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Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
Equivalently, affine shape adaptation can be accomplished by iteratively warping a local image patch with affine transformations while applying a rotationally symmetric filter to the warped image patches. Provided that this iterative process converges, the resulting fixed point will be affine invariant.
The vertical warp yarns are held stationary in tension on a loom (frame) while the horizontal weft (also called the woof) is drawn through (inserted over and under) the warp thread. [1] In the terminology of weaving, each warp thread is called a warp end (synonymous terms are fill yarn and filling yarn ); a pick is a single weft thread that ...
When it is combined with the warping coefficients , a non-rigid warping is generated. A nice property of the TPS is that it can always be decomposed into a global affine and a local non-affine component. Consequently, the TPS smoothness term is solely dependent on the non-affine components.
A reflection about a line or plane that does not go through the origin is not a linear transformation — it is an affine transformation — as a 4×4 affine transformation matrix, it can be expressed as follows (assuming the normal is a unit vector): [′ ′ ′] = [] [] where = for some point on the plane, or equivalently, + + + =.
The shed is created to make it easy to interlace the weft into the warp and thus create woven fabric. Most types of looms have some sort of device which separates some of the warp threads from the others. This separation is called the shed, and allows for a shuttle carrying the weft thread to move through the shed perpendicular to the warp ...
For woven textiles, grain refers to the orientation of the weft and warp threads. The three named grains are straight grain, cross grain, and the bias grain. In sewing, a pattern piece can be cut from fabric in any orientation, and the chosen grain or orientation will affect the way the fabric hangs and stretches and thus the fit of a garment.
The word dobby is a corruption of "draw boy," which refers to the weaver's helpers who used to control the warp thread by pulling on draw threads. A dobby loom is an alternative to a treadle loom. Both are floor looms in which every warp thread on the loom is attached to a single shaft using a device called a heddle. A shaft is sometimes known ...