Creating a Histogram

Previously, we discussed that images are made up of pixels, each represented as numerical values in the eyes of a computer. When displayed, these pixel values are transformed into squares, providing a visual representation that helps us quickly comprehend the image's content. As images consist of data, histograms serve as a tool to better interpret this information.

Table of Contents

1. Creating a Histogram
2. Histograms and Image Acquisition
3. Comparing Images and Histograms
4. The Deceptive Nature of Appearances
5. Utilizing Histograms as Analytical Tools
6. Conclusion
7. References

Histograms and Image Acquisition

Histograms are integral to most microscopy software, especially in the initial stages of image analysis. For example, the histogram of the 8-bit image mentioned above ranges from 0 (black) to 255 (white). While fluorescence images may appear bright through the microscope, capturing satisfactory results often requires extended exposure, which can pose challenges in photomicrography.

The shape and distribution of a histogram can indicate whether the exposure time is appropriate. In many microscopy images, a dark field of view prevails, leading to histograms dominated by low intensity values. Optimal imaging conditions allow for the entire dynamic range to be utilized, enhancing image quality.

The following Python code demonstrates how to analyze images captured under varying exposure conditions.

# Read images with different exposure times

over = sk.io.imread("over.tif")

under = sk.io.imread("under.tif")

good = sk.io.imread("good.tif")

# Create a figure with two rows and three columns of subplots

fig, axs = plt.subplots(2, 3, figsize=(9, 9))

# Display the optimal exposure image

axs[0, 0].imshow(good[:,:,0], cmap="gray")

axs[0, 0].set_title("Optimal Exposure Image")

axs[0, 0].set_axis_off()

scalebar = ScaleBar(0.18, units='um', location='lower right', scale_loc='bottom', length_fraction=0.25)

axs[0,0].add_artist(scalebar)

# Histogram for optimal exposure

axs[1,0].hist(good[:,:,0].flatten(), bins=256)

axs[1,0].set_title("Optimal Exposure")

# Display the underexposed image

axs[0, 1].imshow(under[:,:,0], cmap="gray")

axs[0, 1].set_title("Underexposed Image")

axs[0, 1].set_axis_off()

scalebar = ScaleBar(0.180, units='um', location='lower right', scale_loc='bottom', length_fraction=0.25)

axs[0,1].add_artist(scalebar)

# Histogram for underexposed image

axs[1,1].hist(under[:,:,0].flatten(), bins=256)

axs[1,1].set_title("Underexposed Image")

# Display the overexposed image

axs[0, 2].imshow(over[:,:,0], cmap="gray")

axs[0, 2].set_title("Overexposed Image")

axs[0, 2].set_axis_off()

scalebar = ScaleBar(0.180, units='um', location='lower right', scale_loc='bottom', length_fraction=0.25)

axs[0,2].add_artist(scalebar)

# Histogram for overexposed image

axs[1,2].hist(over[:,:,0].flatten(), bins=255)

axs[1,2].set_title("Overexposed Image")

plt.tight_layout()

Comparing Images and Histograms

Histograms are essential for analyzing and comparing pixel intensity distributions in images. By examining histograms alongside summary statistics (such as mean and standard deviation), we can gain insights into overall brightness and contrast.

In bioimage processing, comparing histograms is critical for evaluating the effects of various treatments on subcellular staining intensities. Observable changes in histograms can indicate underlying biological variations resulting from different experimental conditions.

The Deceptive Nature of Appearances

Visual perception can often mislead. The following Python code illustrates this by showcasing two images: one inverted using a skimage utility and the other inverted visually with the gray_r colormap. While visual differences may be subtle, analyzing histograms and summary statistics reveals significant variations that may not be immediately apparent.

# Create a figure with two rows and two columns of subplots

fig, axs = plt.subplots(2, 2, figsize=(8, 8))

# Original Image

axs[0, 0].imshow(img, cmap="gray_r")

axs[0, 0].set_title("Original Image")

axs[0, 0].set_axis_off()

scalebar = ScaleBar(0.13, units='um', location='lower right', scale_loc='bottom', length_fraction=0.25)

axs[0, 0].add_artist(scalebar)

# Histogram of Original Image

axs[1, 0].hist(img.flatten(), bins=255)

axs[1, 0].set_title("Histogram of Original Image")

# Inverted Image

img_r = util.invert(img)

axs[0, 1].imshow(img_r, cmap="gray")

axs[0, 1].set_title("Inverted Image")

axs[0, 1].set_axis_off()

scalebar = ScaleBar(0.13, units='um', location='lower right', scale_loc='bottom', length_fraction=0.25)

axs[0, 1].add_artist(scalebar)

# Histogram of Inverted Image

axs[1, 1].hist(img_r.flatten(), bins=255)

axs[1, 1].set_title("Histogram of Inverted Image")

plt.tight_layout()

Histograms as Analytical Tools

Histograms are vital in bioimage processing and analysis. Common applications in biosciences include:

• Image Enhancement: Histogram equalization improves image contrast and brightness by redistributing pixel intensity values.
• Thresholding: Histograms assist in establishing thresholds for segmenting objects by analyzing pixel distributions.

Conclusion

Regularly reviewing histograms is a beneficial practice when working with new images, as it enhances data comprehension and aids in early detection of potential issues in image processing workflows.

References:

[2] I. Vangelatos et al., "Eisosome Organization in Aspergillus nidulans," Eukaryot. Cell, vol. 9, no. 10, pp. 1441–1454, 2010, doi: 10.1128/EC.00087–10.

[3] A. Athanasopoulos et al., "Characterization of AnNce102," Sci. Rep., vol. 5, no. 1, 2015, doi: 10.1038/srep15200.

[4] T. Ogama, "A beginner's guide to improving image acquisition," The Biochemist, vol. 42, pp. 22–27, 2020, doi: 10.1042/BIO20200075.

Interactive bioimage analysis with Python and Jupyter is the focus of this webinar, detailing practical applications and techniques in the field.

This video outlines the fundamental concepts of bioimage analysis using Python, providing foundational knowledge for practitioners.