A new authentication algorithm for grid identity trusted computing unlimited by hardware is presented;the trusted root is made as an image data.The grid entity is trusted in the soft platform when its feature of image root is entirely matched with that from the other entities feature database in a scale space process.To recognize and detect the stable image root feature,the non-homogeneous linear expandable scale space is proposed.Focusing on relations between the scale parameter of the inhomogeneous Gaussian function terms and the space evolution of thermal diffusion homogeneous equations,three space evolution operators are constructed to exact and mark the feature from image root.Analysis and verification are carried on the new scale space,operators and the core of making decisions for grid entities certifications.