Rectifying Images

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Tutorial

RectifyingImages

with

TNTmips®

RECTIFICATION

Rectifying Images

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Before Getting Started

You can print or read this booklet in color from MicroImages’ web site. Theweb site is also your source for the newest tutorial booklets on other topics.You can download an installation guide, sample data, and the latest versionof TNTmips.

http://www.microimages.com

This booklet introduces you to the Automatic Resampling process in TNTmips®.This process uses georeference control point information to perform simple recti-fication of distorted images and to transform a raster image into a desiredgeographic coordinate system. The exercises cover the various options for con-trolling the size, extents, and orientation of the rectified image, as well as differentresampling methods and geometric transformation models. Warping of distortedvector or CAD objects is also briefly introduced.

Prerequisite Skills This booklet assumes that you have completed the exercisesin the tutorial booklets Displaying Geospatial Data and TNT Product Concepts.Those exercises introduce essential skills and basic techniques that are not cov-ered again here. You will also find the concepts introduced in the tutorialsGeoreferencing and Introduction to Map Projections helpful in understandingimage rectification. Please consult those booklets for any review you need.

Sample Data The exercises presented in this booklet use sample data that isdistributed with the TNT products. If you do not have access to a TNT productsDVD, you can download the data from MicroImages’ web site. In particular, thisbooklet uses sample files in the RECTIFY and CB_DATA data collections.

More Documentation This booklet is intended only as an introduction to recti-fying and resampling raster images. Details of the process can be found in avariety of tutorial booklets, color plates, and Quick Guides, which are all availablefrom MicroImages’ web site.

TNTmips® Pro and TNTmips Free TNTmips (the Map and Image ProcessingSystem) comes in three versions: the professional version of TNTmips (TNTmipsPro), the low-cost TNTmips Basic version, and the TNTmips Free version. Allversions run exactly the same code from the TNT products DVD and have nearlythe same features. If you did not purchase the professional version (which re-quires a software license key) or TNTmips Basic, then TNTmips operates inTNTmips Free mode. The Automatic Resampling process is not available inTNTview or TNTatlas. All the exercises can be completed in TNTlite using thesample geodata provided.

Randall B. Smith, Ph.D., 19 August 2013© MicroImages, Inc. 1998–2013

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Welcome to Rectifying Images

STEPSstart TNTmipschoose Image /Resample and Reproject/ Automatic from theTNTmips menu

The exercises on pages 4-9introduce the AutomaticResampling process, anddemonstrate various optionsfor determining the cell size,orientation, and extents ofthe output raster. Pages 10-11 discuss the three optionsfor interpolating the cellvalues in the output raster.Geometric transformationmodels are discussed onpages 12-17. Vectorwarping is covered on page18, and a review andreferences are found onpage 19.

In most geographic data sets it is useful to integrateplanimetric map data with aerial or satellite imag-ery. A correctly processed digital map is free ofsignificant geometric distortion and conforms to theprojection and coordinate system of the original map.Raw digital images, on the other hand, are not alignedwith any conventional geographic coordinate system,and they commonly contain internal geometric dis-tortions that result from the image acquisitionprocess. These distortions can arise from tilt of thesensor plane, variations in sensor altitude, Earth cur-vature, lens distortion, and terrain relief, among othercauses. As a result the raw images do not have asimple “map-like” geometry, and accurate map rela-tionships cannot be derived from them.

The Raster Resampling process (sometimes calledwarping or “rubber sheeting”) changes or rectifiesthe geometry of a raster image using the locations ofground control points that provide georeferencecontrol for the image. Depending on the geometrictransformation model you select, the process canremove or reduce internal geometric distortions inthe image and reorient and differentially rescale itso that the lines and columns in the output raster areparallel to the axes of a specific geographic coordi-nate system. Each input raster is processedseparately and each must be georeferenced. Con-trol points must be accurately located, sufficient innumber for the transformation model selected, anddistributed uniformly across the image.

Image rectification / reprojection is not required inall instances. Satellite imagery of low-relief areasmay have minimal internal distortions. The Displayprocess in TNTmips can overlay georeferenced lay-ers with different map projections and coordinatesystems with reasonable registration. However, ifthese raster layers will be used together routinely,resampling to a common map projection can signifi-cantly speed up display times.

To simply rescale, rotate, orflip a raster image withoutreference to geographiccoordinates, use the RasterExtract process (Image /Extract), which allowsthese operations via thecontrols on the Zoom/Orienttabbed panel.

For the sake of brevity, andbecause multiple inputrasters are processedseparately, discussions ofthe resampling process inthe remainder of this bookletrefer to “the input raster” and“the output raster”,regardless of the number ofrasters being used.

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STEPSclick [Select Rasters...]on the Rasters panel ofthe Raster Resamplingwindowuse the standard File /Object Selection windowto select objects TM7,TM4, and TM2 from theSANBRUNO Project File inthe RECTIFY datacollectionon the Settings Panel,select FromGeoreference from theModel menuselect Nearest Neighborfrom the Method menuselect Entire Input fromthe Extents menuselect Manual from theCell Size menuselect Projective Northfrom the Orient menu

Automatic Raster Resampling Window

Use the Display process(Main / Display from theTNTmips menu) to view theinput and output objects forthese exercises.

The Model menuprovides a choice ofdifferent geometrictransformation models.

Keep the current settings andcontinue to the next page.

Choices on the CellSize menu determinethe method used to setthe cell size for theoutput raster.

The Orient menu offersoptions for orienting theoutput raster relative to theoutput projection.

The Rasters panel on the Raster Resampling win-dow allows you to select the input raster(s) forresampling and lists pertinent spatial andgeoreference information. Resampling options areset using the menus on the Settings tabbed panel.Choices on these menus set the methods for deter-mining the cell size, orientation, and geographicextents of the output raster, as well as the geometrictransformation model and the method for interpolat-ing output cell values. You may have found that thechoices specified in the step list on this page werealready selected; these are the initial default selec-tions for each menu. However, if you make a differentchoice from a menu, that choice is saved as the de-fault selection for the next session. Always checkeach of the parameter menus to confirm that yourdesired menu choice is selected.

The Extents menu providesseveral methods for settingthe geographic extents ofthe output raster.

Use the Method menu tochoose one of three methodsfor interpolating cell valuesfor the output raster.

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STEPSpress [Run...]use the standard File /Object selectionprocedures to name anew Project File and theoutput raster objects

Rectifying to the Input Map ProjectionYou will probably use the Automatic Resamplingprocess most often to reproject a georeferenced ras-ter into the coordinate reference system specified inits georeference subobject. To do so, use the de-fault option on the Orient menu (Projective North)and the default Reference System option (Same asinput). Horizontal lines of cells in the output rasterare then parallel to the x axis of the input geographiccoordinate system, and vertical columns are paral-lel to the y coordinate axis. The input rasters used inthis exercise are extracts of a Landsat Thematic Map-per scene georeferenced to the Universal TransverseMercator coordinate system (Zone 10N), so the out-put raster set is aligned to the UTM system.

When you choose Manual as the Cell Size menuoption, the Cell Size fields are automatically set fromthe input object’s georeference information; you canedit these values if desired to change the cell size forthe output product. The cell size, geographic ex-tents, and output projection then determine thenumber of lines and columns in the output raster.

RGB display of input raster set with R= TM7, G = TM4, and B = TM2.

Output raster set (warped and reorientedto the UTM coordinate system), displayedwith UTM grid tick marks along the borderfor emphasis.

Use the default ReferenceSystem option to warp theinput raster into thecoordinate referencesystem specified in itsgeoreference subobject.

In this exercise, we pre-serve the spatial resolutionof the original imagerywhen creating theresampled output set.

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STEPSclick [ReferenceSystem...]in the CoordinateReference Systemwindow, on thePredefined panelnavigate to the Nationaland Local / UnitedStates / Californiagrouping

Warping to a New Map ProjectionClicking the ReferenceSystem button opens theCoordinate ReferenceSystem window, whichallows you to choose adifferent output coordinatereference system.

Output raster set in the NAD27 / SPCS27California Zone 3 (ftUS) coordinatereference system.

You can also warp the input raster to a coordinatereference system other than the one in which it isgeoreferenced. Use the Coordinate Reference Sys-tem window to choose from among many predefinedcoordinate reference systems, coordinate systems,

and datums. In this exercise the input raster set isreoriented to the predefined NAD27 / SPCS27 Cali-fornia Zone 3 (ftUS) coordinate reference system.

Warping a raster to a different coordinate refer-ence system commonly results in a significantrotation of the image, as well as other internal

changes in its geometry. If you warp the entire im-age (as in this exercise), the edges of the resampledimage are not parallel to lines and columns in theoutput raster. The warped and rotated image is em-bedded in a raster that is somewhat larger than theoriginal, with triangular “blank” (nonimage) areas atthe corners. (The blank areas are flagged in the nullmask so they can be rendered transparent when the

raster is displayed.)

choose NAD27 /SPCS27 California zone3 (ftUS), then click [OK]choose Run in theRaster Resamplingwindow and name theoutput raster objects

Use of the Coordinate Reference Systemwindow is introduced in the CoordinateReference Systems tutorial.

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STEPSchoose MatchReference from the CellSize menuwhen prompted, selectthe MAP object from theSANBRUNO Project Filechoose MatchReference from theExtents menu

Warping to a Reference Raster

Reference raster MAP, alignedto the UTM coordinate

system, with acell size of 20meters.

Raster set resampled using thereference raster to specify cell size,orientation, and output extents.

A raster that is already aligned to a geographic co-ordinate system can be selected as a ReferenceRaster to control the cell size, orientation, and/orextents of the output raster created by the resamplingprocess. Cell size and orientation are linked in thisinstance; choosing Match Reference from the CellSize menu automatically selects Match Referenceon the Orient menu (and vice versa). With theseoptions selected, the output rasterassumes the cell size and orientationof the reference raster.

You can use the Match Referenceoption on the Extents menu to trim the output imageto the exact extents of the reference raster. This isan appropriate choice if the reference raster is whollycontained within the area of the input raster image(as in this exercise). If the reference and input ras-ters only partially overlap, you may want to selectthe Overlap Reference option to output only thearea common to both.

The output cell size is setautomatically when you usea reference raster tocontrol the cell size andorientation of the output.The reference projectionoverrides any previouslyselected coordinatereference system.

run the resamplingprocess

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STEPSchoose Projective Northfrom the Orient menuchoose By Image Sizefrom the Cell Size menuenter 600 in the Linesfield and 409 in theColumns field in theRaster Size panechoose User Definedfrom the Extents menuthe previously-selectedNAD27 / SPCS27California zone 3 (ftUS)coordinate referencesystem is once againactive in the ReferenceSystem fieldenter the followingextents ranges: Easting:1425825 to 1455515;Northing: 398700 to442400run the resamplingprocess

Setting Output Extents and Raster SizeWe have covered several options for specifying theextents of the output raster, including Entire Input,Match Reference, and Overlap Reference. The finaloption is User Defined. When you select this optionfrom the Extents menu, the Extents controls becomeactive, allowing you to enter exact geographic ex-tents for the output raster using any availablecoordinate reference system. Click the Coordinatesbutton to open the Coordinate Reference Systemwindow to make your selection.

In some instances you may want the output rasterto have a specific size in lines and columns. The ByImage Size option on the Cell Size menu providesthis capability. The line and column cell sizes arethen determined by the raster size and output ex-tents.

Output rasters in State Plane 1927coordinate system, with extentsspecified in the Extents panel.Compare with image on page 6.

The reference raster used in the last exercise isstill selected and available for use. However, theReference Raster button is dimmed, showing thatthe raster is not in use with the current settings.The previously-selected State Plane coordinatereference system is once again active.

You can use the Queue Job and Save Jobbuttons to run resampling operations under theTNT job processing system. See the TechnicalGuide entitled System: TNTmips JobProcessing System for details.

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STEPSclick [Select Rasters...]on the Rasters paneland select objectsPHOTO_IR, RED, and GREEN

from the CB_TM ProjectFile in the CB_DATA datacollection

Orienting to a Direction

Output raster set reoriented with south at top.

You can orient theoutput raster withany of the fourcardinal directionsat the top.

The vertical axis of an input raster’s map coordinatesystem (such as State Plane or UTM) may not beparallel to the local direction of true north. TheOrient menu allows you to use the georeference in-formation to align the output raster with any of thefour cardinal compass directions at the top. Theseoptions are most useful when the input raster is al-ready aligned with a map coordinate system, and youwant to reorient it with north at the top.

In this example, the edges of the input raster set co-incide with lines of equal latitude (horizontal) andlongitude (vertical), so it is already oriented withnorth at top. Reorienting it to the State Plane projec-tion would cause a clockwise rotation of a fewdegrees. Reorienting it with South at Top exactlyinverts the image.

on the Settings panel,choose Manual from theCell Size menuchoose GeographicSouth from the Orientmenurun the resamplingprocess

RGB display of input rasterset (R = PHOTO_IR, G = RED, andB = GREEN) with a 10,000 footState Plane Coordinate mapgrid in yellow.

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STEPSclick [Select Rasters...]on the Rasters paneland select object PAN

from the SANBRUNO

Project Filein the Cell Size pane onthe Settings panel, enter2.00 in both Line andColumn text fieldsselect Projective Northfrom the Orient menumake sure that NearestNeighbor is still selectedin the Method menurun the resamplingprocess

Cell Value Interpolation in ResamplingThe Automatic Resampling process uses severalsteps to create the transformed output raster. First,the geometric transformation procedure (describedsubsequently) creates a “blank” rectified raster withthe proper extents and scale (cell size). Then a cellvalue is determined for each cell in the rectified ras-ter. To do so, the geometric transformation isreversed for each output cell in order to determineits position in terms of the original raster line andcolumn coordinates. The target output cell may belarger or smaller than an input cell, and it may over-lap several input cells. The output cell value musttherefore be calculated (interpolated) from somecombination of the surrounding input cells.

The Method menu offers several options for inter-polating output cell values. The Nearest Neighbor,Bilinear, and Bicubic methods are illustrated in thediagram below and are discussed on the next page.

Superimposed portion of rectifiedoutput raster. Bold outline indicatescurrent target cell for which a value isbeing interpolated.

Portion of original, distortedraster image.

Input Cells Used by EachResampling Method forthe Current Target Cell

NearestNeighbor

Bilinear

Bicubic

+

+ +

select Bilinear from theMethod menu and runthe process againrepeat with Bicubic asthe resampling method

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Resampling Methods

Nearest Neighbor

Bilinear

Bicubic

Nearest Neighbor Each output cell value in thenearest neighbor method is the unmodified valuefrom the closest input cell. Less computation is in-volved than in the other methods, leading to a speedadvantage for large input rasters. Preservation ofthe original cell values can also be an advantage ifthe resampled raster will be used in later quantita-tive analysis, such as automatic classification.However, nearest neighbor resampling can cause fea-ture edges to be offset by distances up to half of theinput cell size. If the raster is resampled to a differ-ent cell size, a blocky appearance can result from theduplication (smaller output cell size) or dropping(larger cell size) of input cell values.

Bilinear An output cell value in the bilinear inter-polation method is the weighted average of the fourclosest input cell values, with weighting factors de-termined by the linear distance between output andinput cells. This method produces a smoother ap-pearance than the nearest neighbor approach, but itcan diminish the contrast and sharpness of featureedges. It works best when you are resampling to asmaller output cell size

Bicubic The bicubic method calculates an outputcell value from a 4 x 4 block of surrounding inputcells. The output value is a distance-weighted aver-age, but the weight values vary as a nonlinearfunction of distance. This method produces sharper,less blurry images than bilinear interpolation , but itis the most computationally intensive resamplingmethod. It is the preferred method when resamplingto a larger output cell size. Two variants are alsoprovided to produce sharper and smoother results.

Nearest neighbor resampling is the only method that isappropriate for categorical rasters, such as class rastersproduced by the Automatic Classification process. Cellvalues in these rasters are merely arbitrary labels withoutnumerical significance, so mathematical combinations ofadjacent cell values have no meaning.

Raster PAN resampled from acell size of 10 meters to 2meters using threeresampling methods.

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Rectifying a Color Infrared Airslide

Topographic map (object SECTMAP)covering Section 32, resampledto conform to the UTM coordinatesystem. Note the nearly squareshape defined by the roadsbounding the section. Theresidential development in thesoutheastern quarter of thesection was not present when thismap was compiled.

Color infrared photo of Section 32with locations of ground controlpoints used for georeferencing.The image was georeferenced tothe UTM coordinate system usinga UGSG Digital Orthophoto Quadimage with 1-meter cell size.

STEPS:Use the Display process toexamine the following:

RGB display of objectsNIR, RED, and GREEN fromthe SECT32 Project File inthe RECTIFY datacollectionsingle-raster display ofobject SECTMAP in theSECT32 Project File

The remaining exercises use a color-infrared airslideof a mile-square section of agricultural and residen-tial land in eastern Nebraska. The airslide exhibitsseveral types of distortion, and the exercises exam-ine the effects of different geometric transformationmodels in attempting to rectify this image.

The northern and southern sectionlines are not parallel in the photo,and appear to converge towardthe west (compare with the mapbelow). This indicates that thecamera was not pointed straightdown, but was tilted slightlytoward the west when the photowas taken.

Several of the section lines alsoare curved outward slightly.Some of the areas of curvaturecoincide with topographic ridges,suggesting that this is an effect ofrelief displacement. Some of theoutward curvature may also be aradial distortion resulting fromimperfections in the camera lens.

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STEPSclick [Select Rasters...]on the Rasters paneland select objects NIR,RED, and GREEN from theSECT32 Project Filechoose Bicubic from theMethod menuselect Match Referencefrom the Cell Size menuwhen prompted, selectobject SECTMAP from theSECT32 Project File

Geometric Transformation ModelsTo alter the geometry of the input raster, the Auto-matic Resampling process analyzes the locations ofthe ground control points that were assigned in thegeoreference process. These are points in the imagewith known coordinates in a standard coordinatereference system. The process compares the geo-graphic coordinates of the control points to thelocations predicted by the geometric transformationmodel you have selected. The results are used todetermine numerical coefficients for coordinatetransformation equations that convert the originalimage to the desired coordinate reference system.

The Automatic Resampling process incorporates allof the geometric transformation models that are avail-able in the Georeference process for assessing thequality of control point locations. Each transforma-tion model requires a minimum number of controlpoints for solution. The minimum number of con-trol points provides a single, unique solution, butany errors in control point locations directly impactthe transformation. If additional control points areavailable, the process computes a best-fit transfor-mation using least squares adjustment. Thisprocedure chooses the set of coefficients for whichthe sum of the squared residual errors (deviationsbetween predicted and actual locations in the finalcoordinate system) is a minimum.

The quality of the rectification result depends on thenumber, accuracy, and distribution of the controlpoints and the choice of transformation model. Carein the georeference process is the best guarantee ofsuccess in rectification. Position control points sothat they cover most of the image. Adjust controlpoint positions to minimize the residual values (er-ror estimates resulting from the least squaresadjustment) for each control point. Appropriate usesfor some of the transformation models are discussedon the following pages.

The From Georeferenceoption selects thetransformation model thatwas saved with the controlpoint locations in eachobject’s georeferencesubobject. This choicepotentially allows differenttransformation models to beapplied to different rasterobjects in the input list.

Each of the other modelchoices is applied globally toall input raster objects,regardless of the modelused in the georeferenceprocess. The RationalPolynomial method can beused to orthorectify certainsatellite images. See thetutorial entitledOrthorectification usingRational Polynomials.

Keep the current settings andproceed to the next page.

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Affine Model

Skew

Rotate

Rescale

Translate

Affine Transformations

STEPSchoose Affine from theModel menurun the resamplingprocess

In this and the followingexercises we process theentire input image, but usethe SECTMAP raster to controlthe cell size and orientationof the output image. Theimage is resampled from acell size of about 3.37 m toan output cell size of 4.0 m.

The affine transformation model projects coordinatesfrom one plane (defined by the original coordinatesystem) to another parallel plane (defined by theoutput coordinate system). An affine model can in-corporate any or all of the transformations illustrated:translation, rescaling, rotation, and skew (or shear)of the image. Rescaling can accomodate a separatescale factor for each of the two coordinate axis di-rections. Any set of parallel lines in the source imageremain parallel in the output image. The affine modelrequires a minimum of three control points that donot fall on a single straight line.

The affine model is appropriate when you need toconvert a planimetric map raster (or an already-rec-tified image) from its original coordinate system andmap projection to a new planar coordinate system(for example, UTM to State Plane coordinates). Itmay also give satisfactory results if you are rectify-ing a vertical aerial or satellite image of a small areawith little topographic relief (so that the surface ap-proximates a plane, and there is little or no tiltdisplacement or relief displacement).

The affine transformation rotated and rescaled the CIRimage, but did not correct the curvature and convergenceof the section lines (the effects of more complex tiltdistortion and relief displacement).

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STEPSchoose Plane Projectivefrom the Model menurun the resamplingprocess

Plane Projective Model

Oblique perspective view ofa square results in atrapezoidal shape. Theplane projective model canrectify this simple tiltdistortion.

The plane projective modeltransforms coordinates inone plane to anothernonparallel plane using aperspective projection.

The plane projective transformation corrected the tiltdistortion found in the original image. The north and southsection lines are now nearly parallel. However, the subtlecurvature of these lines shows that some distortion arisingfrom relief displacement and/or lens effects still remains.Distortion due to relief displacement is relatively minor forthis image because vertical relief is small (about 110 feet)compared to the image’s horizontal dimensions.

The plane projective model transforms coordinatesbetween any pair of source and target planes, includ-ing nonparallel planes. It employs a perspectiveprojection: projection lines linking input and outputcoordinate locations emanate from a single centralview point, analogous to the imaging geometry ofan aerial camera. For this reason, the plane projec-tive model is commonly used to rectify nonverticalaerial images of relatively flat terrain.

The plane projective model incorporates all of thetransformations found in the affine model. How-ever, the only lines that remain parallel in both thedistorted and rectified images are those that are par-allel to the line of intersection between the twoplanes. The plane projective model requires a mini-mum of four noncolinear control points.

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STEPSchoose Order 3Polynomial from theModel menurun the resamplingprocess

Polynomial ModelsThe Polynomial transformations can correct nonlin-ear distortions in a raster image, as well as the lineardistortions handled by the models discussed previ-ously. Polynomial equations are used to relatecontrol point positions in the distorted image coor-dinates to corresponding positions in the outputgeographic coordinate system. The control pointinformation is used to calculate a best-fit set of coef-ficients for the terms in the equations. The order ofthe polynomial model is the highest exponent usedin the equations, and specifies the allowed complex-ity of the fit, as shown for one direction in theillustration below left.

An Order 2 polynomial describes a fit with one senseof curvature (concave or convex) in any direction.This model can correct for radial lens distortion ordistortion arising from curvature of the Earth in high-altitude or satellite scenes of large areas. An Order 3polynomial allows one change in sense of curvaturein any direction, and an Order 4 polynomial allowsfor an even more complex fit. These models cancorrect more complex image distortions, but may in-troduce distortion in areas between control points,especially around the edges of the image.

The minimum number ofrequired control pointsincreases with thepolynomial order:

Order 2: 6 control pointsOrder 3: 10 control pointsOrder 4: 15 control points

Hypothetical plot of inputversus output control pointposition in one direction,illustrating fit withpolynomials of differentorder.

Input X coordinate

Geo

grap

hic

X c

oord

inat

e

Order 3Polynomial

Order 2Polynomial

Polynomial transformations of thetest image produce very similarresults for all three orders, probablybecause of the small image area,dense network of control points, andsmall amount of terrain distortion.The Order 3 polynomial appears toproduce the best result (shownhere), comparable to the result fromthe plane projective transformation.Several of the section lines are stillbowed outward, an indication ofuncorrected terrain distortion.

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STEPSchoose Piecewise Affinefrom the Model menurun the resamplingprocess

Piecewise Affine Model

The highly localized and variable relief displacement distortion found in aerialphotographs of high-relief areas cannot be corrected using the AutomaticResampling process. Rectification of these images to a map geometry(orthorectification) requires the use of stereo images or an accurate digitalelevation model (DEM). See the tutorial entitled Making DEMs and Orthophotosfor more information.

The transformation models discussed previously allcompute a global best-fit solution for the entire im-age. They are best tailored to remove smoothly vary-ing distortions. Distortions that change significantlyover small areas are not corrected. In fact, a localdistortion that affects the positions of one or twocontrol points will influence the overall fit as muchas other correctly modeled points. As a result, thelocal distortion introduces a smaller component ofdistortion throughout the entire rectified image.

The Piecewise Affine model offers an alternativeapproach. Each control point is assumed to be inthe correct position, and the points are used to seg-ment the image into a network of triangles. An affinetransformation is then computed separately for eachtriangle. A single distorted control point locationonly affects the immediately surrounding triangles.At least six control points are required, but largernumbers produce better results. The Delauney triangulation procedure

is used to compute the optimumtriangular network, with someextrapolated boundary points addedfor completeness.

Example image partitionsusing the control points forthe test image.

The Piecewise Affine transformationof the test image produces a slightimprovement over all of the previousmethods. Because of the largenumber of control points and thegentle relief, the method is able tocorrect some of the terrain distortions,producing straighter sectionboundaries. This method is alsouseful for rectifying scanned mapmosaics that were assembled frompieces with various sources andscales (such as some property maps).

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STEPSchoose Geometric /Reproject from theTNTmips menuin the GeometricWarping window, clickSelect...select vector objectROADS from the SECT32Project Filechoose Plane Projectivefrom the Model optionbuttonclick [Run] and name theoutput object

Reprojecting Vector or CAD Objects

The Geometric Warpingprocess provides a subsetof the transformationmodels that are available inthe Automatic Resamplingprocess for rasters.

Vector object ROADS after warping toUTM using the Plane Projective model,displayed with green line color overthe SECT32 map object.

The Geometric Warping process permanentlyreprojects element locations in a vector or CAD ob-ject to the selected coordinate reference system. Youcan use this process with the From Georeferencemodel option to reproject geometric objects from onecoordinate reference system to another, typically tomatch that of other data you are using frequently ina project. Although the TNTmips Display processcan reproject a vector object on the fly to overlayother objects with a different reference system, theredisplay time for a large vector object may be sig-nificantly longer when reprojection is required.

If a vector (or CAD) object is created from a dis-torted, nongeoreferenced raster image, the resultingobject incorporates the spatial distortions of the par-ent object. These distortions remain even after

georeference control points are assignedto the vector object. For objects withcontrol point georeference, the Geomet-ric Warping process provides a subsetof the geometric transformation modelsdiscussed previously that can be usedto rectify the object.

Obviously, a better strategy is to georeference and rectify source imagerybefore creating a vector overlay. The vector object is then automaticallygeoreferenced and aligned to the desired coordinate reference system.

The ROADS object was created in theSpatial Data Editor by tracing the roadsand fence lines from an ungeoreferencedversion of the raw SECT32 image. It wasthen georeferenced to UTM using a USGSDigital Orthophoto Quad image.

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Review and ReferencesThere are several common situations in which you should use the AutomaticResampling process:

to reproject a set of georeferenced raster images to a common coordinatereference system and cell size to facilitate spatial analysis, classification,change detection in multidate imagery, or other scene-to-scene compari-sons of individual cell values. This includes scanned topographic andplanimetric maps that have been georeferenced but not yet aligned to thedesired coordinate system.

to remove or reduce certain types of simple geometric distortions from aerialor satellite imagery, producing a more map-like image geometry.

You do not need to resample component images before making a mosaic unlessdifferent images exhibit different types of distortion. The Mosaic process appliesa single selected geometric transformation model to rectify all georeferenced im-ages to a common coordinate reference system.

Successful rectification begins with careful georeferencing of the images. Youneed to determine the types of distortion present in the image and choose theappropriate geometric transformation model. Use this model in the georeferenceprocess to evaluate residual errors in control point locations, and again in theAutomatic Resampling process for the actual rectification.

References

Christensen, Albert H.J. (1996). The practice of piecewise fits with particular refer-ence to property mapping. Surveying and Land Information Systems, 56,165-183.

Jensen, John R. (1996). Introductory Digital Image Processing: A Remote Sens-ing Perspective (2nd ed.). Chapter 6, Image Preprocessing: Radiometricand Geometric Correction. Upper Saddle River, NJ: Prentice-Hall. pp. 107-137.

Novak, Kurt (1992). Rectification of digital imagery. Photogrammetric Engi-neering & Remote Sensing, 58, 339-344.

Wolberg, George (1990). Digital Image Warping. Chapter 3, Spatial Transfor-mations. Los Alamitos, CA: IEEE Computer Society Press, p. 41-94.

Wolf, Paul. R. and Ghilani, Charles. D. (1997). Adjustment Computations: Sta-tistics and Least Squares in Surveying and GIS. New York: John Wiley &Sons, 564 p.

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Advanced Software for Geospatial Analysis

Voice: (402) 477-9554 email: info@microimages.comFAX: (402) 477-9559 internet: www.microimages.com

MicroImages, Inc.11th Floor - Sharp Tower206 South 13th StreetLincoln, Nebraska 68508-2010 USA

MicroImages, Inc. publishes a complete line of professional software for advanced geospatialdata visualization, analysis, and publishing. Contact us or visit our web site for detailed prod-uct information.

TNTmips Pro TNTmips Pro is a professional system for fully integrated GIS, imageanalysis, CAD, TIN, desktop cartography, and geospatial database management.

TNTmips Basic TNTmips Basic is a low-cost version of TNTmips for small projects.

TNTmips Free TNTmips Free is a free version of TNTmips for students and profession-als with small projects. You can download TNTmips Free from MicroImages’ web site.

TNTedit TNTedit provides interactive tools to create, georeference, and edit vector, image,CAD, TIN, and relational database project materials in a wide variety of formats.

TNTview TNTview has the same powerful display features as TNTmips and is perfect forthose who do not need the technical processing and preparation features of TNTmips.

TNTatlas TNTatlas lets you publish and distribute your spatial project materials on CD orDVD at low cost. TNTatlas CDs/DVDs can be used on any popular computing platform.

Indexaffine transformation.................................14bilinear interpolation.............................10,11control points..............................3,13,16cubic convolution interpolation.............10,11extents, geographic..............................4,7-9geometric transformation models.......13-17,19georeference.................................3,5,9,13,19interpolation........................................4,10,11

bilinear...........................................10,11cubic convolution.............................10,11

models, geometric transformation...........13-17map projection, orienting to.........................5,6orientation....................................................4

to a direction..........................................9to a map projection...............................5,6to a reference raster..................................7

nearest neighbor resampling...................10,11piecewise affine transformation...................17perspective projection................................15plane projective transformation..................15polynomial transformation........................16reference raster.............................................7relief displacement.......................12,14,15,17resampling............................................3,4,10rubber sheeting........................................3terrain distortion..................................16,17

See relief displacementtilt distortion..................................14,15vector object, warping.................................18scale..............................................4,7warping..............................................3,6,7,18

RECTIFICATION