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Emboss bump mapping is the most common type of bump mapping used by 3D artists. This technique uses texture maps to generate mapping effects even without a custom renderer. It is just an extension and refining of texture embossing.
Emboss bump mapping duplicates the first picture, shifts it to get the desired bump amount and darkens the texture underneath the bump. Then it removes or cuts out the desired shape from the texture on top, and blends the two textures together. This is called two-pass emboss bump mapping because it involves two different textures.
Real bump mapping uses per-pixel lighting, which is calculated at each pixel based on perturbed normal vectors and is therefore very computationally expensive. Emboss bump mapping, however, is a hack done to improve visual quality with less computational power by under-sampling artifacts. It uses diffuse lighting only and has no specular component.
Although emboss bump mapping is not really a legitimate method, in 3D animation and imagery, any method that will make visuals look better is used by artists and developers alike.