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Intersubject Regularity in the Intrinsic Shape of Human V1
Previous studies have reported considerable intersubject variability in the three-dimensional geometry of the human primary visual cortex (V1). Here we demonstrate that much of this variability is due to extrinsic geometric features of the cortical folds, and that the intrinsic shape of V1 is similar across individuals. V1 was imaged in ten ex vivo human hemispheres using high-resolution (200 μm) structural magnetic resonance imaging at high field strength (7 T). Manual tracings of the stria of Gennari were used to construct a surface representation, which was computationally flattened into the plane with minimal metric distortion. The instrinsic shape of V1 was determined from the boundary of the planar representation of the stria. An ellipse provided a simple parametric shape model that was a good approximation to the boundary of flattened V1. The aspect ration of the best-fitting ellipse was found to be consistent across subject, with a mean of 1.85 and standard deviation of 0.12. Optimal rigid alignment of size-normalized V1 produced greater overlap than that achieved by previous studies using different registration methods. A shape analysis of published macaque data indicated that the intrinsic shape of macaque V1 is also stereotyped, and similar to the human V1 shape. Previoud measurements of the functional boundary of V1 in human and macaque are in close agreement with these results
The jump set under geometric regularisation. Part 1: Basic technique and first-order denoising
Let u \in \mbox{BV}(\Omega) solve the total variation denoising problem
with -squared fidelity and data . Caselles et al. [Multiscale Model.
Simul. 6 (2008), 879--894] have shown the containment of the jump set of in that of . Their proof
unfortunately depends heavily on the co-area formula, as do many results in
this area, and as such is not directly extensible to higher-order,
curvature-based, and other advanced geometric regularisers, such as total
generalised variation (TGV) and Euler's elastica. These have received increased
attention in recent times due to their better practical regularisation
properties compared to conventional total variation or wavelets. We prove
analogous jump set containment properties for a general class of regularisers.
We do this with novel Lipschitz transformation techniques, and do not require
the co-area formula. In the present Part 1 we demonstrate the general technique
on first-order regularisers, while in Part 2 we will extend it to higher-order
regularisers. In particular, we concentrate in this part on TV and, as a
novelty, Huber-regularised TV. We also demonstrate that the technique would
apply to non-convex TV models as well as the Perona-Malik anisotropic
diffusion, if these approaches were well-posed to begin with
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