help me find some kind of adon, I need to cut it into a separate mesh based on the unique color of the text superimposed on the object. The tool is similar in function to a knife, but it can be cut out manually and I would like to find an addon that would simplify such work.
As far as I know, there is no Addon that works that way. 
Welcome 
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Hmm… you may have a look into this thread:
Similar, but I need data, colors from texture
Honestly, you’d fair better to look at retopology to make mesh to use as a boolean brush for each shape you want - as I see it, your image is so many colors that any automatic process will be confused in getting the shapes you want to get.
Well… as i understood this you want to slice your object accordign to something one the image. If the object is subdividided and you select the vertices from specidic color… then i thought this may be a solution.
But if you want more precise “slicing” then maybe it will work if you use some edg edetection on the image and vectorize it. Then convert vector to mesh use the Cast modifier to make it more spherical or maybe cylindrical and shrinkwrap this onto the object… ?
Apparently this is the best option, albeit a long one. Thanks for your help
fss.blend (2.1 MB)
You can also use the same method as Daeun.
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Flatten the VU.
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Using TexTools, UV is brought into the 3D space.
https://github.com/franMarz/TexTools-Blender -
Cut and separate the image from the plane and combine it with SurfaceDeform to the UV object
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Use the shape key of the UV object created using TexTools to make it its original shape.
※ TexTools documentation (old materials)
There is a different way. You can take the original image and convert to a 6-8 or 10 color SVG image. That way you have curves for the different colors of the image ( I didn’t find a converter that would pull all the colors from your image since it uses gradients ), but I got most of them…
You can use the curves as a cutter to “Knife Project” or convert them to Mesh and use @Okidoki and @oo_1942 ideas to shape to your vase.
Nice, that’s hella clever
Depending on the context (when the search for slicing was simply to make some relief like topology) maybe even “some” ( aka a lot ) filtering may lead to the wanted result (also using this special smoothed maximum posterized color curved bw image for displace and color because the color image for color distracts the details…)
But this may not what is wanted here as result…