http://imagej.273.s1.nabble.com/cut-paste-w-arbitrary-warp-tp5017962p5017971.html
straight in the destination. In my version, there would be a curving, open
polyline in the source. The destination vertices would first be crudely
> Hi Keneth,
>
> when you say "perturbed polyline" -- do you mean that the n vertices are
> cyclically shifted or could they be fully permuted?
>
> Regarding the geometric part of the mapping, you need a transformation
> preserving straight lines if you want to transform one polygon shape to
> another (i.e., spline models are out of question). Selecting 2
> corresponding point pairs will give you a unique rigid transformation
> (i.e., rotation and uniform scaling only), 3 point pairs define an affine
> transformation and 4 point pairs give a projective transformation (linear
> in homogeneous coordinates). There is no straight line-preserving 2D
> transformation that could map more than n=4 point pairs. The common
> approach for n>4 is to tesselate the image into triangles or quads, and
> transforming these individually with the resulting affine or projective
> transformations, respectively. In this way it should be straightforward to
> map between arbitrary polygons by triangulation.
>
> Hope I understood the question ...
>
> --Wilhelm
>
>
> ________________________________________
> From: ImageJ Interest Group <
[hidden email]> on behalf of Kenneth
> Sloan <
[hidden email]>
> Sent: Sunday, January 29, 2017 21:53
> To:
[hidden email]
> Subject: cut&paste w/arbitrary warp
>
> I’m about to write a Java plug-in to do cut&paste with arbitrary warp. As
> usual, I’d like to make sure I’m not re-inventing the wheel. Here are a
> few of the operations I have in mind:
>
> [in most cases, there will be two images open - think of them as source
> and destination, although I may play a bit fast and loose with this]
>
> For all operations, begin by outlining a (closed, simple) polygon) - P
>
> a) specify 1 point in the source and 1 point in the destination. MOVE the
> pixels in P using simple TRANSLATION
>
> b) specify 2 points (u,v) in the source and 2 points (s,t) in the
> destination, MOVE the pixels in P such that u maps to s and the direction
> from u->v maps to the direction s->t
>
> c) specify2 points (u,v) in the source and 2 points (s,t) in the
> destination. MOVE the pixels in P such that u maps to s and v maps to t
>
> Those are pretty simple - and those may be all I need for the immediate
> application. Now it becomes more complicated.
>
> d) specify segment of P (begin at vertex v1 and end at vertex vn).
> Specify points w1 and wn in the destination. Move and scale the polyline
> v1..vn so that v1->w1 and v2->w2. Next, allow the user to perturb the
> vertices of the new polyline (within reason) to produce w1’..wn'. Finally,
> MOVE the pixels in P s.t. the entire polyline v1..vn maps to the perturbed
> poly line w1’..wn’ AND (the tricky part) the rest of the polygon warps
> “appropriately”.
>
> e) special case of the above - map the entire bouncary polygon P to a
> copied and perturbed boundary w’, warping the interior as needed.
>
> I think I’ve simplified some things by making the number of vertices in v
> and w (and w’) match exactly. Freeform specification of v and w is
> probably not that much harder to implement - but the end users will
> probably be thinking in terms of specific landmark POINTS rather than
> boundaries, per se.
>
> Before someone asks, in all cases “MOVE the pixels in P” means “iterate
> over the pixels in the destination and fetch pixel values from the source.
>
> So…my main question is: does this functionality exist anywhere?
>
> And if so, where can I steal it.
>
> Please note - I know how to do the warping and will (with some work)
> figure out how to implement the interaction. So, I don’t nee advice on
> appropriate methods (but…feel free to offer it anyway!).
> I’m really just interested in whether or not there is an existing tool
> that does what I want.
>
> Once past that - I welcome ideas on improving my specifications (either
> simplifying, or generalizing).
>
> The specific applications is to repair artifacts generated in the creation
> of thin sections of human retina. The most serious problem with these is
> that some of the layers of the retina are fragile, and the tissue
> separates, with one part pulling away (with some warping and bending). The
> goal is to put it back together again, if only crudely. The matching
> doesn’t have to be terribly precise - the point is to create a
> correspondence between features found along the length of one part with
> features found along the length of the other (separated) part. Decisions
> about what warping is “reasonable” may well turn out to depend on the types
> of warping actually present. Mostly, this is a fairly simple separation
> and rotation. I anticipate some issues here near the pivot point, where
> the tissue remains attached. This may, or may not, be important.
>
> And finally…I’ve gone to a generalized “cut and paste” because there may
> be several such “separation and movement” artifacts in the same section. I
> originally thought I could simply throw a mesh over everything and warp
> things back together - but, I’ve seen enough examples that I’m now going to
> count on a trained observer starting from one source image and doing
> successive “cut/paste/warp” operations to put things together manually.
>
> We could *almost” do this by grabbing polygons and moving them using only
> translation and rotation - but again, examples demonstrate that some amount
> of local generalized warping will be necessary.
>
> —
> Kenneth Sloan
>
[hidden email]
>
>
>
>
> --
> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>