BresenhamApplications

8/6/2019 BresenhamApplications

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Applications of Bresenham Path

Discrete Environments


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Discrete Lines


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Discrete Lines


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Discrete Lines


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Discrete Lines with Antialiasing


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Discrete Lines with Antialiasing


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Discrete Lines


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Lneas digitales: conversin a barrido, rasterizado

(scan conversion) o pixelizado

Con anti-aliasing


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Antialiasing


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Bresenham Algorithm(s) Applications

(besides tracing discrete lines and curves):

Z-buffermulti Z-buffers for 3D reconstrs. from projections w occlusions (laser scaner)

- u er vs y across ransparen sur aces an -a ase en-sur ace remova

Ray-tracing / Ray-castingRendering - recursive reflections, shadows

o sono ec eec on anPickingby boundary detection of non-explicit object representations.

MIP (Maximum of Intensity Projection) X-Ray simulation = Integrated intensity

Other functions ofray path memory Volume Rendering, 3D transfer functions

Displacement of discrete image operators (discrete neighborhoods and window kernels).

ro e samp ng voume anayss on t e g tStereological probes 2D/3D texture analysis, v.g., Ratio of Extrema Density, MWRDE,Segmentation guided by radial and sampled profile-signatures

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Resample an image in curvilinear coordinates for Cartesian representation & analysis.


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Bresenham Algorithm(s) Applications

3D Bresenham Applications II:

Spherical, elliptical MIP and Intensity Projection

orma pro ec on on a sur ace

Internal: Depth and thickness - data projectionExternal/internal: Signed distance field samplingMathematical Mor holo -related rocessin /anal sis

Extract stereotomical planes (slices at any orientation) volume resampling

Extract/build (some) discrete ruled surfaces, and other non-linear paths and surfaces

Scan volume in any orientation (linear) volume flooding (oriented traversal)

Roller buffers (sliding windows -incremental neighborhoods) for analysis (histograms,texture tubular sensors etc .

Displacement of objects in discrete space (or following a discrete path).

Processing/Analysis/Tracing followingany (discrete) path or surfaceMost of the above applications over curvilinear paths and surfacesGeneralized, geodesic roller buffers.


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Z-Buffer Imaging


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Depth Cue Using the Z-buffer


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Modeling Laser-Scanner Acquisitions

(A) Range image from a laser scanneracquisition of a real human ear

(B) Simulating (A) by depth projectionusing Bresenham ray-casting in avoxelizeed computer model of the


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Parametrical Visualization: Surface Mapping of LocalParametrical Visualization: Surface Mapping of LocalInformationInformation DistributionsDistributions

m,m, zz A map of the skull thicknessA map of the skull thickness

nn


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Orthogonal slices:Orthogonal slices:Axial (XY), Sagittal(YZ), Coronal (ZX)Axial (XY), Sagittal(YZ), Coronal (ZX)

ZY

Y


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Orthogonal slices:Orthogonal slices:Axial (XY), Sagittal(YZ), Coronal (ZX)Axial (XY), Sagittal(YZ), Coronal (ZX)


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Borders of a Bresenham PlaneDefined by Three Points

Lines are actually traced/read on one plane (ZX, for example) but the initialand final points change according to lines on another plane (YZ in the figure).

No interpolatiion is strictly needed if scale is preserved, but it may improve smoothness


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Oblique slicesOblique slices


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Oblique slicesOblique slices


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A Roller Buffer moving on a Discrete Path

Only new pixels are read and old pixel information is discarded,The buffer or window is fully read/processed only the first time.

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BresenhamApplications