We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks. Our method achieves state-of-the-art results, outperforming Screened Poisson Surface Reconstruction and modern neural network based techniques. Because our approach is based on a simple kernel formulation, it is fast to run and easy to analyze. We provide explicit analytical expressions for our kernel and argue that our formulation can be seen as a generalization of cubic spline interpolation to higher dimensions. In particular, the RKHS norm associated with our kernel biases toward smooth interpolants. Finally, we formulate Screened Poisson Surface Reconstruction as a kernel method and derive an analytic expression for its norm in the corresponding RKHS.
tion would, if it were grave enough to justify the operation, be amenable to relief.As to the gravity of tho operation aud its technique, we may judge by a large accumulation of evidence. The two dangers are shock from hemorrhage, and sepsis. All ease, of root section thus far reported have made excellent recoveries-proof that it adds nothing to the risk of laminectoniy to open the dura.Opening the dura always allows the escape of two or three ounces of cerebro-spinal fluid if the patient is strictly horizontal. The treatment of the durai incision should always be by continuous suture with fine catgut. There is no difficulty whatever in doing this with a small curved eye needle. Leakage of cerebrospinal fluid afterward is practically nothing ; whereas, if no sutures are applied, leakage continues for weeks.The approach to the cord is best done by a quick and simple method which I have devised and practised in mauy cases. A long skin incision is made over the spine by a rather large knife, which by one or two rapid strokes separates the muscle from one side of all the spinous processes to be operated on and touches the lamiuoe at their bases. The knife handle is sufficient to scrape the muscle from the laminae.With a bayonet-shaped cutting pliers the bases of the processes are cut through in rapid succession, and with a curved periosteum elevator the series of spinous processes, with uncut interspiuous ligament and muscles attached on one side, are pressed en masse to that side. The hemorrhage is very slight aud entirely controlled by pressure, with perhaps two or three clamps to be taken off iu a few moments. A properly curved rongeur (such as shown) now begins the destruction of the laminae. Beginning on the base of any process the dura is exposed at one point carefully, aud then the rongeur proceeds up and down with rapidity.Occasional points of venous bleeding may be met, but a narrow strip of iodoform gauze or MacEweu's sticky gauze pressed down upon them by some pointed instrument allows the work to go on rapidly. When the dura has been slit up as far as desired we can roll the cord from side to side without touching it, by lifting the cut edge of the dura. The roots must be picked up by a bluut hook and a quarter to a half inch cut out, without much handling for microscopic observation. A half-dozen small bottles should be provided, as in my second case, to identify the roots and learn of their inflammatory invasion. The dura ought always to be sutured by fine catgut, and the outer soft parts fall together easily because there is no perceptible loss of substance. Drainage of the vertebral groove should be done for one day by a small tube not going far in. No plaster jacket or support is ever needed, as the strength of the spine is in no way impaired.
CONCLUSIONS.A comparatively new and interesting field of work is opened by these few cases.Thus far, even in weak patients, the operation has been devoid of risk.It is sound iu theory, aud has yielded enough results to show that it may become a meritorious oper...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.