Working with Matrices: Adding/Subtracting and Custom Operations

[Jarfi]

TL;DR Summary

How do I combine heatmaps, or images using simple matrix mathematics, in the simplest possible way?

Hello,

I am working with heatmaps and similar. And I want to be able to add/subtract them and a few other custom operations.

Here is a quick rundown:
1: Generate nxn (or nxm if possible) matrix, each element represents a heatmap color, or alternatively this could simply be defined as an image, let's call it M1

2: Generate another nxn matrix, but say with all elements transparents, except a certain area which represents a picture of an object, say a house. Alternatively, it can be an overlay of numbers, all 0 but in the area of interest, there are values 1-255, which can be a picture of something. Let's call it M2

3: I now want to do operations, such as M1 + M2 to get an overlay image, but not only this, I want to be able to control the change of basis or translate the position of the house in matrix M2 before adding it in M1, and do this multiple times, so I can add multiple houses onto the main image.

Main image = M1 + M2 * (location 1 transformation) + M2 * (location 2 transformation) so that I can add two houses to the matrix M1, on location 1 and location 2.

what is the most simple way to do this...? I assume the transformation can be defined in some way , so that all I need is matrix multiplication, so that most programming language can handle it?

But what if the house is size 50x50, and the main matrix is 500x500, but I put the house at location [0,250], so that half of the house would end up outside, but the other half still appears in the matrix, is this possible using some mathematical (non algorithmic) matrix transformation?

 

[jedishrfu]

These actions are more about image processing than about matrix operations.

Basically, it seems you want to adjust pixels, overlay pixels with other pixels, rescale one image to overlay on another image.

There are software libraries and tools to do that. Java has some libraries for as does Python. ImageMagick comes to mind for commands and Gimp for interactive tooling.

 

[Jarfi]

These actions are more about image processing than about matrix operations.

Basically, it seems you want to adjust pixels, overlay pixels with other pixels, rescale one image to overlay on another image.

There are software libraries and tools to do that. Java has some libraries for as does Python. ImageMagick comes to mind for commands and Gimp for interactive tooling.

It seems but it is not. I would like to do this without any clunky libraries, because it's very basic operations on nxn matrices, populated with simple numbers. It seems strange to me to have to revert to using libraries for this.

Again I am plotting heatmaps, not an rgb image

 

[jedishrfu]

These actions aren't really linear algebra though.

Basically you need to write code or use libraries (better ie already debugged) that can do these manipulations.

In the case of the house placement:

// Java based psuedo code overlaying house array onto 
// the land array (realtors and witches beware a house may fall on you)
int land[][] = new int[100][100]; // land area
int house[][] = new int[10][10]; // house

// load land array
// load house array

// house position on land
int housex=25; //x coordinate of top right corner of house image
int housey=35; // y coordinate of top right corner of house image

// overlay house onto land
for(int i=0; i<house.length; i++) {
  for(int j=0; i<house[0].length; j++) {
    land[i+housex][j+housey]=house[i][j];
  }
}

show(land);

 

[Jarfi]

These actions aren't really linear algebra though.

Basically you need to write code or use libraries (better ie already debugged) that can do these manipulations.

In the case of the house placement:

// Java based psuedo code overlaying house array onto
// the land array (realtors and witches beware a house may fall on you)
int land[][] = new int[100][100]; // land area
int house[][] = new int[10][10]; // house

// load land array
// load house array

// house position on land
int housex=25; //x coordinate of top right corner of house image
int housey=35; // y coordinate of top right corner of house image

// overlay house onto land
for(int i=0; i<house.length; i++) {
  for(int j=0; i<house[0].length; j++) {
    land[i+housex][j+housey]=house[i][j];
  }
}

show(land);

This looks correct, and I have thought of doing this. But it also looks really computationally intensive. What If I want to make a moving house, for 30 fps, I need to do ixj=100 operations for each pixel, making 3.000 operations just for moving this single house. Or in case of a moving heamap (for example, a moving weather forecast showing the pressure degree, humidity or temperature) if I overlay more squares it might be 50x50x30 = 75.000 computations per second, the computation time increases exponantially with the size of the picture.

Perhaps it would be quicker to use pointers or something that switches out "blocks" of the matrix for another.
Pseudocode..
*land[(i+housex):(i+housex+5)][(j+housey):(j+housey+10)]=*house;

From my understanding, in computer graphics, they use graphical objects, where each one is basically a set of points connected together forming a polygon(mesh), then each object/matrix is transformed, rotated, translated etc and then added to the "main space" to make it move. There can be many objects, and together they form the image of whatever picture, video or graphics is being generated.

 

[jedishrfu]

ultimately Though those polygon meshes are converted to pixels and overlaid into your image by the graphics card.