677 lines
24 KiB
C++
677 lines
24 KiB
C++
/* nohalo interpolator
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*/
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/*
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This file is part of VIPS.
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VIPS is free software; you can redistribute it and/or modify it
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under the terms of the GNU Lesser General Public License as
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published by the Free Software Foundation; either version 2 of the
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License, or (at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this program; if not, write to the Free
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Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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02111-1307 USA
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*/
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/*
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These files are distributed with VIPS - http://www.vips.ecs.soton.ac.uk
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*/
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/*
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* 2009 (c) Nicolas Robidoux
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*
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* Nicolas thanks Geert Jordaens, John Cupitt, Minglun Gong, Øyvind
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* Kolås and Sven Neumann for useful comments and code.
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*
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* Nicolas Robidoux's research on nohalo funded in part by an NSERC
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* (National Science and Engineering Research Council of Canada)
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* Discovery Grant.
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*/
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/* Hacked for vips by J. Cupitt, 20/1/09
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* Tweaks by N. Robidoux and J. Cupitt 5-15/03/09
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*/
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/*
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* ================
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* NOHALO RESAMPLER
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* ================
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*
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* "Nohalo" is a family of parameterized resamplers with a mission:
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* smoothly straightening oblique lines without undesirable
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* side-effects.
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*
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* The key parameter, which may be described as a "quality" parameter,
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* is an integer which specifies the number of "levels" of binary
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* subdivision which are performed. level = 0 can be thought of as
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* being plain vanilla bilinear resampling; level = 1 is then the
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* first "non-classical" method of the familiy.
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*
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* Although it increases computational cost, additional levels
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* increase the quality of the resampled pixel value unless the
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* resampled location happens to be exactly where a subdivided grid
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* point (for this level) is located, in which case further levels do
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* not change the answer, and consequently do not increase its
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* quality.
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*
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* ===================================================
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* THIS CODE ONLY IMPLEMENTS THE LOWEST QUALITY NOHALO
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* ===================================================
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*
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* This code implement nohalo for (quality) level = 1. Nohalo for
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* higher quality levels will be implemented later.
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*
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* Key properties:
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*
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* =======================
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* Nohalo is interpolatory
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* =======================
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*
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* That is, nohalo preserves point values: If asked for the value at
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* the center of an input pixel, the sampler returns the corresponding
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* value, unchanged. In addition, because nohalo is continuous, if
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* asked for a value at a location "very close" to the center of an
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* input pixel, then the sampler returns a value "very close" to
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* it. (Nohalo is not smoothing like, say, B-Spline
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* pseudo-interpolation.)
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*
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* ========================================================
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* Nohalo is co-monotone (this is why it's called "nohalo")
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* ========================================================
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*
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* What monotonicity means here is that the resampled value is in the
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* range of the four closest input values. Consequently, nohalo does
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* not add haloing. It also means that clamping is unnecessary
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* (provided abyss values are within the range of acceptable values,
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* which is always the case). (Note: plain vanilla bilinear is also
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* co-monotone.)
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*
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* Note: If the abyss policy is an extrapolating one---for example,
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* linear or bilinear extrapolation---clamping is still unnecessary
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* unless one attempts to resample outside of the convex hull of the
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* input pixel positions. Consequence: the "corner" image size
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* convention does not require clamping when using linear
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* extrapolation abyss policy when performing image resizing, but the
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* "center" one does, when upscaling, at locations very close to the
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* boundary. If computing values at locations outside of the convex
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* hull of the pixel locations of the input image, nearest neighbour
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* abyss policy is most likely better anyway, because linear
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* extrapolation produces "streaks" if positions far outside the
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* original image boundary are resampled.
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*
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* ========================
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* Nohalo is a local method
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* ========================
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*
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* The value of the reconstructed intensity surface at any point
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* depends on the values of (at most) 12 nearby input values, located
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* in a "cross" centered at the closest four input pixel centers.
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*
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* ===========================================================
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* When level = infinity, nohalo's intensity surface is smooth
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* ===========================================================
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*
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* It is conjectured that the intensity surface is infinitely
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* differentiable. Consequently, "Mach banding" (primarily caused by
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* sharp "ridges" in the reconstructed intensity surface and
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* particularly noticeable, for example, when using bilinear
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* resampling) is (essentially) absent, even at high magnifications,
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* WHEN THE LEVEL IS HIGH (more or less when 2^(level+1) is at least
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* the largest local magnification factor, which means that the level
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* 1 nohalo does not show much Mach banding up to a magnification of
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* about 4).
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*
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* ===============================
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* Nohalo is second order accurate
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* ===============================
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*
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* (Except possibly near the boundary: it is easy to make this
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* property carry over everywhere but this requires a tuned abyss
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* policy---linear extrapolation, say---or building the boundary
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* conditions inside the sampler.) Nohalo is exact on linear
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* intensity profiles, meaning that if the input pixel values (in the
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* stencil) are obtained from a function of the form f(x,y) = a + b*x
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* + c*y (a, b, c constants), then the computed pixel value is exactly
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* the value of f(x,y) at the asked-for sampling location. The
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* boundary condition which is emulated by VIPS throught the "extend"
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* extension of the input image---this corresponds to the nearest
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* neighbour abyss policy---does NOT make this resampler exact on
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* linears at the boundary. It does, however, guarantee that no
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* clamping is required even when resampled values are computed at
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* positions outside of the extent of the input image (when
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* extrapolation is required).
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*
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* ===================
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* Nohalo is nonlinear
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* ===================
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*
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* In particular, resampling a sum of images may not be the same as
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* summing the resamples. (This occurs even without taking into account
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* over and underflow issues: images can only take values within a
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* banded range, and consequently no sampler is truly linear.)
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*
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* ====================
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* Weaknesses of nohalo
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* ====================
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*
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* In some cases, the first level nonlinear computation is wasted:
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*
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* If a region is bichromatic, the nonlinear component of the level 1
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* nohalo is zero in the interior of the region, and consequently
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* nohalo boils down to bilinear. For such images, either stick to
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* bilinear, or use a higher level (quality) setting. (There is no
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* real harm in using nohalo when it boils down to bilinear if one
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* does not mind wasting cycles.)
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*
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* Low quality levels do NOT produce a continuously differentiable
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* intensity surface:
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*
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* With a "finite" level is used (that is, in practice), the nohalo
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* intensity surface is only continuous: there are gradient
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* discontinuities because the "final interpolation step" is performed
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* with bilinear. (Exception: if the "corner" image size convention is
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* used and the magnification factor is 2, that is, if the resampled
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* points sit exactly on the binary subdivided grid, then nohalo level
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* 1 gives the same result as as level=infinity, and consequently the
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* intensity surface can be treated as if smooth.)
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*/
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#ifdef HAVE_CONFIG_H
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#include <config.h>
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#endif /*HAVE_CONFIG_H*/
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#include <vips/intl.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <vips/vips.h>
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#include <vips/internal.h>
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#include "templates.h"
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#ifndef vips_restrict
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#ifdef __restrict
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#define vips_restrict __restrict
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#else
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#ifdef __restrict__
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#define vips_restrict __restrict__
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#else
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#define vips_restrict
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#endif
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#endif
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#endif
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/*
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* FAST_PSEUDO_FLOOR is a floor and floorf replacement which has been
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* found to be faster on several linux boxes than the library
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* version. It returns the floor of its argument unless the argument
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* is a negative integer, in which case it returns one less than the
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* floor. For example:
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*
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* FAST_PSEUDO_FLOOR(0.5) = 0
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*
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* FAST_PSEUDO_FLOOR(0.) = 0
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*
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* FAST_PSEUDO_FLOOR(-.5) = -1
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*
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* as expected, but
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*
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* FAST_PSEUDO_FLOOR(-1.) = -2
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*
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* The locations of the discontinuities of FAST_PSEUDO_FLOOR are the
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* same as floor and floorf; it is just that at negative integers the
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* function is discontinuous on the right instead of the left.
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*/
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#define FAST_PSEUDO_FLOOR(x) ( (int)(x) - ( (x) < 0. ) )
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/*
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* FAST_MINMOD is an implementation of the minmod function which only
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* needs two conditional moves. (Most implementations need at least
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* three branches.) In the Nohalo code, the square of the first
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* argument is used in two different minmod computations. The product
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* is also precomputed to keep it out of branching way. (Nicolas: I
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* think that this may be the first two branch minmod.)
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*/
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#define FAST_MINMOD(a,b,ab,abmaa) \
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( (ab)>=0. ? ( (abmaa)>=0. ? (a) : (b) ) : 0. )
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#define VIPS_TYPE_INTERPOLATE_NOHALO \
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(vips_interpolate_nohalo_get_type())
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#define VIPS_INTERPOLATE_NOHALO( obj ) \
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(G_TYPE_CHECK_INSTANCE_CAST( (obj), \
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VIPS_TYPE_INTERPOLATE_NOHALO, VipsInterpolateNohalo ))
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#define VIPS_INTERPOLATE_NOHALO_CLASS( klass ) \
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(G_TYPE_CHECK_CLASS_CAST( (klass), \
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VIPS_TYPE_INTERPOLATE_NOHALO, VipsInterpolateNohaloClass))
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#define VIPS_IS_INTERPOLATE_NOHALO( obj ) \
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(G_TYPE_CHECK_INSTANCE_TYPE( (obj), VIPS_TYPE_INTERPOLATE_NOHALO ))
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#define VIPS_IS_INTERPOLATE_NOHALO_CLASS( klass ) \
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(G_TYPE_CHECK_CLASS_TYPE( (klass), VIPS_TYPE_INTERPOLATE_NOHALO ))
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#define VIPS_INTERPOLATE_NOHALO_GET_CLASS( obj ) \
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(G_TYPE_INSTANCE_GET_CLASS( (obj), \
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VIPS_TYPE_INTERPOLATE_NOHALO, VipsInterpolateNohaloClass ))
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typedef struct _VipsInterpolateNohalo {
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VipsInterpolate parent_object;
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} VipsInterpolateNohalo;
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typedef struct _VipsInterpolateNohaloClass {
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VipsInterpolateClass parent_class;
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} VipsInterpolateNohaloClass;
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static void inline
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nohalo_sharp_level_1( const double uno_two,
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const double uno_thr,
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const double dos_one,
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const double dos_two,
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const double dos_thr,
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const double dos_fou,
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const double tre_one,
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const double tre_two,
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const double tre_thr,
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const double tre_fou,
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const double qua_two,
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const double qua_thr,
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double* vips_restrict r1,
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double* vips_restrict r2,
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double* vips_restrict r3 )
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{
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/*
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* This function calculates the missing three double density pixel
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* values. The caller does bilinear interpolation on them and
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* dos_two.
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*/
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/*
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* THE STENCIL OF INPUT VALUES:
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*
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* Nohalo's stencil is the same as, say, Catmull-Rom, with the
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* exception that the four corner values are not used:
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*
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* (ix-1,iy-2) (ix,iy-2)
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* = uno_two = uno_thr
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*
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* (ix-2,iy-1) (ix-1,iy-1) (ix,iy-1) (ix+1,iy-1)
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* = dos_one = dos_two = dos_thr = dos_fou
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*
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* (ix-2,iy) (ix-1,iy) (ix,iy) (ix+1,iy)
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* = tre_one = tre_two = tre_thr = tre_fou
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*
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* (ix-1,iy+1) (ix,iy+1)
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* = qua_two = qua_thr
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*
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* The indices associated with the values shown above are in the
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* case that the resampling point is closer to (ix-1,iy-1) than the
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* other three central positions. Pointer arithmetic is used to
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* implicitly reflect the input stencil in the other three cases,
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* For example, if the sampling position is closer to dos_two (that
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* is, if relative_x_is_rite = 1 but relative_y_is_down = 0 below),
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* then dos_two corresponds to (ix,iy-1), dos_thr corresponds to
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* (ix-1,iy-1) etc. Consequently, the three missing double density
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* values are halfway between dos_two and dos_thr, halfway between
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* dos_two and tre_two, and at the average of the four central
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* positions.
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*/
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/*
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* Computation of the nonlinear slopes: If two consecutive pixel
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* value differences have the same sign, the smallest one (in
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* absolute value) is taken to be the corresponding slope; if the
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* two consecutive pixel value differences don't have the same sign,
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* the corresponding slope is set to 0. (In other words, apply
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* minmod to comsecutive slopes.)
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*/
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/*
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* Dos(s) horizontal differences:
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*/
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const double prem_dos = dos_two - dos_one;
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const double deux_dos = dos_thr - dos_two;
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const double troi_dos = dos_fou - dos_thr;
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/*
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* Tre(s) horizontal differences:
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*/
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const double prem_tre = tre_two - tre_one;
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const double deux_tre = tre_thr - tre_two;
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const double troi_tre = tre_fou - tre_thr;
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/*
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* Two vertical differences:
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*/
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const double prem_two = dos_two - uno_two;
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const double deux_two = tre_two - dos_two;
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const double troi_two = qua_two - tre_two;
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/*
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* Thr(ee) vertical differences:
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*/
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const double prem_thr = dos_thr - uno_thr;
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const double deux_thr = tre_thr - dos_thr;
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const double troi_thr = qua_thr - tre_thr;
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/*
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* Useful sums:
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*/
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const double dos_two_plus_dos_thr = dos_two + dos_thr;
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const double dos_two_plus_tre_two = dos_two + tre_two;
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/*
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* Products useful for minmod:
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*/
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const double deux_prem_dos = deux_dos * prem_dos;
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const double deux_deux_dos = deux_dos * deux_dos;
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const double deux_troi_dos = deux_dos * troi_dos;
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const double deux_prem_two = deux_two * prem_two;
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const double deux_deux_two = deux_two * deux_two;
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const double deux_troi_two = deux_two * troi_two;
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const double deux_prem_tre = deux_tre * prem_tre;
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const double deux_deux_tre = deux_tre * deux_tre;
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const double deux_troi_tre = deux_tre * troi_tre;
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const double deux_prem_thr = deux_thr * prem_thr;
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const double deux_deux_thr = deux_thr * deux_thr;
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const double deux_troi_thr = deux_thr * troi_thr;
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/*
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* Useful sum:
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*/
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const double deux_thr_plus_deux_dos = deux_thr + deux_dos;
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/*
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* Differences useful for minmod:
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*/
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const double deux_prem_minus_deux_deux_dos = deux_prem_dos - deux_deux_dos;
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const double deux_troi_minus_deux_deux_dos = deux_troi_dos - deux_deux_dos;
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const double deux_prem_minus_deux_deux_two = deux_prem_two - deux_deux_two;
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const double deux_troi_minus_deux_deux_two = deux_troi_two - deux_deux_two;
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const double deux_prem_minus_deux_deux_tre = deux_prem_tre - deux_deux_tre;
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const double deux_troi_minus_deux_deux_tre = deux_troi_tre - deux_deux_tre;
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const double deux_prem_minus_deux_deux_thr = deux_prem_thr - deux_deux_thr;
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const double deux_troi_minus_deux_deux_thr = deux_troi_thr - deux_deux_thr;
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/*
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* Compute the needed "right" (at the boundary between one input
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* pixel areas) double resolution pixel value:
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*/
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const double four_times_dos_twothr =
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FAST_MINMOD( deux_dos, prem_dos, deux_prem_dos,
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deux_prem_minus_deux_deux_dos )
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-
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FAST_MINMOD( deux_dos, troi_dos, deux_troi_dos,
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deux_troi_minus_deux_deux_dos )
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+
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2. * dos_two_plus_dos_thr;
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/*
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* Compute the needed "down" double resolution pixel value:
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*/
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const double four_times_dostre_two =
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FAST_MINMOD( deux_two, prem_two, deux_prem_two,
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deux_prem_minus_deux_deux_two )
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-
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FAST_MINMOD( deux_two, troi_two, deux_troi_two,
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deux_troi_minus_deux_deux_two )
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+
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2. * dos_two_plus_tre_two;
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/*
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* Compute the "diagonal" (at the boundary between thrr input
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* pixel areas) double resolution pixel value:
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*/
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const double piece_of_eight_times_dostre_twothr =
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four_times_dos_twothr
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+
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four_times_dostre_two
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+
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2. * deux_thr_plus_deux_dos;
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const double eight_times_dostre_twothr =
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piece_of_eight_times_dostre_twothr
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+
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FAST_MINMOD( deux_tre, prem_tre, deux_prem_tre,
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deux_prem_minus_deux_deux_tre )
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-
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FAST_MINMOD( deux_tre, troi_tre, deux_troi_tre,
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deux_troi_minus_deux_deux_tre )
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+
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FAST_MINMOD( deux_thr, prem_thr, deux_prem_thr,
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deux_prem_minus_deux_deux_thr )
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-
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FAST_MINMOD( deux_thr, troi_thr, deux_troi_thr,
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deux_troi_minus_deux_deux_thr );
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/*
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* Return the first newly computed double density values:
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*/
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*r1 = four_times_dos_twothr;
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*r2 = four_times_dostre_two;
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*r3 = eight_times_dostre_twothr;
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}
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/* Call nohalo_sharp_level_1 with an interpolator as a parameter.
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* It'd be nice to do this with templates somehow :-( but I can't see a
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* clean way to do it.
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*/
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#define NOHALO_SHARP_LEVEL_1_INTER( inter ) \
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template <typename T> static void inline \
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nohalo_sharp_level_1_ ## inter( PEL* vips_restrict pout, \
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const PEL* vips_restrict pin, \
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const int bands, \
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const int lskip, \
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const double relative_x, \
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const double relative_y ) \
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{ \
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T* vips_restrict out = (T *) pout; \
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\
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const int relative_x_is_rite = ( relative_x >= 0. ); \
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const int relative_y_is_down = ( relative_y >= 0. ); \
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\
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const int sign_of_relative_x = 2 * relative_x_is_rite - 1; \
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const int sign_of_relative_y = 2 * relative_y_is_down - 1; \
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\
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const int corner_reflection_shift = \
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relative_x_is_rite * bands + relative_y_is_down * lskip; \
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\
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const T* vips_restrict in = ( (T *) pin ) + corner_reflection_shift; \
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\
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const int shift_1_pixel = sign_of_relative_x * bands; \
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const int shift_1_row = sign_of_relative_y * lskip; \
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\
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const double w = ( 2 * sign_of_relative_x ) * relative_x; \
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const double z = ( 2 * sign_of_relative_y ) * relative_y; \
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\
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const int uno_two_shift = shift_1_row; \
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const int uno_thr_shift = shift_1_row - shift_1_pixel; \
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\
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const int dos_one_shift = shift_1_pixel; \
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const int dos_two_shift = 0; \
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const int dos_thr_shift = -shift_1_pixel; \
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const int dos_fou_shift = -2 * shift_1_pixel; \
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\
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const int tre_one_shift = dos_one_shift - shift_1_row; \
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const int tre_two_shift = -shift_1_row; \
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const int tre_thr_shift = dos_thr_shift - shift_1_row; \
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const int tre_fou_shift = dos_fou_shift - shift_1_row; \
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\
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const int qua_two_shift = tre_two_shift - shift_1_row; \
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const int qua_thr_shift = tre_thr_shift - shift_1_row; \
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\
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const double x = 1. - w; \
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const double w_times_z = w * z; \
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const double x_times_z = x * z; \
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const double w_times_y_over_4 = .25 * ( w - w_times_z ); \
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const double x_times_z_over_4 = .25 * x_times_z; \
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const double x_times_y_over_8 = .125 * ( x - x_times_z ); \
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\
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int band = bands; \
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\
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do \
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{ \
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double four_times_dos_twothr; \
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double four_times_dostre_two; \
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double eight_times_dostre_twothr; \
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\
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const double dos_two = in[dos_two_shift]; \
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\
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nohalo_sharp_level_1( in[uno_two_shift], in[uno_thr_shift], \
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in[dos_one_shift], dos_two, \
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in[dos_thr_shift], in[dos_fou_shift], \
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in[tre_one_shift], in[tre_two_shift], \
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in[tre_thr_shift], in[tre_fou_shift], \
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in[qua_two_shift], in[qua_thr_shift], \
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&four_times_dos_twothr, \
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&four_times_dostre_two, \
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&eight_times_dostre_twothr ); \
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\
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const T result = bilinear_ ## inter<T>( w_times_z, \
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x_times_z_over_4, \
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w_times_y_over_4, \
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x_times_y_over_8, \
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dos_two, \
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four_times_dos_twothr, \
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four_times_dostre_two, \
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eight_times_dostre_twothr ); \
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\
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in++; \
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*out++ = result; \
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} while (--band); \
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}
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NOHALO_SHARP_LEVEL_1_INTER( float )
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NOHALO_SHARP_LEVEL_1_INTER( signed )
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NOHALO_SHARP_LEVEL_1_INTER( unsigned )
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/* We need C linkage for this.
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*/
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extern "C" {
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G_DEFINE_TYPE( VipsInterpolateNohalo, vips_interpolate_nohalo,
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VIPS_TYPE_INTERPOLATE );
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}
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static void
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vips_interpolate_nohalo_interpolate( VipsInterpolate* vips_restrict interpolate,
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PEL* vips_restrict out,
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REGION* vips_restrict in,
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double absolute_x,
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double absolute_y )
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{
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/*
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* VIPS versions of Nicolas's pixel addressing values. Double bands for
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* complex images.
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*/
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const int lskip = IM_REGION_LSKIP( in ) / IM_IMAGE_SIZEOF_ELEMENT( in->im );
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const int bands_actual = in->im->Bands;
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const int bands =
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( im_iscomplex( in->im ) ? 2 * bands_actual : bands_actual );
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/*
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* floor's surrogate FAST_PSEUDO_FLOOR is used to make sure that the
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* transition through 0 is smooth. If it is known that absolute_x
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* and absolute_y will never be less than 0, plain cast---that is,
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* const int ix = absolute_x---should be used instead. Actually,
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* any function which agrees with floor for non-integer values, and
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* picks one of the two possibilities for integer values, can be
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* used. FAST_PSEUDO_FLOOR fits the bill.
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*
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* Then, x is the x-coordinate of the sampling point relative to the
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* position of the center of the convex hull of the 2x2 block of
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* closest pixels. Similarly for y. Range of values: [-.5,.5).
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*/
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const double absolute_y_minus_half = absolute_y - .5;
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const double absolute_x_minus_half = absolute_x - .5;
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const int iy = FAST_PSEUDO_FLOOR (absolute_y);
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const double relative_y = absolute_y_minus_half - iy;
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const int ix = FAST_PSEUDO_FLOOR (absolute_x);
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const double relative_x = absolute_x_minus_half - ix;
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/*
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* Move the pointer to (the first band of) the top/left pixel
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* of the 2x2 group of pixel centers which contains the
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* sampling location in its convex hull:
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*/
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const PEL * vips_restrict p = (PEL *) IM_REGION_ADDR( in, ix, iy );
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#define CALL( T, inter ) \
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nohalo_sharp_level_1_ ## inter<T>( out, \
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p, \
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bands, \
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lskip, \
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relative_x, \
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relative_y );
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switch( in->im->BandFmt ) {
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case IM_BANDFMT_UCHAR:
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CALL( unsigned char, unsigned );
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break;
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case IM_BANDFMT_CHAR:
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CALL( signed char, signed );
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break;
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case IM_BANDFMT_USHORT:
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CALL( unsigned short, unsigned );
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break;
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case IM_BANDFMT_SHORT:
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CALL( signed short, signed );
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break;
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case IM_BANDFMT_UINT:
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CALL( unsigned int, unsigned );
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break;
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case IM_BANDFMT_INT:
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CALL( signed int, signed );
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break;
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/* Complex images handled by doubling of bands, see above.
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*/
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case IM_BANDFMT_FLOAT:
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case IM_BANDFMT_COMPLEX:
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CALL( float, float );
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break;
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case IM_BANDFMT_DOUBLE:
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case IM_BANDFMT_DPCOMPLEX:
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CALL( double, float );
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break;
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default:
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g_assert( 0 );
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break;
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}
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}
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static void
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vips_interpolate_nohalo_class_init( VipsInterpolateNohaloClass *klass )
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{
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VipsObjectClass *object_class = VIPS_OBJECT_CLASS( klass );
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VipsInterpolateClass *interpolate_class =
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VIPS_INTERPOLATE_CLASS( klass );
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object_class->nickname = "nohalo";
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object_class->description = _( "Edge-enhancing bilinear" );
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interpolate_class->interpolate =
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vips_interpolate_nohalo_interpolate;
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interpolate_class->window_size = 4;
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}
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static void
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vips_interpolate_nohalo_init( VipsInterpolateNohalo *nohalo )
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{
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}
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