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Topic: Bilinear interpolation

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Trilinear interpolation

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	Linear interpolation - Wikipedia, the free encyclopedia
		In numerical analysis a linear interpolation of certain points that are in reality values of some function f is typically used to approximate the function f.
		Linear interpolation can also be extended to bilinear interpolation for interpolating functions of two variables.
		Bilinear interpolation is often used as a crude anti-aliasing filter.
	en.wikipedia.org /wiki/Linear_interpolation (630 words)

	UnrealWiki: Bilinear Filtering
		The general idea when interpolating bilinearly is that the colour of an unknown pixel should be spaced proportionally between the colour values of the pixels around it.
		Bilinear filtering is one method by which different mipmaps are interpolated between when a frame is rendered, not the method by which the mipmaps are generated.
		A bilinear filter is simply a transformation that uses bilinear interpolation, but it is not technically a requirement for mipmapping, nor is mipmapping a requirement for bilinear filtering of textures onto a surface.
	wiki.beyondunreal.com /wiki/Bilinear_Filtering (852 words)

	* Bilinear Interpolation - (GIS): Definition (Site not responding. Last check: 2007-10-27)
		Bilinear interpolation uses the four blue values surrounding the center of each yellow cell.
		Bilinear interpolation is used in resampling a raster object to create a new raster object with a different cell size,...
		214 interpolation method where the value is obtained by linear interpolation on the two axes (row and column)...
	www.mimihu.com /gis/bilinear_interpolation.html (216 words)

	Interpolation
		Bilinear: Bilinear interpolation uses the information from a pixel (let's call it the original pixel) and four of the pixels that touch it to determine the color of the new pixels that are created from the original pixel.
		Bicubic: Bicubic interpolation uses the information from an original pixel and sixteen of the surrounding pixels to determine the color of the new pixels that are created from the original pixel.
		Bicubic interpolation is a big improvement over the previous two interpolation methods for two reasons: (1) Bicubic interpolation uses data from a larger number of pixels and (2) Bicubic interpolation uses a Bicubic calculation that is more sophisticated than the calculations of the previous interpolation methods.
	ronbigelow.com /articles/interpolation/interpolation.htm (2878 words)

	bilinear interpolation Definition: TechEncyclopedia from TechWeb
		A texture mapping technique that produces a reasonably realistic image, also known as "bilinear filtering" and "bilinear texture mapping." An algorithm is used to map a screen pixel location to a corresponding point on the texture map.
		The term bilinear refers to the performing of interpolations in two dimensions (horizontal and vertical).
		Two horizontal interpolations are made (texels 1-2 and 3-4), and then the results are averaged together for the vertical interpolation.
	www.techweb.com /encyclopedia/defineterm.jhtml?term=bilinearinterpolation (427 words)

	Bilinear interpolation -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-27)
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, bilinear interpolation is an extension of (Click link for more info and facts about linear interpolation) linear interpolation for (Click link for more info and facts about interpolating) interpolating functions of two variables.
		Note that the result of bilinear interpolation is independent of the order of interpolation.
		The obvious extension of bilinear interpolation to three dimensions is called (Click link for more info and facts about trilinear interpolation) trilinear interpolation.
	www.absoluteastronomy.com /encyclopedia/b/bi/bilinear_interpolation.htm (205 words)

	Geometric Image Manipulation
		Bilinear interpolation, also known as first-order interpolation, linearly interpolates pixels along each row of the source image, then interpolates along the columns.
		Bilinear interpolation assigns to Point D in the destination a value that is a bilinear function of the four pixels nearest S in the source image.
		Bicubic interpolation reduces resampling artifacts even further by using the 16 nearest neighbors in the interpolation and by using bicubic waveforms rather than the linear waveforms used in bilinear interpolation.
	java.sun.com /products/java-media/jai/forDevelopers/jai1_0_1guide-unc/Geom-image-manip.doc.html (9090 words)

	[No title]
		During bilinear interpolation, cubic convolution and sin(x)/x, the last pixel and/or scanline will be reused to produce the grey level values for the georeferenced image if the uncorrected pixel window used to calculate the corrected matrix grey level value falls outside the bounds of the uncorrected image at its corner edges.
		Bilinear interpolation determines the grey level from the weighted average of the four closest pixels to the specified input coordinates, and assigns that value to the output coordinates.
		The image is slightly sharper than that produced by bilinear interpolation, and it does not have the disjointed appearance produced by nearest neighbour interpolation.
	www.pcigeomatics.com /cgi-bin/pcihlp/GCPWORKS\|Theory\|Resampling (1254 words)

	What's the point? Interpolation and extrapolation with a regular grid DEM
		Double linear interpolation attempts to minimise the likelihood of such errors by averaging the linear plane heights of the two triangles into which a grid cell can be divided by one of its diagonals.
		The bilinear function is akin to fitting a hyperbolic paraboloid to the four vertices of the grid cell.
		The trend (or slopes) of the surface are important for interpolation, since we should not be constrained to using the nearest 3 or 4 vertices of the DEM cell.
	www.geovista.psu.edu /sites/geocomp99/Gc99/082/gc_082.htm (6132 words)

	Spatial Transformations (Image Processing Toolbox) (Site not responding. Last check: 2007-10-27)
		Interpolation is the process by which we estimate an image value at a location in between image pixels.
		For bilinear interpolation, the output pixel value is a weighted average of pixels in the nearest 2-by-2 neighborhood.
		For bicubic interpolation, the output pixel value is a weighted average of pixels in the nearest 4-by-4 neighborhood.
	www.haystack.edu /computing/matlab6.5/help/toolbox/images/geom3.html (264 words)

	r.bilinear (Site not responding. Last check: 2007-10-27)
		It uses the bilinear interpolation method, a simple algorithm usually applied only to completely defined raster areas (input data void of null data values).
		These data, if included, are used to interpolate values for cells that are north or south of a line intersecting the cell centers of the first or last row of input, respectively.
		For longitude-latitude databases, the interpolation algorithm is based on degree fractions, not on the absolute distances between cell centers.
	www.grass-kr.org /html/r.bilinear.html (544 words)

	Interpolation: Digital Imaging: Glossary: Learn: Digital Photography Review
		Some digital cameras use interpolation to produce a larger image than the sensor captured or to create digital zoom.
		Most image viewing and editing software use this type of interpolation to enlarge a digital image for the purpose of closer examination because it does not change the color information of the image and does not introduce any anti-aliasing.
		For the same reason, it is not suitable to enlarge photographic images because it increases the visibility of jaggies.
	www.dpreview.com /learn/?/Glossary/Digital_Imaging/Interpolation_01.htm (446 words)

	Bilinear interpolation - Wikipedia, the free encyclopedia
		In mathematics, bilinear interpolation is an extension of linear interpolation for interpolating functions of two variables.
		The four red dots show the data points and the green dot is the point at which we want to interpolate.
		The obvious extension of bilinear interpolation to three dimensions is called trilinear interpolation.
	www.wikipedia.org /wiki/Bilinear_interpolation (252 words)

	Graphics.com
		Bilinear interpolation produces anti-aliased pixels within the new, enlarged image, because whole number values for new pixels are not possible.
		Although bilinear interpolation produces good anti-aliased pixels, it is not the most sophisticated interpreting method for resizing images.
		Bicubic interpolation is the most processor-intensive resizing method because it involves the most calculations, but the aesthetic results are also the most faithful to the original image.
	www.graphics.com /modules.php?name=Sections&op=printpage&artid=56 (1124 words)

	Bilinear interpolation - InformationBlast
		Bilinear interpolation is the process of taking a two-dimensional set of numbers and interpolating the values linearly, finding a point using a weighted average of four values.
		The idea behind two-dimensional interpolation is that having some periodic plane of discrete data you can predict the value of a non-integer x and y within the plane.
		Note that the result of bilinear interpolation is independent of the order of interpolation, that is, performing the linear interpolations in the other order, vertically, then horizontally, would also produce an equivalent expression for the predicted value.
	www.informationblast.com /Bilinear_interpolation.html (193 words)

	High Quality Reconstruction on Bcc Grids (Site not responding. Last check: 2007-10-27)
		If the sample rate drops under the half cell border distance, sheared trilinear interpolation is used instead of bilinear interpolation, which is the generalization of the bilinear interpolator.
		Bilinear interpolation is the fastest but the reconstruction quality is limited due to the mere bilinear interpolation on the cell borders.
		Barycentric interpolation is also limited in quality because it is only linear interpolation, but it not much faster than sheared trilinear interpolation because of the costly calculation of the barycentric coordinates.
	www.cg.tuwien.ac.at /~matt/bcc_volrend/raycast (1284 words)

	Map Algebra
		By translating and rescaling the coordinates, which will not change the interpolation, we may suppose the yellow square is centered at (x, y) and the centers of the surrounding blue cells are located at (0,0), (1,0), (0,1), and (1,1), where they have values Z
		Note that the term "bilinear" derives from the process of linear interpolation (twice in one direction, then once in the perpendicular direction), not from the formula for Z. The formula involves a term with x * y, which is not linear.
		In these figures, interpolation occurs only between the values X=0.0 and X=1.0 because this is the range of X values whose neighbors are located at points -1, 0, 1, and 2.
	www.quantdec.com /SYSEN597/GTKAV/section9/map_algebra.htm (1792 words)

	Abstract (Site not responding. Last check: 2007-10-27)
		During the discussion at the 1999 SEG meeting in Houston, I met an opinion, that the bicubic travel time interpolation is very time consuming, and that the bilinear interpolation is much faster.
		The interpolation method is coded in program 'mtt.for', where the kind of the interpolation scheme may be selected.
		The difference between the computational time required for the bicubic interpolation and the computational time required for the bilinear interpolation is negligible with respect to the computational time required to run the whole program.
	seis.karlov.mff.cuni.cz /papers/r10pb2.htm (402 words)

	FSPViewer
		Here are some information about the interpolators used by the program: they are a little technical, but you will not need to fully understand them in order to use the program.
		For example when the zoom factor is 50% the interpolators will use four times the pixels, so Lanczos3 will use 144 pixels in the base image foe each pixel on the screen.
		Auto uses the "bilinear" setting when you are panning slowly to avoid the "shimmering" effect, and it uses the "none" setting when you are panning faster so that the viewer is more responsive.
	www.fsoft.it /panorama/FSPViewer.htm (3972 words)

	Bilinear interpolation in time and space
		In the case of bilinear interpolation, the approximate function is given by,
		The function is approximated by bilinear interpolation within a cell defined by the four corner samples.
		In general bilinear interpolation is a reasonable interpolation method for sampling intervals up to about half of the Nyquist frequency.
	sepftp.stanford.edu /public/docs/sep77/dave1/paper_html/node10.html (179 words)

	Geographical Distribution of Biomass Carbon in Tropical Southeast Asian Forests: A Database (Site not responding. Last check: 2007-10-27)
		The bilinear interpolation method of resampling identifies the four nearest input cell centers surrounding the output grid-cell center, then calculates a weighted mean of those values, and assigns the mean to the output grid-cell center.
		Bilinear interpolation is recommended for continuous surfaces because a known point or phenomenon determines the assigned value (e.g., elevation, and slope).
		Nearest neighbor, bilinear interpolation, and cubic convolution algorithms were each used to resample actual and potential carbon biomass estimates in the BIOMASS grid to a 0.25-degree resolution.
	cdiac.esd.ornl.gov /epubs/ndp/ndp068/ndp068.html (5755 words)

	Graphics (Site not responding. Last check: 2007-10-27)
		Interpolation is always made on the original bit depth (e.g.
		Interpolation does not change the stored image data, only how the image is displayed.
		Using bilinear interpolation, a 2 by 2 neighbourhood is used to make a linear estimation of values "inbetween" the original pixel values.
	www.algonet.se /~sgis/CM2-7Help/citym23.htm (329 words)

	Description of Bilinear Interpolation (Site not responding. Last check: 2007-10-27)
		pixels : the average of the upper, lower, left and right pixel values is assigned as the G value of the interpolated pixel.
		position : the average of two adjacent pixel values in corresponding color is assigned to the interpolated pixel.
		position : the average of four adjacent diagonal pixel values is assigned to the interpolated pixel.
	www-ise.stanford.edu /~tingchen/algodep/bilinear.html (93 words)

	Interpolated Textures (Site not responding. Last check: 2007-10-27)
		Bilinear interpolation for quadrilaterals was done by solving a quadratic formula for u and v, the texture coordinates, in relation to the x, y, z, coordinates.
		Triangular interpolation wasn't any problem because I used triangular interpolation previously for ray-triangle intersection to determine if a point was inside a triangle.
		Notice how the texture is "warped" to conform to the interpolation along the two sides of a triangle face.
	www.cse.ohio-state.edu /~woodring/782lab1/inter.html (211 words)

	IP.com's Prior Art Database
		Disclosed is a method for bilinear interpolation for parallel data-driven architecture.
		Bilinear interpolation determines the value of a new pixel from the weighted average of the four neighbor pixels closest to the specified input coordinates for color images this process is repeated for each color plane.
		The bilinear interpolation algorithm is used for zooming (scaling) an image in and out.
	www.priorartdatabase.com /IPCOM/000029814 (464 words)

	Technical overview (Site not responding. Last check: 2007-10-27)
		Horizontal interpolations can be bilinear interpolations or 12 points cubic interpolations.
		No namelist variable is available to switch from 12 points to bilinear interpolations.
		Routine FPMIMAX is used to give to the interpolated quantity the value of the nearest model grid point (used for maximum and minimum temperature at 2 meters).
	www.ecmwf.int /research/ifsdocs_old/TECHNICAL/Chap2_FULL-POS5.html (547 words)

	Glossary
		Two-dimensional cubic interpolation of pixel values based on the 16 pixels in a 4 x 4 pixel neighborhood.
		Two-dimensional linear interpolation of pixel values based on the four pixels in a 2 x 2 pixel neighborhood.
		Two-dimensional interpolation of pixel values in which the amplitude of the interpolated sample is the amplitude of its nearest neighbor.
	java.sun.com /products/java-media/jai/forDevelopers/jai1_0_1guide-unc/Glossary.doc.html (447 words)

	6.0 Image Aspect Ratio (Site not responding. Last check: 2007-10-27)
		The blocky apparance (vertical edginess seen in the brighter rings) is due to the Mach Band effect (also seen in the ramp example).
		Bilinear Interpolation, below, gets rid of this effect by doing some pixel averaging.
		Expanded image has been smoothed a bit due to Bilinear Interpolation.
	www.nist.gov /lispix/imlab/AspectR/aspect.html (268 words)

	Thou shalt love thy neighbour as thyself. There is none other commandment greater than these. - bilinear interpolation ... (Site not responding. Last check: 2007-10-27)
		Increasingly, in the age of when concerned can easily contact their elected officials, 2 pc relier pc relier tÃ©lÃ©vision Ã demonstrate a level of commitment that is not always apparent in an e-mail.
		Some may say that a good deal of that figure is produced by bilinear interpolation monitoring bank counters and parking lots, but I do not.
		In Casnovia alone several hundred films are made a year, and only a tiny portion of them end in the bilinear interpolation.
	www.theborough.co.uk /bilinear-interpolation.html (503 words)

	Digital zooming system utilizing image buffers and employing an approximated bilinear interpolation method - Patent ...
		vertical operation means for magnifying said horizontally interpolated image signal by an approximated bilinear interpolation of said horizontally interpolated image signal in a vertical direction to provide a vertically and horizontally interpolated image signal in dependence upon a second plurality of control signals; and
		magnifying said horizontally interpolated image signal in dependence upon an approximate bilinear interpolation of said horizontally interpolated image signal in a vertical direction to generate a vertically and horizontally interpolated image signal in response to second ones of said plurality of control signals.
		The nearest neighbor interpolation method embodied out of the theory of an interpolation for a zoom process has an advantage that the hardware is simple, but has a disadvantage that the so-called "mosaic phenomenon" appears in the zoomed image.
	www.freepatentsonline.com /5307167.html (4609 words)

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