#### Useful links

## 1. Introduction

Universal framework for science and engineering supports advanced math. Additionally, the framework supports digital image processing. Both of these features are useful for GIS. This article shows how the framework can be used for GIS.

## 2. Background

GIS contains a lot of tasks related to digital image processing. One of task is definition of area of snow. The following is a picture provided by NASA Earth observations.

Filtration can be used for definition of area of snow. Besides digital image processing, GIS includes problems related to comparison of several images. This comparison is useful to study about Global warming problems and/or deforestation problems. Here we'll consider filtering and comparison of images.

## 3 Samples

### 3.1 Filtration

Let us consider a problem of definition of area of snow. First of all, we need a clear picture of snow. Such a picture can be obtained by filtration of the above picture. The scheme of filtration is presented in the following picture:

The **Earth** object contains the prototype image. The **Result of processing** object contains the result of filtration. The **Formulas** object contains the filtration math. Here, filtration math is defined by the following expression:

Where *r*, *g*, and *b* are intensities of red, green, and blue colors, respectively. The constant *a* is the border value. *x* and *y* are intensities of "snow exists" or "snow does not exist", respectively. The filtration result is presented below:

### 3.2 Web based application

The previous sample requires downloading the GIS image from the Internet and following its processing. Present day applications use Internet directly without explicit downloads. So, the framework contains a component which can use Internet images directly. The following picture presents the properties of this component:

We can change the URL of the image using the text editor at the top of the presented form. Using this component, we can also consider filtering. But, we use the Internet image instead of the local image.

The size of this file is substantially lower then the size of the file in section 3.1.

### 3.3 Comparison of images

Let us consider a sample of comparison of two images. We have two images with the following URLs:

These images are presented below:

To compare them effectively, we need a strong mathematical comparison. So we should consider a picture as a math object. A picture has a lot of math properties. The width and height of a picture are some of these properties. In my article devoted digital image processing, pictures are being considered as statistical selections. A picture can be defined by three functions of coordinate variables *x* and *y* of a pixel. These functions correspond to the red, green, and blue colors, respectively. So, we can compare these functions. It is clear that we can generate a lot of comparison algorithms. Indeed, a comparison algorithm depends on the purpose. The purpose of this article is exhibition of methods. So, we'll consider a simple algorithm which compares the intensity of red color. This algorithm is presented in the following picture:

Objects **Picture 1** and **Picture 2** contain the pictures which we would like to compare. Both **P 1** and **P 2** objects contain color functions of **Picture 1** and **Picture 2**, respectively. The **Input **object contains the input coordinates *x* and *y* of both **P 1** and **P 2**. The *Formula_1* of **Input** corresponds to the *x* coordinate, and *Formula_2* of **Input** corresponds to the *y* coordinate. Outputs of **P 1** and **P 2** are being used in the **Result** component. Properties of the **Result** component are presented below:

This formula has the following meaning. *x* is the first output of **P 1** or the function of red color intensity. *y* is a similar parameter of **P 2** (it is not visible in this picture). *a* and *b* are constants. So this function has a linear dependence on the difference of intensities of red color of **Picture 1** and **Picture 2**. This formula is used by the **Compare** object. The Compare object has the following properties:

These properties have the following meaning. Coordinates *x* and *y* of the Result picture correspond to the "constants" (aliases) of the **Input** object. All colors (red, green, and blue) of the result picture correspond to *Formula_1* of the **Result** object. The **Input** object has the following properties:

Inputs of this objects are *x* and *y*. Outputs of this object are *Formula_1* and *Formula_2*. What role has this object? This object closes the backward loop. The result picture is being calculated step by step. During these steps, coordinates *x*, *y* have different values. These values are set to *x*, *y* of the **Input** object, and so these values are set to *Formula_1* and *Formula_2* of **Input**. Then, *Formula_1* and *Formula_2* are being used by **P 1** and **P 2**. The outputs of **P 1** and **P 2** are then used by the **Result **object, and the output of **Result** is used in the result picture. Thus, we have a closed loop.

The result picture is presented below:

This sample requires 2 GB of RAM.

## Points of interest

To say the truth, I know nothing much about GIS. I can say the same about 90% of my developments.

## Conclusion

In 2009, when I wrote "The incredible machine" article, I had been asked: "Could this software be used for weather prediction". I had promised to write an article related to meteorology. So this article can be regarded as an article related to meteorology. The software needs good samples. I am waiting for some good samples from readers. Maybe, I'll extend this article with new samples in future. Any suggestions would be useful.