# ImgLib2 Examples

 Name Examples Software ImgLib2 Author Stephan Preibisch Maintainer Stephan Preibisch, Curtis Rueden Source on GitHub

## Jupyter notebook

This tutorial is also available in Jupyter notebook form here!

## Introduction & required files

This page shows eight increasingly complex examples of how to program with ImgLib2. The intention of these examples are not to explain ImgLib2 concepts, but rather to give some practical hints how to work with the library and to grasp the principles in a learning-by-doing way.

All examples presented on this page are always entire classes including a main method to run them. Simply copying them into your favorite editor (e.g. the Script Editor) and compile & run them. The required Java libraries (jar files) are part of ImageJ and can be found in ImageJ.app/jars/:

• imglib2 (the core)
• imglib2-algorithm (algorithms implemented in ImgLib2)
• imglib2-algorithm-gpl (for example 6b and 6c: GPL-licensed algorithms implemented in ImgLib2—ships with Fiji only, not plain ImageJ2, for licensing reasons)
• imglib2-ij (the ImageJ interaction)
• imglib2-realtransform (for example 8)
• scifio (for reading and writing files)
• ij (ImageJ 1.x core, used for display)

Alternately, you can access the examples from the ImgLib-tutorials Git repository . After cloning the source code, open the project in your favorite IDE. See Developing ImgLib2 for further details.

## Example 1 - Opening, creating and displaying images

The first example illustrates the most basic operations of opening, creating, and displaying image content in ImgLib2. It will first focus on entires images (**Img**), but also show how to display subsets only.

### Example 1a - Wrapping ImageJ images

If you are already an ImageJ programmer, you might find it the easiest way to simply wrap an ImageJ image into ImgLib2. Here, the data is not copied, so editing the image in ImgLib2 will also modify the ImageJ ImagePlus.

Internally, we use a compatibility Img to represent the data which is as fast as ImageJ but in the case of higher dimensionality (>2d) is slower than ImgLib2 can do with the ArrayImg. Furthermore you are limited in dimensionality (2d-5d), in the type of data (UnsignedByteType, UnsignedShortType, FloatType and ARGBType) and maximal size of each 2d-plane (max. 46000x46000).

### Example 1b - Opening an ImgLib2 image

The typical way to open an image in ImgLib2 is to make use of the SCIFIO importer. Below you see two examples of how to open an image as (a) its own type (e.g. UnsignedByteType) and (b) as float (FloatType). For (a) we assume, however, that the file contains some real valued numbers as defined by the interface RealType. Color images are opened as well and color is represented as its own dimension (like in the ImageJ Hyperstacks).

Note that for (a) we use an ArrayImg to hold the data. This means the data is held in one single java basic type array which results in optimal performance. The absolute size of image is, however, limited to 2^31-1 (~2 billion) pixels. The type of Img to use is set by passing an ImgOptions configuration when calling the ImgOpener.

In (b) we use a CellImg instead. It partitions the image data into n-dimensional cells each holding only a part of the data. Further, SCIFIO takes care of caching cells in and out of memory as needed, greatly reducing the memory requirement to work with very large images.

The SCIFIO importer also requires Types that implement NativeType, which means it is able to map the data into a Java basic type array. All available Types until now are implementing NativeType, if you want to work with some self-developed Type it would be easiest to copy the opened Img afterwards. Please also note that until now, the only Img that supports non-native types is the ListImg which stores every pixel as an individual object!

Important: it does not matter which type of Img you use to hold the data as we will use Iterators and RandomAccesses to access the image content. It might be, however, important if you work on two Img at the same time using Iterators, see Example2.

### Example 1c - Creating a new ImgLib2 image

Another important way to instantiate a new ImgLib2 Img is to create a new one from scratch. This requires you to define its Type as well as the ImgFactory to use. It does additionally need one instance of the Type that it is supposed to hold.

Once you have one instance of an Img, it is very easy to create another one using the same Type and ImgFactory, even if it has a different size. Note that the call img.firstElement() returns the first pixel of any Iterable, e.g. an Img.

### Example 1d - Displaying images partly using Views

By using the concept of Views it is possible to display only parts of the image, display a rotated view, and many more cool things. Note that you can also concatenate them. Views are much more powerful than shown in this example, they will be increasingly used throughout the examples.

A View almost behaves similar to an Img, and in fact they share important concepts. Both are RandomAccessible, and Views that are not infinite are also an Interval (i.e. those Views have a defined size) and can therefore be made Iterable (see example 2c). In ImgLib2, all algorithms are implemented for abstract concepts like RandomAccessible, Iterable or Interval. This enables us, as can be seen below, to display a View the exact same way we would also display an Img.

Shows the original image, the View of an interval, as well as the by 90 degree rotated version of the view. Note that only the original image in kept in memory, both Views are completely virtual.

## Example 2 - How to use Cursor, RandomAccess and Type

The following examples illustrate how to access pixels using Cursor and RandomAccess, their basic properties, and how to modify pixel values using Type.

Accessing pixels using a Cursor means to iterate all pixels in a way similar to iterating Java collections. However, a Cursor only ensures to visit each pixel exactly once, the order of iteration is not fixed in order to optimize the speed of iteration. This implies that that the order of iteration on two different Img is not necessarily the same, see example 2b! Cursors can be created by any object that implements IterableInterval, such as an Img. Views that are not infinite can be made iterable (see example 2c). Note that in general a Cursor has significantly higher performance than a RandomAccess and should therefore be given preference if possible.

In contrast to iterating image data, a RandomAccess can be placed at arbitrary locations. It is possible to set them to a specific n-dimensional coordinate or move them relative to their current position. Note that relative movements are usually more performant. A RandomAccess can be created by any object that implements RandomAccessible, like an Img or a View.

Localizable is implemented by Cursor as well as RandomAccess, which means they are able to report their current location. However, for Cursor we differentiate between a LocalizingCursor and a normal Cursor. A LocalizingCursor updates his position on every move, no matter if it is queried or not whereas a normal Cursor computes its location on demand. Using a LocalizingCursor is more efficient if the location is queried for every pixel, a Cursor will be faster when localizing only occasionally.

The Sampler interface implemented by Cursor and RandomAccess provides access to the Type instance of the current pixel. Using the Type instance it is possible to read and write its current value. Depending on the capabilities of the Type more operations are available, e.g. +,-,*,/ if it is a NumericType.

Note that IterableInterval implements the java.lang.Iterable interface, which means it is compatible to specialized Java language constructs:

// add 5 to every pixel
for ( UnsignedByteType type : img )


### Example 2a - Duplicating an Img using a generic method

The goal of this example is to make a copy of an existing Img. For this task it is sufficient to employ Cursors. The order of iteration for both Img’s will be the same as they are instantiated using the same ImgFactory. It is possible to test if two IterableInterval have the same iteration order:

boolean sameIterationOrder =
interval1.iterationOrder().equals( interval2.iterationOrder() );


The copy method itself is a generic method, it will work on any kind of Type. In this particular case it works on a FloatType, but would also work on anything else like for example a ComplexDoubleType. The declaration of the generic type is done in the method declaration:

public < T extends Type< T > > Img< T > copyImage( ... )


< T extends Type< T > > basically means that T can be anything that extends Type. These can be final implementations such as FloatType or also intermediate interfaces such as RealType. This, however, also means that in the method body only operations supported by Type will be available. Note that the method returns a T, which also means that in the constructor from which we call method it will also return an **Img** as we provide it with one.

### Example 2b - Duplicating an Img using a different ImgFactory

WARNING: The copyImageWrong method in this example makes a mistake on purpose! It intends to show that the iteration order of Cursors is important to consider. The goal is to copy the content of an ArrayImg (i.e. an Img that was created using an ArrayImgFactory) into a CellImg. Using only Cursors for both images will have a wrong result as an ArrayImg and a CellImg have different iteration orders. An ArrayImg is iterated linearly, while a CellImg is iterate cell-by-cell, but linearly within each cell.

Shows the result if two Cursors are used that have a different iteration order. Here we are wrongly copying an ArrayImg (left) into a CellImg (right).

The correct code for the copy-method (in copyImageCorrect) requires the use of a RandomAccess. We use a Cursor to iterate over all pixels of the input and a RandomAccess which we set to the same location the output. Note that the setPosition() call of the RandomAccess directly takes the Cursor as input, which is possible because Cursor implements Localizable. Please also note that we use a LocalizingCursor instead of a normal Cursor because we need the location of the Cursor at every pixel.

### Example 2c - Generic copying of image data

In order to write a method that generically copies data requires an implementation for the underlying concepts of RandomAccessible, Interable and Interval. In that way, it will run on Img, View and any other class implemented for these interfaces (even if they do not exist yet).

Therefore we design the copy method in a way that the target is an IterableInterval and the source is RandomAccessible. In this way, we simply iterate over the target and copy the corresponding pixels from the source.

As the source only needs to be RandomAccessible, it can be basically anything that can return a value at a certain location. This can be as simple as an Img, but also interpolated sparse data, a function, a ray-tracer, a View, ….

As the target needs to be an IterableInterval, it is more confined. This, however does not necessarily mean that it can only be an Img or a View that is not infinite. It simply means it has to be something that is iterable and not infinite, which for example also applies to sparse data (e.g. a list of locations and their values).

## Example 3 - Writing generic algorithms

Examples 1 and 2 tried to introduce important tools you need in order to implement algorithms with ImgLib2. This example will show three generic implementations of algorithms computing the min/max, average as well as the center of mass.

The core idea is to implement algorithms as generic as possible in order to maximize code-reusability. In general, a good way to start is to think: What are the minimal requirements in order to implement algorithm X? This applies to all of the following three concepts:

• Type: You should always use the most abstract Type possible, i.e. the one that just offers enough operations to perform your goal. In this way, the algorithm will be able to run on Types you might not even have thought about when implementing it. A good example is the min&max search in example 3a. Instead of implementing it for FloatType or the more abstract RealType, we implement it for the even more abstract Comparable & Type.
• Image data: Every algorithm should only demand those interfaces that it requires, not specific implementations of it like Img. You might require RandomAccessible (infinite), RandomAccessibleInterval (finite), Iterable (values without location), IterableInterval (values and their location) or their corresponding interfaces for real-valued locations RealRandomAccessible, RealRandomAccessibleRealInterval and IterableRealInterval. Note that you can concatenate them if you need more than one property.
• Dimensionality: Usually there is no reason to restrict an algorithm to a certain dimensionality (like only for two-dimensional images), at least we could not really come up with an convincing example
If the application or plugin your are developing addresses a certain dimensionality (e.g. stitching of panorama photos) it is understandable that you do not want to implement everything n-dimensionally. But try to implement as many as possible of the smaller algorithm you are using as generic, n-dimensional methods. For example, everything that requires only to iterate the data is usually inherently n-dimensional.

Following those ideas, your newly implemented algorithm will be applicable to any kind of data and dimensionality it is defined for, not only a very small domain you are currently working with. Also note that quite often this actually makes the implementation simpler.

Searching for the minimal and maximal value in a dataset is a very nice example to illustrate generic algorithms. In order to find min/max values, Types only need to be able to compare themselves. Therefore we do not need any numeric values, we only require them to implement the (Java) interface Comparable. Additionally, no random access to the data is required, we simply need to iterate all pixels, also their location is irrelevant. The image data we need only needs to be Iterable.

Below we show three small variations of the min/max search. First we show the implementation as described above. Second we illustrate that this also works on a standard Java ArrayList. Third we show how the implementation changes if we do not only want the min/max value, but also their location. This requires to use IterableInterval instead, as Cursor can return their location.

#### Example 3a - Variation 2

Note that this example works just the same way if the input is not an Img, but for example just a standard Java ArrayList.

#### Example 3a - Variation 3

If we want to compute the location of the minimal and maximal pixel value, an Iterator will not be sufficient as we need location information. Instead the location search will demand an IterableInterval as input data which can create Cursors. Apart from that, the algorithm looks quite similar. Note that we do not use a LocalizingCursor but only a Cursor the location happens only when a new maximal or minimal value has been found while iterating the data.

### Example 3b - Computing average

In a very similar way one can compute the average intensity for image data. Note that we restrict the Type of data to RealType. In theory, we could use NumericType as it offers the possibility to add up values. However, we cannot ensure that NumericType provided is capable of adding up millions of pixels without overflow. And even if we would ask for a second NumericType that is capable of adding values up, it might still have numerical instabilities. Note that actually every Java native type has those instabilities. Therefore we use the RealSum class that offers correct addition of even very large amounts of pixels. As this implementation is only available for double values, we restrict the method here to RealType.

## Example 4 - Specialized iterables

Example 4 will focus on how to work with specialized iterables. They are especially useful when performing operations in the local neighborhood of many pixels - like finding local minima/maxima, texture analysis, convolution with non-separable, non-linear filters and many more. One elegant solution is to write a specialized Iterable that will iterate all pixels in the local neighborhood. We implemented two examples:

• A HyperSphere that will iterate a n-dimensional sphere with a given radius at a defined location.
• A LocalNeighborhood that will iterate n-dimensionally all pixels adjacent to a certain location, but skip the central pixel (this corresponds to an both neighbors in 1d, an 8-neighborhood in 2d, a 26-neighborhood in 3d, and so on …)

### Example 4a - Drawing a sphere full of spheres

In the first sample we simply draw a sphere full of little spheres. We therefore create a large HyperSphere in the center of a RandomAccessibleInterval. Note that the HyperSphere only needs a RandomAccessible, we need the additional Interval simply to compute the center and the radius of the large sphere. When iterating over all pixels of this large sphere, we create small HyperSpheres at every n’th pixel and fill them with a random intensity.

This example illustrates the use of specialized Iterables, and emphasizes the fact that they can be stacked on the underlying RandomAccessible using the location of one as the center of a new one. Note that we always create new instances of HyperSphere. The code reads very nicely but might not offer the best performance. We therefore added update methods to the HyperSphere and its Cursor that could be used instead.

Another interesting aspect of this example is the use of the ImagePlusImgFactory, which is the compatibility container for ImageJ. If the required dimensionality and Type is available in ImageJ, it will internally create an ImagePlus and work on it directly. In this case, one can request the ImagePlus and show it directly. It will, however, fail if Type and dimensionality is not supported by ImageJ and throw a ImgLibException.

Shows the result of example 4a for the (a) two-dimensional, (b) three-dimensional and (c) four-dimensional case. The image series in (c) represents a movie of a three-dimensional rendering. The images of (b) and (c) were rendered using the ImageJ 3d Viewer.

### Example 4b - Finding and displaying local minima

In this example we want to find all local minima in an image an display them as small spheres. To not capture too much of the noise in the image data, we first perform an in-place Gaussian smoothing with a sigma of 1, i.e. the data will be overwritten with the result. A complete documentation of the gauss package for ImgLib2 can be found here.

We display the results using a binary image. Note that the BitType only requires one bit per pixel and therefore is very memory efficient.

The generic method for minima detection has some more interesting properties. The type of the source image data actually does not require to be of Type, it simply needs something that is comparable. The LocalNeighborhood will iterate n-dimensionally all pixels adjacent to a certain location, but skip the central pixel (this corresponds to an both neighbors in 1d, an 8-neighborhood in 2d, a 26-neighborhood in 3d, and so on …). This allows to efficiently detect if a pixel is a local minima or maxima. Note that the Cursor that performs the iteration can have special implementations for specific dimensionalities to speed up the iteration. See below the example for a specialized three-dimensional iteration:

Acces plan for a 3d neighborhood, starting at the center position marked by (x). The initial
position is, in this example, NOT part of iteration, which means the center pixel is not iterated.
Note that every step except for the last one can be done with a very simple move command.

upper z plane (z-1)        center z plane (z=0)        lower z plane(z+1)
-------------          -------------           -------------
| 2 | 1 | 8 |          | 11| 10| 9 |           | 20| 19| 18|
|------------          -------------           -------------
| 3 | 0 | 7 |          | 12| x | 16|           | 21| 25| 17|
|------------          -------------           -------------
| 4 | 5 | 6 |          | 13| 14| 15|           | 22| 23| 24|
-------------          -------------           -------------

Please note as well that if one would increase the radius of the RectangleShape to more than 1 (without at the same time changing the View on source that creates an inset border of exactly this one pixel), this example would fail as we would try to write image data outside of the defined boundary. OutOfBoundsStrategies which define how to handle such cases is discussed in example 5.

Shows the result of the detection of local minima after the Gaussian blurring. (a) depicts the input image, (b) the blurred version (sigma=1) and (c) all local mimina drawn as circles with radius 1.

## Example 5 - Out of bounds

Many algorithms like convolutions require to access pixels outside of an Interval, i.e. also pixels outside of an image. In ImgLib2 this is handled using Views which convert a RandomAccessibleInterval into an infinite RandomAccessible using an OutOfBoundsStrategy. Those infinite RandomAccessibles are able to return pixel values at any arbitrary location.

Important: One should never access pixels outside of the defined Interval as it will in most cases result in unexpected behavior, depending on the kind of underlying RandomAccessible. If it is for example an Img, it will return wrong values or throw an exception.

Which OutOfBoundsStrategies to use depends on task you want to perform. For convolutions we suggest the mirror strategy as it introduces the least artifacts. When working on Fourier images, the periodic strategy applies best as it correctly mimics its spatial properties. Random Value strategies might be useful to avoid accidental correlations and constant value strategies are the most performant and might work well for simple operations or to avoid exceptions when accidental writing or reading outside of the Interval occurs.

Illustrates the effect of various OutOfBoundsStrategies. (a) shows out of bounds with a constant value, (b) shows a mirroring strategy, (c) shows the periodic strategy, and (d) shows a strategy that uses random values.

## Example 6 - Basic built-in algorithms

ImgLib2 contains a growing number of built-in standard algorithms. In this section, we will show some of those, illustrate how to use them and give some examples of what it might be used for.

Typically algorithms provide static methods for simple calling, but they also have classes which you can instantiate yourself to have more options.

Important: Algorithms do not allow to work on a different dimensionality than the input data. You can achieve that by selecting hyperslices using Views (see Example 6a - version 4). In this way you can for example apply two-dimensional gaussians to each frame of a movie independently.

### Example 6a - Gaussian convolution

The Gaussian convolution has its own wiki page. You can apply the Gaussian convolution with different sigmas in any dimension. It will work on any kind RandomAccessibleInterval. Below we show a examples of a simple gaussian convolution (variation 1), convolution using a different OutOfBoundsStrategy (variation 2), convolution of a part of an Interval (variation 3), and convolution of in a lower dimensionality than the image data (variation 4).

Shows the result of the four examples for Gaussian convolution. (a) shows a simple Gaussian convolution with sigma=8. (b) shows the same Gaussian convolution but using an OutOfBoundsConstantValue instead. (c) shows the result when convolving part of the image in-place. (d) shows the result when individually convolving 1-dimensional parts on the image.

#### Example 6a - Gaussian convolution (variation 1 - simple)

Here, we simply apply a Gaussian convolution with a sigma of 8. Note that it could be applied in-place as well when calling Gauss.inFloatInPlace( … ). The Gaussian convolution uses by default the OutOfBoundsMirrorStrategy.

#### Example 6a - Gaussian convolution (variation 2 - different OutOfBoundsStrategy)

Here we use an OutOfBoundsStrategyConstantValue instead. It results in continuously darker borders as the zero-values from outside of the image are used in the convolution. Note that the computation is done in-place here. However, we still need to provide an ImgFactory as the Gaussian convolution needs to create temporary image(s) - except for the one-dimensional case.

#### Example 6a - Gaussian convolution (variation 3 - only part of an Interval)

Here we only convolve part of an Interval, or in this case part of the Img. Note that for convolution he will actually use the real image values outside of the defined Interval. The OutOfBoundsStrategy is only necessary if the kernel is that large so that it will actually grep image values outside of the underlying Img.

Note: if you wanted, you could force him to use an OutOfBoundsStrategy directly outside of the Interval. For that you would have to create an RandomAccessibleInterval on the Img, extend it by an OutOfBoundsStrategy and give this as input to the Gaussian convolution.

#### Example 6a - Gaussian convolution (variation 4 - with a lower dimensionality)

This example shows howto apply an algorithm to a lower dimensionality as the image data you are working on. Therefore we use Views to create HyperSlices which have n-1 dimensions. We simply apply the algorithm in-place on those Views which will automatically update the image data in the higher-dimensional data.

Specifically, we apply 1-dimensional Gaussian convolution in 30-pixel wide stripes using a sigma of 16. ‘‘Note that whenever you request an HyperSlice for a certain dimension, you will get back a View that contains all dimensions but this one.’’

### Example 6b - Convolution in Fourier space

In image processing it is sometimes necessary to convolve images with non-separable kernels. This can be efficiently done in Fourier space exploiting the convolution theorem. It states that a convolution in real-space corresponds to a multiplication in Fourier-space, as vice versa. Note that the computation time for such a convolution is independent of the size and shape of the kernel.

Note that it is useful to normalize the kernel prior to Fourier convolution so that the sum of all pixels is one. Otherwise, the resulting intensities will be increased.

Shows the effect of the Fourier convolution. The left image was convolved with the kernel depicted in the lower left corner, the right panel shows the convolved image. Note that the computation speed does not depend on the size or the shape of the kernel.

Important: This source code is only GPLv2!

### Example 6c - Complex numbers and Fourier transforms

In this example we show how to work with complex numbers and Fourier transforms. We show how to determine the location of a template in an image exploiting the Fourier Shift Theorem. We therefore compute the Fast Fourier Transform of a template, invert it and convolve it in Fourier space with the original image.

Computing an FFT is straight forward. It does not offer a static method because the instance of the FFT is required to perform an inverse FFT. This is necessary because the input image needs to be extended to a size supported by the 1-d FFT method (edu_mines_jtk.jar). In order to restore the complete input image remembering those parameters is essential.

For the display of complex image data we provide Converters to display the gLog of the power-spectrum (default), phase-spectrum, real values, and imaginary values. It is, however, straight forward to implement you own Converters.

Note that for inverting the kernel we use methods defined for ComplexType, also the basic math operations add, mul, sub and div are implemented in complex math. The inverse FFT finally takes the instance of the FFT as a parameter from which it takes all required parameters for a correct inversion.

The final convolution of the inverse template with the image is performed using the FourierConvolution (see example 6b). Note that all possible locations of the template in the image have been tested. The peak in the result image clearly marks the location of the template, while the computation time for the whole operation takes less than a second.

Shows the result and intermediate steps of the template matching using the Fourier space. In the upper panel you see the input image as well as the template that we use from matching. Below we show four different views of the Fast Fourier Transform of the template: the power spectrum, the phase spectrum, the real values, and the imaginary values. In the lower panel you see the result of the convolution of the inverse template with the image. The position where the template was located in the image is significantly visible. In the bottom right corner you see the inverse FFT of the inverse kernel.

Important: This source code is only GPLv2!

## Example 7 - Interpolation

Interpolation is a basic operation required in many image processing tasks. In the terminology of ImgLib2 it means to convert a RandomAccessible into a RealRandomAccessible which is able to create a RealRandomAccess. It can be positioned at real coordinates instead of only integer coordinates and a return a value for each real location. Currently, three interpolation schemes are available for ImgLib2:

• Nearest neighbor interpolation (also for available for any kind of data that can return a nearest neighbor like sparse datasets)
• Linear interpolation
• Lanczos interpolation

In the example we magnify a given real interval in the RealRandomAccessible which is based on the interpolation on an Img and compare the results of all three interpolation methods.

Shows the result for three different interpolators when magnifying a small part of the image by 10x. The nearest neighbor interpolation is computed fastest and is the most versatile as it requires no computation but just a lookout. The result is, however, very pixelated. The linear interpolation produces reasonable results and computes quite fast. The Lanczos interpolation shows visually most pleasing results but also introduces slight artifacts in the background.

## Example 8 - Working with sparse data

ImgLib2 supports sparsely sampled data, i.e. collections of locations together with their value. Such datasets typically implement the IterableRealInterval interface, which means they can be iterated and have real-valued locations in n-dimensional space. Currently ImgLib2 supports to store such collections either as list (RealPointSampleList) or KDTree. The RealPointSampleList can be iterated, whereas the KDTree additionally supports three efficient ways of searching for nearest neighboring points in the n-dimensional space (NearestNeighborSearch, KNearestNeighborSearch, and RadiusNeighborSearch).

In order to display sparse data ImgLib2 currently supports two interpolation schemes, the NearestNeighborInterpolation and the InverseDistanceWeightingInterpolation. They can compute a value for every location in space by returning either the value of the closest sample or an interpolated, distance-weighted value of the k nearest neighbors to the sampled location. The interpolation scheme therefore converts any IterableRealInterval into a RealRandomAccessible that can be displayed by wrapping it into a RandomAccessible and defining Interval using Views.

This is, however, not only useful for display. Note that you execute on such data any algorithm or method that is implemented for RealRandomAccessible or RandomAccessible, like Gaussian convolution in the first example. Note that none of these ever exists in memory, it is done completely virtual on just the sparse samples.

### Example 8a - Create random sparse data, display and convolve it

In this example we create a certain number of random samples with random intensities inside a certain Interval. Using nearest neighbor interpolation we wrap it into a RealRandomAccessible, wrap it again into a RandomAccessible, define an Interval on it and display it. On the same virtual data we perform a Gaussian convolution and show it, too.

On the left hand side it shows nearest-neighbor rendered random sparse data as created in example 8a. The right hand side shows the result of a Gaussian convolution, run directly on the virtual RandomAccessibleInterval.

### Example 8b - Randomly sample an existing image and display it

In this example we sample an existing image at random locations and render the result using a nearest neighbor interpolation as well as a distance-weighted average of the k nearest neighbors.

Shows the result of sparse sampling of an existing image using a varying number of random samples. The upper panel shows the rendering using nearest neighbor interpolation, the lower panel uses an interpolated, distance-weighted value of the k nearest neighbors relative to each sampled location (i.e. each pixel).