It is called flood fill algorithm. It fills a region of a particular color pixel by pixel. Total count of pixels is the area. In practical for accurate area measurement it is done with some other steps like thinning, tolerance, converting pixel to inch etc.

You can see in this video how every lines are extracted by a special chain code. Then the lines are simplified By Ramer Douglas Peucker algorithm and reduced points can be saved as dxf file.

Whoitam Map Measurement is very user friendly and easy to use. It is special for measuring scanned image. It makes easy, difficult process of measuring and adjusting map with few steps. It is accurate with many features. You can zoom to measure small length, get results with common units and real world inch, measure automated area and vectorize it automatically, merge image and measure it flying, use many filters useful to measure and finally save whole things as a project file.

This feature helps to make a vector(dxf file) from a raster image for editing
them by Adobe Illustrator or AutoCad software. To make a vector from a
raster image first you have to make a Black-White and CenterLine image.
You can do these by Whoitam Image Measurement easily.

Step 1: Main Menu>Image>Filter>Other>Threshold… or Threshold 2… or
Auto Threshold
This will make a Black-White image.

Step 2: Main Menu>Image>Filter>Other>Make CenterLine
This will make a CenterLine image.

Now Main Menu>Tools>Raster To Vector…
as shown in video. After Vectorisation you can save the vector as a dxf file.

An object in image mean, an identifiable portion of an image that
can be interpreted as a single unit. The shape of these objects can
be any type. Here white color will be determined as background and
other colors as objects. Count Object means getting the width, height
amount, position, area of these objects. Here to count object first
you have to adjust the threshold for making your objects visible.
Then click “Count”.

Make CenterLine filter makes it easy to measure area. You don’t need to stretch the selection to fit it through center of the boundary. So, you will get the area at a time.

It needs a good camera. Whole image has to be proportionally equal. Put a ruler on image when taking image by camera. This is need for calibration and identify 1 inch.

It is a little script. You will get it in “Script Samples” folder. It is a sample only. Like it you can do almost all geometric calculation by script and visualize it. It is very easy.

In version 5.25 “Mean” option added in Main Menu>Tools>Option>Magic Selection/Color Bucket Settings…. Enabling this option makes area always same and accurate at a particular tolerance, even in noisy environment and clicking anywhere in a region. You will get this image in “Trial Images” folder to test yourself.