semantic Segmentation: This type of segmentation assigns each pixel in an image to a specific class, essentially labeling each pixel with the object or region it belongs to. It's commonly used for object detection and scene understanding.
Instance Segmentation: Here, individual instances of objects are separated and labeled separately. This is especially useful when multiple objects of the same class are present in the image.
Boundary Detection: Some segmentation methods focus on identifying the boundaries that separate different objects or regions in an image.
Methods: Image segmentation can be achieved through various techniques, including traditional methods like thresholding, clustering, and region growing, as well as more advanced techniques involving deep learning, such as using convolutional neural networks (CNNs) and fully convolutional networks (FCNs).
Challenges: Image segmentation can be challenging due to variations in lighting, color, texture, and object shape. Overlapping objects and unclear boundaries further complicate the task.
Applications: Image segmentation is used in diverse fields. For example, in medical imaging, it helps identify organs or abnormalities. In autonomous vehicles, it aids in identifying pedestrians, other vehicles, and obstacles.
Evaluation: Measuring the accuracy of segmentation methods can be complex. Metrics like Intersection over Union (IoU) and Dice coefficient are often used to compare segmented results to ground truth.
Data Annotation: Creating ground truth annotations for segmentation can be labor-intensive, as each pixel must be labeled. This has led to the development of datasets and tools to facilitate annotation.
Semantic Segmentation Networks: Deep learning architectures like U-Net, Mask R-CNN, and Deeplab have significantly improved the accuracy of image segmentation by effectively learning complex patterns and features.
Image segmentation plays a fundamental role in understanding and processing images, enabling computers to "see" and interpret visual information in ways that mimic human perception.
Image segmentation is a computer vision task that involves dividing an image into meaningful and distinct segments or regions. The goal is to partition an image into segments that represent different objects or areas of interest within the image. Image segmentation plays a crucial role in various applications, such as object detection, medical imaging, autonomous vehicles, and more.
Image segmentation
This document discusses different techniques for image segmentation, which is the process of partitioning an image into meaningful regions or objects. It covers several main methods of region segmentation, including region growing, clustering, and split-and-merge. It also discusses techniques for finding line and curve segments in an image, such as using the Hough transform or edge tracking procedures. Finally, it provides examples of applying these segmentation techniques to extract regions, straight lines, and circles from images.
Jagmohan presentation2008
The document discusses real-time ray tracing of implicit surfaces on the GPU. It presents several contributions: analytical root finding for surfaces up to order 4 achieving frame rates of 1100-5821; applying Mitchell's interval method for surfaces up to order 5 at 60-965 FPS; and marching points methods for arbitrary implicits at 38-825 FPS. Adaptive marching points were also introduced for arbitrary implicits achieving 60-920 FPS. Traditional and recent methods for rendering implicit surfaces are reviewed.
Implementation
This document discusses algorithms for rasterization and scan conversion in computer graphics. It covers:
1. Rasterization algorithms like DDA and Bresenham's line algorithm for determining which pixels are inside a primitive defined by vertices.
2. Scan conversion of line segments using DDA and Bresenham's algorithm. DDA uses floating point addition while Bresenham uses only integer operations.
3. Polygon filling algorithms like the odd-even rule and winding number to determine if a point is inside or outside a polygon. Shading is determined by interpolating colors across spans.
Saga.lng
This document contains documentation text for various SAGA GIS modules and functions. It includes descriptions of parameters, data types, file formats, and other technical details. Sections are devoted to topics like geoprocessing algorithms, data formats, coordinate systems, and the contributions of individual SAGA developers.
Line clipping
The document discusses the Cohen-Sutherland line clipping algorithm. It describes how the algorithm performs initial tests on a line to determine if intersection calculations are needed by checking for trivial acceptance or rejection of line segments. If a line cannot be fully accepted or rejected, it is divided at a clip edge and the process is repeated iteratively until the line is fully processed. An example of applying the algorithm to clip a line against a rectangle is also provided.
Metrology
The document discusses various metrology concepts including limits, fits and tolerances, limit gauges, angular measurement, and surface finish measurement. It defines key terms like tolerance, allowance, fits, and describes methods for measuring angles, tapers, diameters and surface finishes using instruments like micrometers, plug gauges, ring gauges and depth gauges. Design principles for limit gauges are also covered, emphasizing that gauges should not accept parts outside tolerances to avoid violating basic metrological principles.
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This document discusses image representation and description techniques. It begins by explaining that image segmentation results in a set of regions that need to be represented, often by their boundaries or internal characteristics, and described using features. Several boundary and regional representation and description methods are then outlined, including chain codes, shape numbers, Fourier descriptors, statistical moments, topology, and textures.
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Representation image
- 1. Representation and Description for image Processing
- 2. Segmentation Raw data (pixels) Representations Computation of descriptors external characteristics (boundary) internal characteristics (pixels comprising the region) shape characteristics regional properties such as color & texture
- 4. Chain Codes Polygonal Approximations – Minimum perimeter polygons – Merging techniques – Splitting techniques Signatures Boundary Segments Skeletons Technique of representation
- 5. Chain Codes Problem1: - Long chains of codes - Easily disturbed by noise, and sidetracked Solution: - Resampling using larger grid spacing Problem2: - start point Solution: - Normalizations Before resample: 000000766…1111 After resampling: 076666…12
- 6. • normalized – circular sequence – Ex. First difference of 4-direction chain code 10103322 is 3133030. – 2 10103322 – 33133030
- 8. Polygonal Approximations • Determine which points on the boundary to use • Minimum perimeter polygons o Choose an appropriate grid - The boundary is enclosed by a set of concatenated cells o Allow the boundary to shrink as a rubber band The maximum error per grid cell is √2d, where d is the dimension of a grid cell
- 10. Merging Techniques • least square error line fit 1. Merge points along a boundary until the least square error line fit of the points merged so far exceeds a threshold 2. Record the the two end point of the line 3. Repeat Steps 1 and 2 until all boundary points are processed .
- 12. problem • Merging technique problem: – No guarantee for corner detection • Solution: – Splitting: to subdivide a segment successively into two parts until a given criterion is satisfied. – Objective: seeking prominent inflection points.
- 13. Splitting techniques: 1. Start with an initial guess, e.g., based on majority axes 2. Calculate the orthogonal distance from lines to all points 3. If maximum distance > threshold, create new vertex there 4. Repeat until no points exceed criterion
- 15. Signatures • Signature: a 1D functional representation of a boundary • To generate: – Plot the distance from the centroid to the boundary as a function of angles. • The signature is often unique for a region – We can distinguish the region by its signature • Independent of translation, but not rotation & scaling .
- 17. • r(ϴ)= D/cos ϴ 0<= ϴ<60 • = D/cos(120- ϴ) 60<= ϴ<120 • = D/cos(180- ϴ) 120<= ϴ<180 • = D/cos(240- ϴ) 180<= ϴ<240 • = D/cos(300- ϴ) 240<= ϴ<300 • = D/cos(360- ϴ) 300<= ϴ<360
- 19. Boundary segments • The boundary can be decomposed into segments. – Useful to extract information from concave تقعر parts of the objects. • A good way to achieve this is to calculate the convex Hull of the region enclosed by the boundary Hull • Can be a bit noise sensitive 1. Smooth prior to Convex hull calculation 2. Calculate Convex Hull on polygon approximation
- 20. Skeletons • To reduce a plane region to a graph - by e.g. obtaining the skeleton of the region via thinning. • Find medial axis transformation (MAT): The MAT of region R with border B is found as: • For each point p in R, we find its closest neighbor in B. • If p has more than one such neighbor, it belongs to the Medial Axis.
- 21. • Assume foreground pixels = “1” , Background = “0” • 1st pass Flag a contour point p for deletion if the following conditions are satisfied: • (a) 2 <= N(p1) <= 6 • (b) T(p1) = 1; • (c) p2 * p4 * p6 = 0 11.1.1 • (d) p4 * p6 * p8 = 0 N(p1) is the number of nonzero neighbors of p1 T(p1) is the number of 0-1 transitions in the ordered sequence of p2, p3, . . . , p8, p9,p2. If (a) – (d) are not violated, the point is marked for deletion • Points are not deleted until the end of the pass • This way the data stays intact until the pass is complete Thinning Algorithm 0 0 1 1 p1 0 1 0 1 p2 p4 p6 p4 p6 p8
- 22. • 2nd pass • Conditions (a) and (b) are the same as the 1st pass • (c) and (d) are different [call these (c’) and (d’)]: – (c’) p2 * p4 * p8 = 0 – (d’) p2 * p6 * p8 = 0 • Delete all points that are flagged from the 2nd pass Repeat 1st pass and 2nd pass until no contour point is deleted during an iteration p4p8 p2 p2 p6 p8
- 23. Examples NO NO
- 24. • In the first case • N(p) = 5, S(p) = 1, p2 · p4 · p6 = 0, and p4 · p6 · p8 = 0, then p is flagged for deletion. • In the second case • N(p) = 1, so( 2 :5 N(p,) <0 6) is violated and p is left unchanged. • In the third case • p2 · p4 · p6 = 1 and p4 · p6 · p8 = 1, so conditions (p2 · p4 · p6 = 0) and (p4 · p6 · p8 = 0) violated and p is left unchanged. • In the forth case • S(p) = 2, so condition (T ( p l) = 1) is violated and p is left unchange