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Computerized Geometry and Image Processing (3V 2 ) Geometric strategies for advanced picture ... Center is on advanced picture or picture investigation. Center of the field ...

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Computerized Geometry and Image Processing Dietmar Saupe Course Outline SS 2006

Digital Geometry and Image Processing (3V+2Ü) Geometric strategies for advanced picture examination Scope: Graduate course Information Engineering expert and PhD understudies Classes (Vorlesung), D. Saupe Tuesdays 8:15h-11h, Z714 (preparatory) Problem sessions (Übg.), V. Bondarenko Thursdays 14:00h-15:30h, Z714 (preparatory)

Primary course reading material Reinhard Klette, Azriel Rosenfeld Digital Geometry Morgan Kaufmann (Elsevier) 2004 UB will have duplicates

Secondary course book R.C. Gonzales, R.E. Woods Digital Image Processing Prentice-Hall (second Ed.) 2002 third version UB has duplicates

Digital Geometry Geometric strategies for advanced picture examination Focus is on computerized picture or picture investigation Core of the field Related scientific fundamenals It is not yet another treatment of an extremely expansive scope of issues, calculations, heuristics, and „useful" advances

Introduction Color (pictures) A RGB picture Its 3 shading channels Histograms

Introduction Early advanced pictures A Greek rock mosaic, point of interest from "The Lion Hunt" in Pella,Macedonia, around 300 BC. Design woven by a Jacquard linger: a highly contrasting silk representation of Jacquard himself, woven under the control of a "system" comprising of around 24,000 cards (one is appeared on the left). Mid nineteenth century, before Babbage!

Introduction Digital pictures in 2005 Standard 16 Megapixel CCD cameras advancing Specialized cameras in photogrammetry of 100 Megapixels 3D imaging modalities (CT, MRI, ...) 3D-laser range scanners Leon Harmon of Bell Labs: picture of Lincoln (252 pixels), "The Recognition of Faces", Scientific American, (Nov. 1973). A 380 degree all encompassing picture of Auckland, New Zealand, 2002, 500 Megapixels

Introduction Grid of squares versus matrix of focuses Two ideas for pixels (cells) Is the worth a part of the pixel? A photo P is a mapping of a limited rectangular framework area into the reals Generalization to 3D: voxel

Introduction Adjacency Version 1 Cell 1-contiguousness and pixel 4-nearness (left) Neighborhoods (right) Version 2 Cell 0-contiguousness and pixel 8-nearness (left) Neighborhoods (right) In 3D: Cells? Voxels?

Introduction Replace the X\'s! Top: X-contiguous cells X-nearby pixels Bottom: X-neighboring cells X-adjoining pixels

Introduction Same in 3D! X-nearby 3-cells : X= ? (left, center, right) X-adjoining voxels : X= ? (left, right)

Introduction Grid point network Points are 4-associated? 8-associated? Foundation 4-associated? 8-associated?

Introduction Equivalent classes Equivalence connection R on limited framework Reflexive, symmetric, transitive Yields identicalness classes For a photo P-comparability: Pixels p,q: pRq iff P(p)=P(q)

Introduction Component marking Assume 4-nearness of pixels Frequent undertaking: name the 4-associated segments of the proportionality classes Some calculations Fill calculation: Rosenfeld-Pfaltz naming plan

Introduction Image examine groupings Examples: Space filling bends (Peano, Hilbert)

Topics (Chapters) Metrics Basics: Norms, Minkowski measurements, whole number esteemed measurements, prompted topology, Hausdorff metric Grid point measurements, ways, geodesics, inherent separations Metrics on pictures: separation changes average hub

Topics (Chapters) Adjacency diagrams Graphs and connectedness, essential chart hypothesis, Euler trademark and planarity Boundaries, cycles, boondocks in rate pseudographs Inner (dark) pixel fringe (dark) pixel co-outskirt (dim) pixel

Topics (Chapters) Topology Topological spaces, advanced topologies Concepts homeomorphy, isotopy (top. identicalness) Simplicial buildings, triangulations

Topics (Chapters) Curves and surfaces: topology, geometry Jordan bends, bends in frameworks Surfaces and manifolds, ... in 3D frameworks Arc length, bend, points, zones Surfaces and solids Principal, gaussian, mean shape Tracing surfaces

Topics (Chapters) Curves and surfaces in matrices Straightness, 2D and 3D Measuring circular segment length, ebb and flow, corners Digital planes Measuring surface zone, ebb and flow

Selected Topics Moments and their estimation Other picture properties Spatial relations

Selected Topics (not secured) Hulls and charts (convexity, Voronoi) Transformations (t. bunches, symmetries, amplification, ...) Morphological administrators (widening, disintegration, disentanglement, division, ...) Deformations (topological-protecting def., contracting, diminishing, ...)