Skoltech researchers developed a method to accurately evaluate fibrous material porosity from a single image

December 23, 2025

Researchers from Skoltech Engineering Center’s Hierarchically Structured Materials Laboratory developed a new method to determine the porosity of fibrous materials using a single image taken with a standard optical microscope. The algorithm analyzes the perspective effect and statistical variations in fiber thickness across the material’s layers to enable calculation of true volumetric porosity with an average error of just 3.5%. This approach outperforms conventional 2D image analysis techniques by a large margin and could be used by manufacturers to control material quality in real time. The research was published in the journal Measurement.

Center for Digital Engineering

Image 1. Fibers and their intersections. Source: Fibrous material porosity determination by image analysis using the perspective effect.

Fibrous materials are used extensively in many industries, including biomedicine, energy production, acoustic insulation, and composite materials. Their mechanical strength, permeability, and efficiency depend on a key feature – porosity, or the free space between fibers. However, conventional methods require sophisticated equipment, such as microtomographs, or complex physical measurements to accurately evaluate porosity.

Existing image analysis methods based on digital porosity, or the percentage of open areas in a 2D image, often produce errors of 50% or higher because they fail to consider the material’s 3D structure and fiber depth distribution.

To address this issue, the Skoltech team proposed a novel approach using perspective effect analysis of a single image. In optical microscopy, fibers in the lower layers of a material look thinner due to the perspective effect. The new algorithm statistically analyzes how apparent fiber thickness changes with brightness, which decreases with depth. Using this data, the method calculates the material’s depth and true volumetric porosity.

Image 2. An example of a transducer, performance of which can be enhanced by introducing fibrous materials in a certain range of porosities in its design. Credit: Anton Biriukov.

The developed methodology comprises three stages: preliminary digital image processing (for images obtained by a non-optical camera, artificial modeling of perspective distortions is additionally possible, including for electron microscope images), identification of fibers and their characteristics using the Ridge Detection algorithm in the Fiji software, and subsequent calculation of porosity based on fiber distribution statistics across layers.

This method quickly and precisely evaluates the porosity of various fibrous materials, including electrospun nanofibers used in filters or medical products, as well as aerospace composite materials. Easy to implement and automatable, this method is ideal for real-time quality control using machine vision on the production line. Its modest equipment requirements, such as a standard optical microscope, could facilitate its widespread adoption in research and industry.

“Our method solves the fundamental problem of transitioning from a 2D image to a 3D representation of a material’s structure. Rather than merely counting pixels on the surface, we look deep into the material to see how apparent fiber thickness changes. Therefore, we can accurately determine true porosity without using expensive 3D reconstruction equipment,” study lead author and Skoltech Engineering Systems PhD student Anton Biriukov commented.

Image 3a). Visualization of the perspective distortion effect, processed to obtain depth information. In the schematic, D₁ is the apparent size (e.g., diameter) of a near fiber in the image, and D₂ is the apparent size of a far fiber. H₁ is the known distance from the camera to the top layer, while H₂ is the unknown distance between layers (sample thickness). Since the average true thickness of the fibers is constant across all layers, the depth H₂ can be calculated. The underlying equation, shown in the figure, uses the apparent reduction in object size (D₂ compared to D₁) caused by perspective distortion. For instance, if objects appear identical to the camera, the ratio D₂/D₁ equals 1, and H₂ equals 0. While this relationship may not hold for individual fibers, it provides a reliable result when averaged across hundreds of fibers in a single image. Image 3b). Confirmation of decreasing fiber thickness and brightness with depth, from which the true image depth is calculated. The graph shows a direct correlation between the average brightness of the fibers (horizontal axis, “Level on intensity”) and their apparent thickness (vertical axis, "Fiber width, μm"). On average, the deeper a fiber is located within the structure, the darker (lower intensity) and thinner it appears to the camera. Source: Fibrous material porosity determination by image analysis using the perspective effect.

“In my opinion, the inventive aspect of our research was the use of 3D-printed physical models of the fibrous material, which provided true porosity values and left no doubt about the reliability of the proposed method,” Professor Alexander Korsunsky, the study leader and the head of the Hierarchically Structured Materials Laboratory at Skoltech Engineering, explained.