Christmas is just around the corner. The days are short, the nights are even longer. And with a bit of luck, there will even be snow. The crystals that slowly trickle from the sky and cover everything with a white dress only look the same at first glance.
The US-American Wilson Bentley was already fascinated by the white ice formations as a child, and not only to build snowmen or go sledding on them. He was fascinated by the uniqueness and the different shapes that the snowflakes only reveal under the microscope. When he was just 20 years old, in 1885, he achieved something sensational: photographing a snowflake in its purest form. At that time, black-and-white photography was just experiencing its first heyday. There were no high-resolution SLR cameras yet and the exposure time was between eight and one hundred seconds.
Figure 1: Bentley W. (1902), Studies among the snow crystals during the winter of 1901-02. Monthly Weather Review
It took years of technical difficulties and numerous failures before the first snowflake was photographed. During his lifetime, Bentley photographed another 5,000 snow crystals, among which not even two were identical.
But snowflakes have one thing in common with us humans: We look more or less similar. But what is „similar“?
For this, statistics has developed a whole series of concepts known as „cluster analysis“. To roughly summarise, the idea is that individuals – people, animals, plants, or even snowflakes – shall be more similar to each other within a single cluster than between two different clusters. Similarity is defined as the distance between different characteristics. For example, two children are more similar regarding their age than father and son, but not necessarily regarding their hair colour.
However, such clustering problems can quickly become very complex. Especially if you have no idea how many clusters there are, which features are relevant for the clustering and to what extent, and whether the clusters are very sharply separated or have rather smooth transitions.
This is where an AI algorithm comes into play, the so-called „self-organising maps“ or SOMs. With a combination of a SOM and classical statistical methods, the hidden patterns in the snow crystals become visible. Such a map of the snow landscape can be generated amazingly fast with Viscovery, a very intuitively usable software from the Viennese AI company of the same name.
Figure 2: Self-organizing map from Viscovery Software GmbH, https://www.viscovery.net/demos/snow-crystals-classification
As a tribute to the „Snowflake Man“ and his breathtaking photographs, Viscovery has compiled a selection of 974 photographs by Wilson Bentley and coded them in such a way that they have become machine-readable data sets. They consist of the rotation-variant image moments up to the third order and the mean amplitudes of 7 different frequency bands. In the SOM, the snowflakes are then grouped into 18 clusters. Clicking on any point in the map shows the snow crystal that represents that point the best. When clicking on another point, the map shows the snow crystal that is visually most similar to the one clicked on before.
Figure 3: Photo of a snow crystal under the microscope, https://www.viscovery.net/demos/snow-crystals-classification
We spent quite a bit of time with the snowflake map and realised: There’s a bit of Wilson Bentley in all of us. We now see snow with different eyes: the smallest and most ephemeral things on our planet can hide the greatest miracles.
Have a peaceful Christmas and a happy and healthy New Year 2023!
Click here for the Viscovery Showcase!
This demo shows how photographic images can be ordered in a map with respect to their visual characteristics. In this example, images of snow crystals are ordered based on previous image preprocessing to determine similarity.
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