1. Image Registration January 2001 Gaia3D Inc. Sanghee Shin(shshin@gaia3d.com) Gaia3D Seminar Material

2. Gaia3D Inc. Aim of Image Registration Scanned maps, softcopy aerial photos, satellite images and other kinds of images usually don’t have any absolute coordinates. Image registration is a kind of process to assign a absolute geographic location (e.g. latitude and longitude) to a image on the basis of its relevant feature’s location. Geospatial relationships can be established between images and CAD, TIN, DEM or other kinds of geospatial data after image registration. Only then can we be assured of not comparing “apples and oranges” if we have placed all information in a precise registration.

3. Gaia3D Inc. Glossary of Terms(1) Referencing –Referencing is the techniques that reference image pixels to a master coordinate set. This set can be pixel coordinates of a master(reference) image or geographic/geodetic coordinate system(absolute referencing or georeferencing). This process does not involve an actual geometric transformation of the image to be referenced but rather the calculation of a coordinate transformation function. Registration –Registration is the process that comes after the computation of a coordinate transformation function. It involves the actual pixelwise geometric transformation of the slave images into the geometry of a master image or master dataset(e.g. GIS). We can then say that the image is “registered to a dataset.” After this process, the image can be overlaid on a per-pixel basis. Registration also involves reformatting of output pixel size and assignment of new gray values.

4. Gaia3D Inc. Glossary of Terms(2) Rectification –Rectification is the process of regisering a remote sensing image to a geographic/geodetic coordinate system(e.g. UTM or latitude, longitude coordinates) This process uses the same techniques as the registration process above, but now the master dataset is an absolute coordinate system. It is also called “geocoding.” Registration/rectification techniques can be combined if an image is registered to a geocoded master image. Resampling –Resampling is a part of the registration/rectification process. It involves the assignment of new gray values or digital numbers(DNs) for each pixel. As the location of registered or geocoded pixels will not actually project to an exact pixel location in the new image, new gray values have to be interpolated. Because this step involves a new sampling of data, it is called resampling.

5. Gaia3D Inc. Glossary of Terms(3) GeoCoding (GeoReferencing) –The process of assigning a geographic location (e.g. latitude and longitude) to a geographic feature on the basis of its address. This is beneficial because existing addresses can be automatically converted into a GIS database. The digital record for the feature must have a field which can be linked to a geographic base file with known geographic coordinates. This can simply be a relational data base join in which the geographic coordinates of the basemap are linked to the address records and made spatial. In most cases, a spatial search is required to determine the best geographic representation for each address. Georeferencing is an important tool for emergency response, package delivery and marketing applications. Georeferencing software and the creation and maintenance of base maps has become a significant business.

6. Gaia3D Inc. Process of Image Registration Collecting control points or ground control points(GCP) –Read absolute coordinates like (x, y) in meters from master image or master geospatial data set. Collecting relevant points in slave image –Read relative coordinates like pixels from slave image. Determining transformation method –Helmert, Affine, Projective, 2 nd Order, 3 rd Order, etc Determining resampling method –Nearest Neighborhood, BiLinear, BiCubic, etc

7. Gaia3D Inc. Collecting Points Collecting Control Points –Reading absolute coordinates of control points –P(x 0,y 0 ) Collecting Image Points –Reading pixel coordinates of relevant image points –P(x,y) It’s a kind of 2D transformation. So, F(x,y) = (x 0,y 0 )

8. Gaia3D Inc. 2D Transformation Method(1) Helmert –P`=[Rotation][Scaling][Translation.xy] P –x 0 = Ax - By + C –y 0 = Bx + Ay + D –More than 2 points needed Affine –P`=[Rotation][Scaling.xy][Translation.xy]P –x 0 = Ax + By + C –y 0 = Dx + Ey + F –More than 3 points needed Translation Rotation Scaling

9. Gaia3D Inc. 2D Transformation Method(2) Projective –x 0 = (Ax + By + C) / (Px + Qy + R) –y 0 = (Dx + Ey + F) / (Px + Qy + R) –More than 4 points needed Polynomial with higher degree –x 0 = A + Bx + Cy + Dx 2 + Exy + Fy 2 + … –y 0 = A` + B`x + C`y + D`x 2 + E`xy + F`y 2 + … –2 nd Order : more than 6 points needed –3 rd Order : more than 10 points needed Projection

10. Gaia3D Inc. Least Square Method Why LSM? –Most transformed points will not lie exactly on a expected control points(even when it should.) So, We need a mathematical method for determining the equation for the best-fit transformation. This method is called the Least-Square method. What is LSM? –F(x,y) – (x 0, y 0 ) = (d x, d y ) where d means deviation –(d x1, d y1 ), (d x2, d y2 ), (d x3, d y3 ), …, (d xn, d yn )

11. Gaia3D Inc. Image Resampling Resampling –Resampling is the process of determining new values for grid cells in an output grid that result from applying some geometric transformation to an input grid. The input grid may be in a different coordinate system, at a different resolution, or may be rotated with respect to the output grid.

12. Gaia3D Inc. Resampling Method(1) Nearest Neighbor Method –Nearest neighbor resampling uses the digital value from the pixel in the original image which is nearest to the new pixel location in the corrected image. This is the simplest method and does not alter the original values, but may result in some pixel values being duplicated while others are lost. This method also tends to result in a disjointed or blocky image appearance –Z(x,y) = Z @ min (d1, d2, d3, d4) –Discrete image generated

13. Gaia3D Inc. Resampling Method(2) Bilinear Method –Bilinear interpolation resampling takes a weighted average of four pixels in the original image nearest to the new pixel location. The averaging process alters the original pixel values and creates entirely new digital values in the output image. This may be undesirable if further processing and analysis, such as classification based on spectral response, is to be done. If this is the case, resampling may best be done after the classification process.

14. Gaia3D Inc. Resampling Method(3) Cubic Convolution –Cubic convolution resampling goes even further to calculate a distance weighted average of a block of sixteen pixels from the original image which surround the new output pixel location. As with bilinear interpolation, this method results in completely new pixel values. However, these two methods both produce images which have a much sharper appearance and avoid the blocky appearance of the nearest neighbour method.