# Why do we need reference points in GIS

## Help

Raster data is generally created when scanning maps or capturing aerial and satellite images. Scanned map datasets typically do not contain spatial reference data embedded in the file or external to it. In the case of aerial and satellite images, the positional accuracy achieved is often insufficient, so that the data are not congruent with existing data. In order for raster datasets to work in conjunction with other spatial data, an adjustment or geographic referencing to the map coordination system may need to be made. A map coordinate system is defined via a map projection (a method for mapping the curved surface of the earth onto a plane).

When you geographically reference the raster data, you define the location using map coordinates and assign the coordinate system of the data frame. Georeferencing raster data enables this data to be viewed, queried, and analyzed along with other geographic data. The Georeferencing toolbar enables you to georeference raster datasets, raster layers (which may have raster capabilities), image services, and raster products.

The general steps involved in geo-referencing raster datasets are:

- In ArcMap, add the grid that you want to align with the projected data.
##### Note:

In the layer list on the Georeferencing toolbar, raster layers, image service layers, and CAD layers are displayed as valid data types. The layers must either be in the same coordinate system as the data frame or have no defined spatial reference.

- Add links that connect known locations in the raster dataset to known locations in map coordinates. Using the Automatic Registration tool you can create links automatically.
- Save the geographic referencing information when you are satisfied with the customization (also known as a "registry").
- Permanent conversion of the raster dataset (optional).

Watch the georeferencing video demonstrating how to georeference a raster dataset.

### Align the grid with control points

In general, with georeferencing, you align the raster data with existing spatial data (target data), such as: For example, on georeferenced rasters or a feature class for vectors that is in the desired map coordinate system. Several control points must therefore be determined on the earth's surface, whose position coordinates are known. These positions must be present both in the raster dataset and in the spatial reference data (target data). Control points are positions that can be determined both in the raster dataset and in real coordinates. Many different types of features can be used as identifiable locations, such as road junctions and crossings of waterways, the delta of a river, ridges, the end of a headland, the corner of a field, street corners, or the intersection of two rows of hedges.

The control points are used to create a polynomial transform that changes the raster dataset from the original location to the spatially correct coordinates. The connection of a control point in the raster dataset (starting point) with the corresponding point in the target data (target point) is called a link.

In the following illustration, a control point (yellow cross) is positioned over the vector target data at a street intersection, and the associated control point (green cross) is positioned over the raster dataset. The corresponding link is shown by the blue connecting line between the two control points.

The number of links to create depends on the complexity of the transform you want to use to transform the raster dataset into map coordinates. Inserting more links does not automatically lead to a better registration. Whenever possible, you should spread the links across the entire raster dataset rather than concentrating them in one area. One link near each corner of the raster dataset and a few links across the area are enough to get a good result.

Typically, the greater the overlap between the raster dataset and the target data, the better the fit. The points with which the raster dataset is geographically referenced are spread out more widely. For example, if the target data were only a quarter of the area of the raster dataset, the points to which the raster dataset could align would be limited to the area of the overlap. The areas outside the overlap are therefore probably not transformed correctly.

Always keep in mind that georeferenced data can only be as good as the transformation parameters used. To avoid errors as much as possible, you should choose data in the highest possible resolution and with the largest scale to be used as the target for georeferencing.

### Transform the grid

When you have created enough links, you can permanently transform the raster dataset into map coordinates of the target data. You can determine the correct positions of the map coordinates of all cells in the grid with a polynomial, spline, fitting or projective transformation.

The polynomial transformation uses a polynomial that is calculated based on the control points and an algorithm for fitting using the least squares method. The polynomial is optimized for global accuracy, but cannot guarantee local accuracy. The polynomial transformation uses two formulas: one to calculate the X coordinate (output) and one to calculate the Y coordinate for an XY position (input). The goal of the least squares algorithm is to derive a general formula that can be applied to all points, but usually with little shift in the positions of the control points. The number of uncorrelated control points required for this method is one for the transformation 0, three for the affine transformation of the first order, six for the second order and ten for the third order. With lower order polynomials a random error is usually output and with higher order polynomials an extrapolation error is usually output.

With a first order polynomial transformation, images are often geographically referenced. The following is the equation for transforming a raster dataset using affine polynomial transform (first order). You will see how six parameters are used to define how the rows and columns of a grid are transformed into map coordinates.

A polynomial transformation 0 is used for the data offset. This is often used when data is already georeferenced, but a small offset makes the data more consistent. Only one link is required to perform a polynomial transform 0. It's a good idea to create a few links and then choose the link that is as specific as possible.

Move, scale, and rotate the raster dataset using a first-order (or affine) transform. Straight lines on the raster dataset typically appear as straight lines in the transformed raster dataset as well. Therefore, squares and rectangles are converted into parallelograms of any scale and any angular orientation.

With at least three links, the math equation used in a first order transformation can represent each grid point exactly at the target location. More than three links can produce errors or residuals that are spread across all of the links. You should enter more links, however, because if only three links are used and one of them is broken, it will have a much greater impact on the transformation. As a result, the overall accuracy of the transformation increases, although creating more links will result in errors in the mathematical transformation.

The higher the order of the transformation, the more complex the distortion that can be corrected. In general, you rarely need fourth order transformations. For higher-order transformations, more links are required, which in turn lead to significantly longer computing times. If you just need to stretch, shrink, scale, and rotate your raster dataset, consider using a first-order transform. If warping the raster dataset is necessary, consider using a second or third order transform.

Spline transform is a true rubbersheeting technique that optimizes local accuracy, but not global accuracy. It is based on a spline function, a piecewise composite polynomial in which continuity and smoothness are maintained between neighboring polynomials. In the case of a spline, the source control points are precisely transformed into target control points. Accuracy cannot be guaranteed for pixels beyond the control points. This transformation is useful when the control points are important and need to be precisely registered. Adding more control points can increase the overall accuracy of the spline transformation. At least ten control points are required for a spline.

In the fit transformation, optimization is done for both least squares fit and local accuracy. It is based on an algorithm in which a polynomial transformation and TIN interpolations (Triangulated Irregular Network) are combined. In the case of an adaptation transformation, a polynomial transformation is carried out with two groups of control points. A TIN interpolation is then used to optimize the local adaptation of the control points to the target control points. At least three control points are required for an adjustment.

Projective transformation can deform lines so that they stay straight. As a result, lines that were previously parallel may not stay parallel. The projective transformation is particularly useful for skewed images, scanned maps, and some image products such as: B. Landsat and Digital Globe. At least four links are required to perform a projective transformation. If only four links are used the RMS error will be 0. If more points are used the RMS error will be a little over 0.

### Interpret the RMS error

Once the general formula has been derived and applied to the control point, a measure of the error is returned: the residual error. The error is the difference between the set position of the control points and the actual position of the point. The total error can be calculated using the root mean square value of all residuals and results in the RMS error. This value describes how even the transformation is between the various control points (left). If the errors are particularly large, you can remove and add control points to adjust the errors.

The RMS error can provide good information about the accuracy of the transformation. However, you shouldn't confuse a low RMS error with an accurate registry. The transformation can still contain significant errors, e.g. B. can be attributed to a badly entered control point. The more control points of the same quality you can insert, the more precisely the polynomial can convert the input data into output coordinates. As a rule, fitting and spline transformations result in an RMS error of close to 0 or equal to 0. However, this does not mean that the image is perfectly georeferenced.

The forward residual tells you the error in the same units as the data frame spatial reference. The inverse residual shows you the error in the pixel units. The forward inverse residual is a measure of how close the accuracy is, measured in pixels. Any residuals that are closest to zero are considered more precise residuals.

### Resampling of the raster dataset

You perform a geometric transformation when rectifying, transforming, projecting, or resampling raster datasets, converting the projection, or changing the size of cells. Geometric transformation is the process of changing the geometry of a raster dataset in terms of its coordinate range. Types of geometric transformations include rubbersheeting (usually used for geographic referencing), projection (transforming the data from one projection to another using the projection information), transfer (evenly shifting the coordinate system), and rotation (rotating all coordinates by a certain angle ) and changing the cell size of the dataset.

After applying the geometric transformation to the input raster, the cell centers of the input raster rarely match the cell centers of the output raster. Nevertheless, values must be assigned to the centers.

Although it appears that every cell in a raster dataset is being transformed to the map coordinate, in reality the process is reversed. In geographic referencing, a matrix of empty cells is calculated in map coordinates. Each empty cell is assigned a value based on a process called resampling.

The three most popular resampling methods are nearest neighbor resampling, bilinear interpolation, and cubic convolution. These methods assign a value to each blank cell by examining the cells in the ungeoreferenced raster dataset.

Nearest neighbor resampling is the fastest method of resampling and is suitable for categorized or thematic data because it does not change the value of the input cells. If the position of the cell center point on the output raster dataset is also known on the input raster, this method determines the position of the closest cell center point on the input raster and assigns the value of that cell to the cell in the output raster.

Nearest neighbor resampling does not change the values of the cells in the input raster dataset. The value 2 in the input raster is retained in the output raster and is not changed to 2,2 or 3. Because the output cell values remain unchanged, nearest neighbor resampling should be used for nominal or ordinal data, where each value represents a class, part, or classification (category data such as land use, soil, or forest types).

With bilinear interpolation, the value of the output raster is determined based on the value of the four closest input cell centers. The new value for the output cell is a weighted average of these four values, adjusted to account for the distance of these cells from the center of the output cell on the input raster. This interpolation method produces a smoother looking surface than that which would result from the "nearest neighbor resampling" method.

Since the values for the output cells are calculated according to the relative position and value of the input cells, bilinear interpolation is preferred for data where the position of a known point or geographic object determines the value assigned to the cell (i.e., continuous surfaces). The elevation, slope, noise level of an airport and the salinity of the groundwater near an estuary are phenomena that are represented as continuous surfaces and that have been very precisely resampled using bilinear interpolation.

Cubic convolution is similar to bilinear interpolation, except that it calculates the weighted average of the 16 densest input cell centers and their values. In the case of cubic convolution, the data are i. d. Usually sharpened more than with bilinear interpolation, since more cells are included in the calculation of the output value. Therefore, this resampling method is often used when resampling images, e.g. B. for satellite images or aerial images.

Bilinear interpolation or cubic convolution should not be used with category data because the categories will not be preserved in the output raster dataset. However, all three methods can be used for continuous data, whereby the method "nearest neighbor resampling" gives a block-shaped output, the bilinear interpolation gives smoother results and the cubic convolution gives results with a sharp expression. For large resampling projects, it is recommended that you create a prototype, apply multiple resampling techniques to it, and evaluate them carefully to determine the most appropriate method for your data.

### Should you rectify the grid?

You can permanently transform raster datasets after georeferencing them by selecting the Rectify command on the Georeferencing toolbar or using the Rectify tool. You can also save the transformation information in the auxiliary files by selecting Update Georeferencing on the Georeferencing toolbar.

The rectification or rectification creates a new raster dataset that is geographically referenced using the map coordinates and the spatial reference. You can save this as BIL, BIP, BMP, BSQ, DAT, GIF, GRID, IMG, JPEG, JPEG 2000, PNG or TIFF. ArcGIS does not require you to permanently transform raster datasets to display them with other spatial data.A permanent transformation is recommended, however, if you are performing an analysis or want to use the raster dataset in another software package in which external geographic referencing information created in the world file is not recognized.

Updating the georeferencing saves the transformation information in external files. No new raster dataset will be created. This only happens if you permanently transform the raster dataset. For file-based raster datasets, e.g. For example, in TIFF format, the transformation is usually saved in an external XML file (with the extension "AUX.XML"). If the raster dataset is an unprocessed image (e.g. BMP) and the transformation is affine, it is written to a world file. For a raster dataset in a geodatabase, the Update Georeferencing command saves the transformation of the geographic data in an additional internal file of the raster dataset. Updating a raster layer, image service, or mosaic layer updates only the layer within the map document. The georeferencing information is not saved back to the source.

The following table shows how destination types are saved.

#### Georeferencing of different grids

Data type | Result |
---|---|

Raster dataset | The Update Georeferencing command updates the raster dataset. |

Raster layer | The raster layer is updated using the Update Georeferencing command. The source rasters are not affected. |

Image service layer | Image services are not updated on the server. After Update Georeferencing is performed, you can save the map document (.mxd) or create a layer (.lyr) file to save the georeferencing. |

Raster product | The underlying raster dataset files are not updated from the raster product. After Update Georeferencing is performed, you can save the map document (.mxd) or create a layer (.lyr) file to save the georeferencing. |

One-function grid | The underlying raster files are not updated using a raster function. After Update Georeferencing is performed, you can save the map document (.mxd) or create a layer (.lyr) file to save the georeferencing. |

##### License:

An ArcGIS for Desktop Standard or ArcGIS for Desktop Advanced license is required to rectify or update the georeferencing of raster datasets in an enterprise database.

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