Better Nohalo comments
This commit is contained in:
Nicolas Robidoux
parent
4f9e33aaf4
commit
4112bcc70a
@ -1,7 +1,7 @@
|
||||
/* Nohalo subdivision followed by LBB (Locally Bounded Bicubic)
|
||||
* interpolation
|
||||
*
|
||||
* N. Robidoux and C. Racette 11/5--17/5/2009
|
||||
* N. Robidoux, C. Racette and J. Cupitt 11/5--18/5/2009
|
||||
*
|
||||
* N. Robidoux 1/4-29/5/2009
|
||||
*
|
||||
@ -68,7 +68,7 @@
|
||||
*
|
||||
* "Nohalo" is a resampler with a mission: smoothly straightening
|
||||
* oblique lines without undesirable side-effects. In particular,
|
||||
* without much blurring and with absolutely no added haloing.
|
||||
* without much blurring and with no added haloing.
|
||||
*
|
||||
* In this code, one Nohalo subdivision is performed. The
|
||||
* interpolation is finished with LBB (Locally Bounded Bicubic).
|
||||
@ -79,28 +79,35 @@
|
||||
* Nohalo is interpolatory
|
||||
* =======================
|
||||
*
|
||||
* That is, nohalo preserves point values: If asked for the value at
|
||||
* That is, Nohalo preserves point values: If asked for the value at
|
||||
* the center of an input pixel, the sampler returns the corresponding
|
||||
* value, unchanged. In addition, because nohalo is continuous, if
|
||||
* value, unchanged. In addition, because Nohalo is continuous, if
|
||||
* asked for a value at a location "very close" to the center of an
|
||||
* input pixel, then the sampler returns a value "very close" to
|
||||
* it. (Nohalo is not smoothing like, say, B-Spline
|
||||
* pseudo-interpolation.)
|
||||
*
|
||||
* ========================================================
|
||||
* Nohalo is co-monotone (this is why it's called "nohalo")
|
||||
* ========================================================
|
||||
* ====================================================================
|
||||
* Nohalo subdivision is co-monotone (this is why it's called "no-halo")
|
||||
* ====================================================================
|
||||
*
|
||||
* What monotonicity more or less means here is that the resampled
|
||||
* value is in the range of the four closest input values. This
|
||||
* property is why there is no added haloing. It also implies that
|
||||
* clamping is unnecessary (provided abyss values are within the range
|
||||
* of acceptable values, which is always the case). (Note: plain
|
||||
* vanilla bilinear is also co-monotone.)
|
||||
* One consequence of monotonicity is that additional subdivided
|
||||
* values are in the range of the four closest input values, which is
|
||||
* a form of local boundedness. (Note: plain vanilla bilinear and
|
||||
* nearest neighbour are also co-monotone.) LBB is also locally
|
||||
* bounded. Consequently, Nohalo subdivision followed by LBB is
|
||||
* locally bounded. When used as a finishing scheme for Nohalo, the
|
||||
* standard LBB bounds imply that the final interpolated value is in
|
||||
* the range of the nine closest input values. This property is why
|
||||
* there is very little added haloing, even when a finishing scheme
|
||||
* which is not strictly monotone. Another consequence of local
|
||||
* boundedness is that clamping is unnecessary (provided abyss values
|
||||
* are within the range of acceptable values, which is "always" the
|
||||
* case).
|
||||
*
|
||||
* Note: If the abyss policy is an extrapolating one---for example,
|
||||
* linear or bilinear extrapolation---clamping is still unnecessary
|
||||
* unless one attempts to resample outside of the convex hull of the
|
||||
* UNLESS one attempts to resample outside of the convex hull of the
|
||||
* input pixel positions. Consequence: the "corner" image size
|
||||
* convention does not require clamping when using linear
|
||||
* extrapolation abyss policy when performing image resizing, but the
|
||||
@ -115,6 +122,10 @@
|
||||
* Nohalo is a local method
|
||||
* ========================
|
||||
*
|
||||
* The interpolated pixel value when using Nohalo subdivision followed
|
||||
* by LBB only depends on the 21 (5x5 minus the four corners) closest
|
||||
* input values.
|
||||
*
|
||||
* ===============================
|
||||
* Nohalo is second order accurate
|
||||
* ===============================
|
||||
@ -122,15 +133,15 @@
|
||||
* (Except possibly near the boundary: it is easy to make this
|
||||
* property carry over everywhere but this requires a tuned abyss
|
||||
* policy---linear extrapolation, say---or building the boundary
|
||||
* conditions inside the sampler.) Nohalo is exact on linear
|
||||
* conditions inside the sampler.) Nohalo+LBB is exact on linear
|
||||
* intensity profiles, meaning that if the input pixel values (in the
|
||||
* stencil) are obtained from a function of the form f(x,y) = a + b*x
|
||||
* + c*y (a, b, c constants), then the computed pixel value is exactly
|
||||
* the value of f(x,y) at the asked-for sampling location. The
|
||||
* boundary condition which is emulated by VIPS throught the "extend"
|
||||
* boundary condition which is emulated by VIPS through the "extend"
|
||||
* extension of the input image---this corresponds to the nearest
|
||||
* neighbour abyss policy---does NOT make this resampler exact on
|
||||
* linears at the boundary. It does, however, guarantee that no
|
||||
* linears near the boundary. It does, however, guarantee that no
|
||||
* clamping is required even when resampled values are computed at
|
||||
* positions outside of the extent of the input image (when
|
||||
* extrapolation is required).
|
||||
@ -139,23 +150,23 @@
|
||||
* Nohalo is nonlinear
|
||||
* ===================
|
||||
*
|
||||
* In particular, resampling a sum of images may not be the same as
|
||||
* summing the resamples. (This occurs even without taking into account
|
||||
* over and underflow issues: images can only take values within a
|
||||
* banded range, and consequently no sampler is truly linear.)
|
||||
* Both Nohalo and LBB are nonlinear, consequently their composition
|
||||
* is nonlinear. In particular, resampling a sum of images may not be
|
||||
* the same as summing the resamples. (This occurs even without taking
|
||||
* into account over and underflow issues: images can only take values
|
||||
* within a banded range, and consequently no sampler is truly
|
||||
* linear.)
|
||||
*
|
||||
* ====================
|
||||
* Weaknesses of nohalo
|
||||
* Weaknesses of Nohalo
|
||||
* ====================
|
||||
*
|
||||
* In some cases, the initial subdivision computation is wasted:
|
||||
*
|
||||
* If a region is bichromatic, the nonlinear component of the level 1
|
||||
* nohalo is zero in the interior of the region, and consequently
|
||||
* nohalo boils down to bilinear. For such images, either stick to
|
||||
* bilinear, or use a higher level (quality) setting. (There is no
|
||||
* real harm in using nohalo when it boils down to bilinear if one
|
||||
* does not mind wasting cycles.)
|
||||
* If a region is bi-chromatic, the nonlinear component of Nohalo
|
||||
* subdivision is zero in the interior of the region, and consequently
|
||||
* Nohalo subdivision boils down to bilinear. For such images, LBB is
|
||||
* probably a better choice.
|
||||
*/
|
||||
|
||||
#ifdef HAVE_CONFIG_H
|
||||
@ -741,9 +752,25 @@ lbbicubic( const double c00,
|
||||
|
||||
/*
|
||||
* Computation of the four min and four max over 3x3 input data
|
||||
* sub-blocks of the 4x4 input stencil. (Because there is
|
||||
* redundancy, only 17 minima and 17 maxima are needed; if done with
|
||||
* conditional moves, only 28 different flags are involved.)
|
||||
* sub-blocks of the 4x4 input stencil.
|
||||
*
|
||||
* Surprisingly, we have not succeeded in using the fact that the
|
||||
* data comes from the (co-monotone) method Nohalo so that it is
|
||||
* known ahead of time that
|
||||
*
|
||||
* dos_thr is between dos_two and dos_fou
|
||||
*
|
||||
* tre_two is between dos_two and qua_two
|
||||
*
|
||||
* tre_fou is between dos_fou and qua_fou
|
||||
*
|
||||
* qua_thr is between qua_two and qua_fou
|
||||
*
|
||||
* tre_thr is in the convex hull of dos_two, dos_fou, qua_two and qua_fou
|
||||
*
|
||||
* to minimize the number of flags and conditional moves.
|
||||
*
|
||||
* Suggestions welcome!
|
||||
*/
|
||||
const double m1 = (dos_two <= dos_thr) ? dos_two : dos_thr ;
|
||||
const double M1 = (dos_two <= dos_thr) ? dos_thr : dos_two ;
|
||||
@ -1033,20 +1060,20 @@ lbbicubic( const double c00,
|
||||
}
|
||||
|
||||
/*
|
||||
* Call Nohalo with an interpolator as a parameter.
|
||||
* Call Nohalo+LBB with a careful type conversion as a parameter.
|
||||
*
|
||||
* It would be nice to do this with templates somehow---for one thing
|
||||
* this would allow code comments!---but we can't figure a clean way
|
||||
* to do it.
|
||||
*/
|
||||
#define NOHALO_INTER( inter ) \
|
||||
template <typename T> static void inline \
|
||||
nohalo_ ## inter( PEL* restrict pout, \
|
||||
const PEL* restrict pin, \
|
||||
const int bands, \
|
||||
const int lskip, \
|
||||
const double x_0, \
|
||||
const double y_0 ) \
|
||||
#define NOHALO_CONVERSION( conversion ) \
|
||||
template <typename T> static void inline \
|
||||
nohalo_ ## conversion( PEL* restrict pout, \
|
||||
const PEL* restrict pin, \
|
||||
const int bands, \
|
||||
const int lskip, \
|
||||
const double x_0, \
|
||||
const double y_0 ) \
|
||||
{ \
|
||||
T* restrict out = (T *) pout; \
|
||||
\
|
||||
@ -1261,28 +1288,28 @@ lbbicubic( const double c00,
|
||||
qua_thr, \
|
||||
qua_fou ); \
|
||||
\
|
||||
{ \
|
||||
const T result = to_ ## inter<T>( double_result ); \
|
||||
in++; \
|
||||
*out++ = result; \
|
||||
} \
|
||||
{ \
|
||||
const T result = to_ ## conversion<T>( double_result ); \
|
||||
in++; \
|
||||
*out++ = result; \
|
||||
} \
|
||||
\
|
||||
} while (--band); \
|
||||
}
|
||||
|
||||
|
||||
NOHALO_INTER( fptypes )
|
||||
NOHALO_INTER( withsign )
|
||||
NOHALO_INTER( nosign )
|
||||
NOHALO_CONVERSION( fptypes )
|
||||
NOHALO_CONVERSION( withsign )
|
||||
NOHALO_CONVERSION( nosign )
|
||||
|
||||
|
||||
#define CALL( T, inter ) \
|
||||
nohalo_ ## inter<T>( out, \
|
||||
p, \
|
||||
bands, \
|
||||
lskip, \
|
||||
relative_x, \
|
||||
relative_y );
|
||||
#define CALL( T, conversion ) \
|
||||
nohalo_ ## conversion<T>( out, \
|
||||
p, \
|
||||
bands, \
|
||||
lskip, \
|
||||
relative_x, \
|
||||
relative_y );
|
||||
|
||||
|
||||
/*
|
||||
|
||||
Loading…
Reference in New Issue
Block a user