Shape feature extraction is a key research direction on wheat leaf disease recognition. In order to resolve the problem of translation, scaling and rotation transformation invariance on shape matching, the invariant moment theory was introduced to shape feature extraction and seven Hu invariant moment parameters were defined as shape features. Meanwhile the present algorithm was used and new pa...

Let G be a locally compact abelian group with Haar measure, and Y measure space. Suppose that H is reproducing kernel Hilbert space of functions on $$G\times Y$$ , such naturally embedded into $$L^2(G\times Y)$$ invariant under the translations associated elements G. Under some additional technical assumptions, we study W*-algebra $${\mathcal {V}}$$ translation-invariant bounded linear operator...

We consider random translation-invariant frustration-free quantum spin Hamiltonians on $\mathbb Z^D$ in which the nearest-neighbor interaction every direction is randomly sampled and then distributed across lattice. Our main result that, under a small rank constraint, are automatically they gapped with positive probability. This extends previous results 1D chains to all dimensions. The argument...