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.
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]
skimage napari
# %%
# 2D image inspection using skimage and napari
# %%
# Load an image
fromOpenIJTIFFimportopen_ij_tiffimage_url="https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__nuclei_noisy_different_intensity.tif"image,*_=open_ij_tiff(image_url)# %%
# Inspect what the image actually is
print(type(image))# %%
# Inspect the pixel values
print(image)# %%
# Inspect the image dimensions
print(image.shape)# %%
# Create a napari viewer for looking at the image
fromnapari.viewerimportViewernapari_viewer=Viewer()# %%
# Jupyter notebook exercise:
# Code completion: Type `napari_viewer.` and press `TAB`
# Get help: Type `napari_viewer.add_image` and press `SHIFT-TAB`
# %%
# Add the image the viewer
napari_viewer.add_image(image)# %%
# Pixel value inspection in napari:
# However with the mouse over the image and observe the pixel indices and values
# %%
# Fetch single pixel values
print(image[4,8])# in the background
print(image[31,42])# inside a nucleus
# %%
# Extract a line of pixel values across the objects
print(image[20,:])# %%
# Napari:
# Use the plot profile plugin to inspect a line of pixel values
# %%
# Extract one object as a square of pixel values
print(image[7:30,10:26])# %%
# Compute the image min and max
# Jupyter: Use TAB to find the min and max functions
print(image.min(),image.max())# %%
# Compute and show the image histogram
importmatplotlib.pyplotaspltimportnumpyasnpplt.hist(image.flatten(),bins=np.arange(image.min(),image.max()+1))plt.show()# instead, we could end the above line with ";"
# %%
# Napari:
# Alternative loading of data
# Remove the currently shown image
# Drag and drop image from browser onto napari
# Rename the layer to: image
# %%
# Fetch the image data from napari and check its shape
image=napari_viewer.layers['image'].dataprint(image.shape)
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);
# %%
# 3D image inspection using skimage and napari
# %%
# Load an image
fromOpenIJTIFFimportopen_ij_tiffimage_url="https://github.com/NEUBIAS/training-resources/raw/master/image_data/xyz_8bit__mri_head.tif"image,axes,*_=open_ij_tiff(image_url)# %%
# Inspect the image shape
print(image.shape)# %%
# Inspect the image axes
print(axes)# %%
# Inspect all image pixel values, and appreciate that this is not useful for larger 3D data
print(image)# %%
# Create a napari viewer and add the image
fromnapari.viewerimportViewernapari_viewer=Viewer()napari_viewer.add_image(image)# %%
# Napari:
# - However with the mouse over the image and observe the pixel indices and values
# - Use the slider to change the position of the 3rd dimension
# %%
# Extract the pixels that belong to the tip of the nose
print(image[1,9:19,89:102])# %%
# Compute the image min and max
print(image.min(),image.max())# %%
# Compute the image histogram
importmatplotlib.pyplotaspltimportnumpyasnpplt.hist(image.flatten(),bins=np.arange(image.min(),image.max()+1));
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:
ImageJ GUI
Collagen image inspection using the ImageJ GUI
Open the image mentioned in the activity preface
Read image dimensions in image header
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
Answer the question
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
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.
