I am trying to validate black and white images (more of a clipart images - not photos) for an engraving machine.
One of the major things I need to take into consideration is the size of areas (or width of lines) since the machine can't handle lines that are too thin - so I need to find areas that are thinner than a given threshold.

Take this image for example:

The strings of the harp might be too thin to engrave.

I am reading about Matlab and OpenCV but image processing is an area I am learning about for the first time.

I am a Java / C# developer so implementation done with one of those languages will be best for me but any direction will be greatly appreciated.

A solution using matlab utilizing image morphological operations:

Define the minimal thickness of allowed area, for example, minThick=4

BW = imread('https://i.stack.imgur.com/oXKep.jpg'); 
BW = BW(:,:,1) < 128; %// convert image to binary mask
se = strel('disk', minTick/2, 0); %// define a disk element   
eBW = imerode( BW, se ); %// "chop" half thickness from mask
deBW = imdilate( eBW, se ); %// dilate the eroded mask

Eroding and dilating should leave regions that are thicker than minThick unchanged, but it will remove the thin areas

invalidArea = BW & ~deBW; %// pixels that are in BW but not in deBW

Resulting with:

You can read more about imdilate and imerode in the linked documentation.