## 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")

## Activities

#### Inspect a 2D image

Explore the content of a 2D image:

• Examine image dimensions
• Examine individual (or a range of) pixel values
• Plot line profiles
• Compute and plot pixel value histograms
• Compute pixel value statistics, such as min, max

Example data:

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
• Orient yourself by checking where the lowest pixel indices are
• Line profile. Draw a line and [Analyze > Plot Profile] or [Ctrl + K].
• Histogram [Analyze > Histogram] or [Ctrl + H]

## 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);

## Pixel operation in Galaxy

• Navigate to Galaxy
• In the tools panel on the left, click `Upload Data`
• Click `Paste/Fetch data` button
• Paste the URL of xy_8bit__nuclei_noisy_different_intensity.tif and click `Start` .
• After the upload finishes, click the `Close` button. The image will then be available in your Galaxy history.
• Pixel operations
• In the `Tools` panel, search for `Operate on pixels with ImageJ2`, and click on it.
• In the main window
• `Select image`: select the image `xy_8bit__nuclei_noisy_different_intensity.tif` from the dropdown list.
• `Operation`: Explore different operations from the dropdown list. Refer to the `What it does` section for explainations of each operation.
• `Value`: Some operations requires a value, input corresponding the value.
• Click `Run Tool` to start the operation.
• Results will be available in the Galaxy History panel once the process bar turns green.

#### Inspect a 3D image

Explore the content of a 3D image:

• Essentially follow the instructions for inspecting a 2D image (see above actitvity)
• Depending on the software that you are using it may be more or less convenient to deal with the 3rd dimension

Example data:

Show activity for:

## skimage napari

#### Inspect tissue culture collagen secretion image

• Open image: collagen_fluorescence.tif
• Examine the image dimensions
• Inspect intensity values at various places in the image (the elongated bright signal is secreted collagen)
• Hover with the mouse to inspect the gray values
• Zoom into the image
• Draw a line profile
• Compute a histogram, in a region with both background and bright collagen signal

Show activity for:

## Collagen image inspection using the ImageJ GUI

• Open the image mentioned in the activity preface
• Mouse hover to see gray value and pixel position in the ImageJ status bar
• Zoom in and out using the arrow up and down keys
• Draw a line ROI and use `Analyze > Plot Profile`
• Use the `Live` button to explore different image regions
• Create a histogram using `Analyze > Histogram`
• Draw a rectangluar ROI to restrict the histogram computation to a small region
• Use the `Live` button to explore different image regions
• Understand what you see in the histogram

## Assessment

1. If someome gives you a 2D image file and tells you to measure the value of the pixel at the indices `(7,8)` without telling you which programming language to use. Is that a precise enough instruction? If not, how many different pixels could that actually refer to?

## Solution

1. Unfortunately this instruction is not precise enough and, in practice it could refer to four different pixels, depending on whether this is meant to be zero or one-based indexing and depending whether this is row or column-major ordering. See here for more details.

## Explanations

### 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.

## Follow-up material

Recommended follow-up modules: