Mathematics in Photography”

By Scott Hamilton

Last week I started a series on linking science, technology, engineering and mathematics to the arts as an argument to continue teaching various arts alongside the core subjects in our school systems. I would argue even further that the arts are a core subject in our education system which is often neglected. Last week I wrote about the link between Music and Mathematics. This week I want to focus on one of the visual arts, photography.

Before we reached the digital age of photography, a lot of chemistry was used in the art of film developing. Don’t get me wrong, there is still a lot of science and chemistry involved in photography, just not at the artist’s level as most of this has been replaced by electronics in the digital camera and offloaded to the camera sensor design engineers. However, I would like to propose that these design engineers likely took an interest in the art of photography before going on to develop new methods of image capture. The engineers behind the design of the latest camera technology have a passion for capturing the best images possible or the technology would not be improving.

The art of photography now involves computers more heavily than nearly any other field of art. There are thousands of programs created for the management, manipulation and editing of images, from the simple ability to share photos on Facebook to the more complex abilities to create new images from existing photos by merging multiple images in different ways. It has become possible in recent years to create photographic images that are nearly impossible to distinguish from real events. This is all made possible through advanced techniques in image manipulation. The computer software used to edit images utilizes complex matrix math to generate filters that modify the sharpness, tone and colors of photographic images.

Among my favorite things to do with photography are two things that involve very complex mathematical formulas. The first is the colorization of old black and white photos, and the second is selective colorization of images. Did you know that it is possible to take photos from the early 1900s, along with samples of fabric from the era, and recreate the images in full color? The technique used matches various shades of gray to specific colors and replaces all the pixels in the digital image with their new color.

To understand the complexity you need to first understand a couple of terms. The first is the pixel, which in simple terms is the smallest sample of color from an image. The second is image resolution, which tells how big the image is in pixels, or how many samples are taken across the rows of an image and how many rows are sampled in the image. Resolution can be specified as a pixel count in each direction (3840×2160) or as a single number (4K), which is the width in pixels rounded to the nearest thousand, or more commonly in photography in megapixels (8MP) which is the total number of pixels in the images specified in the millions. So an 8MP, 4K and (3840×2160) resolution all describe the same size image and it is also the most common size in use today. This means to colorize an image one must examine and modify around eight million pixels.

Selective colorization is where you take a photograph and convert it to black and white, modifying all eight million pixels, and then overlay the original color photograph in select sections to bring the color to a single item, like a red cardinal in a cedar tree. For more details about math and science in photography you can read the excellent article on the topic at https://www.bryanhansel.com/2014/photography-curiosity-creativity-math-science/.

There are many other areas where math is used in photography and they overlap with drawing and painting as they deal with the composition of the image, which is a topic for next week. Until then, stay safe and learn something new.

Scott Hamilton is an Expert in Emerging Technologies at ATOS and can be reached with questions and comments via email to sh*******@te**********.org or through his website at https://www.techshepherd.org.

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