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From Odwiki

Texture filtering is basically AntiAliasing for 2D images. There are many different methods for filtering textures, but in general the filter will take a given texel (Texture Pixel) and calculate a new color for that point based on the color change in adjacent texels. The filter will allow you to specify a width in S(U) and T(V) either together or individually. A width of 0 essentially point samples a texture where as a larger width of 4, in both S and T, is the equivalent of quartering your texture's resolution. The higher the value the blurrier and less detailed your textures will become, however minimal texture filtering is usually desirable to combat aliasing in texture maps which can make a surface appear to shimmer when animated.

Texture Filtering in Houdini

Houdini's texture function actually supports several methods of filtering:

• Box
• Gaussian
• Bartlett/Triangular
• Catmull-Rom
• Sinc Sharpening
• Hanning
• Blackman
• Mitchell
• Point Sampling (no filter)

Each filter behaves differently because they use different shapes and sampling methods, so it's best to try them all so you can get a feel for them. The filters will also allow you to specify widths in S and/or T either together or individually.

Houdini and mantra support an image format called ".rat" (Random Access Texture) which, among other things, are MipMapped. This accelerates filtereds texture lookups a great deal by storing prefiltered levels along with the texture.