## Learning Objectives

After completing this lesson, learners should be able to:
• Understand that a digital image is typically stored as an N-dimensional array.

• Learn that the image array elements are called pixels (2D) or voxels (3D).

• Examine the values and locations of pixels/voxels in an image.

## Motivation

Digital images are a very important subset of the more general mathematical definition of an image. The vast majority of available algorithms and visualisation tools operate on digital images and all (as far as we know) scientific microscopes output digital images. Thus, for microscopy based science, it is crucial to understand the basic properties of digitial images and how to effectively inspect their content.

## Concept map

graph TD Im("Digital image") --- A("N-D array") A --- E("Elements/Pixels/Voxels") A --- DT("Data type") A --- D("Shape/Size/Dimensions") E --- V("Value") E --- I("Indices")

## Figure Digital image pixel array and gray-scale rendering. This array (image) has two dimensions with 21 x 21 elements (pixels). The pixel values (black numbers) can be addressed by their respective pixel indices (green numbers).

### Digital image dimensions

There are several ways to describe the size of a digital image. For example, the following sentences describe the same image.

• The image has 2 dimensions, the length of dimension 0 is 200 and the length of dimension 1 is 100.
• The image has 2 dimensions, the length of dimension 1 is 200 and the length of dimension 2 is 100.
• The image has a size/shape of (200, 100).
• The image has 200 x 100 pixels.

Note that “images” in bioimaging can also have more than two dimensions and one typically specifies how to map those dimensions to the physical space (x,y,z, and t). For example, if you acquire a 2-D movie with 100 time points and each movie frame consisting of 256 x 256 pixels it is quite common to represent this as a 3-D array with a shape of ( 256, 256, 100 ) accompanied with metadata such as ( (“x”, 100 nm), (“y”, 100 nm), (“t”, 1 s) ); check out the module on spatial calibration for more details on this.

## Activities

• Open image: xy_8bit__nuclei_noisy_different_intensity.tif
• Explore different ways to inspect pixel values and indices, e.g.,
• Examine image dimensions
• Examine individual (or a range of) pixel values
• Plot line profiles
• Compute and plot pixel value histograms

Show activity for:

## Explore pixel values and indices

• Open image: xy_8bit__nuclei_noisy_different_intensity.tif
• Explore different ways to inspect pixel values and indices
• Mouse hover
• Line profile. Draw a line and [Analyze > Plot Profile] or [Ctrl + K].
• Histogram [Analyze > Histogram] or [Ctrl + H]
• Check where the lowest pixel indices are in the displayed image:
• Most commonly: Upper left corner, which is different to conventional coordinate systems.

## MATLAB

% This MATLAB script illustrates how to explore different ways % to inspect pixel values and indices % It is recommended to read comments and to run sections separately % one after the other with the corresponding command in the Editor Toolstrip %% Choose and load the image %% % Read input image in_image = webread('https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__nuclei_noisy_different_intensity.tif'); % Display input image figure imagesc(in_image) axis equal %% 1 - Explore pixels with mouse (Data Tips) %% % In the Figure window, click the Data Tips symbol % (text baloon icon on the top right corner of the image) % or select from [Tools>Data Cursor] in the Figure Toolstrip % Now if you click on the image a Data Tip window will appear % showing the coordinates [X,Y], the pixel intensity [Index] % and the assigned colour in the current display [R,G,B] % To exit the Data Tips mode, click again on the Data Tips icon % To stop displaying Data Tips, right click on the image and select % [Delete All Data Tips] % N.B. The point with the lowest coordinates [X,Y = 0,0] is normally found % on the top left corner %% 2 - Explore by linescans %% % Draw a line across the image to evaluate its intensity profile % 1. Click on the starting point of the line on the image % 2. Click on the end point of the line on the image % 3. Press [Enter] [x_coord, y_coord, line_profile] = improfile; % Plot sampled line on the image hold on plot(x_coord, y_coord, 'w.') % Create new figure showing the line profile figure plot(line_profile, 'k', 'LineWidth', 2) xlabel('Distance (pixels)') ylabel('Gray value') set(findall(gcf, '-property', 'FontSize'), 'FontSize', 14) %% 3 - Explore by plotting the image histogram %% % Produce the image histogram figure histogram(in_image) xlabel('Gray value') ylabel('Counts') set(findall(gcf, '-property', 'FontSize'), 'FontSize', 14) % Calculate some metrics from the histogram % Number of pixels included in the count: px_count = size(in_image,1)*size(in_image,2); % Mean gray value px_mean = nanmean(in_image(:)); % Standard deviation for gray values px_std = nanstd(double(in_image(:))); % Minimum gray value px_min = nanmin(in_image(:)); % Maximum gray value px_max = nanmax(in_image(:)); % Mode for gray values [px_mode, px_mode_frequency] = mode(in_image(:)); % Print metrics to screen fprintf('Count = %i\n', px_count); fprintf('Mean = %.3f\n', px_mean); fprintf('StdDev = %.3f\n', px_std); fprintf('Min = %i\n', px_min); fprintf('Max = %i\n', px_max); fprintf('Mode = %i (%i)\n', px_mode, px_mode_frequency);

## Assessment

### 2-D image inspection

Open image xy_8bit__nuclei_noisy_different_intensity.tif. Hint: For certain exercises the inspection of the histogram will help

1. What is the value of the pixel at the indices (x=20,y=20)?
2. What is the highest value in the image?
3. What is the most frequently occurring value in the image?
4. Where is this pixel with the indices (x=0,y=0)? Why is this potentially confusing?
5. How many pixels does this image have in the x direction?
6. What is the highest pixel index in the x direction?
7. If you were to rotate the image by 90 degrees, would it change the image histogram?

## Solution

1. 82
2. 129
3. 55
4. Top left; normally x/y coordinate systems have their origin at the bottom left
5. 59
6. 58
7. No, the gray value histogram is independent of the pixel locations

### 3-D image inspection

1. What is the value of the voxel at the indices (x=93,y=124,z=13)?
2. Which is the highest value in the image?

1. 47
2. 255

## Follow-up material

Recommended follow-up modules: