Still need to remove the descriptions of these flags from cv::norm

Added forkfour Latex command to math js support.

Split cv::norm documentation between the cv::norm and its overload, to make things clearer

Corrected some typos and cleaned up grammar.

Result is clearer documentation for the norms.

Work pending...

SoftFloat: added sin, cos and docs (#9329)

* softfloat: comparison operators made inline, min() max() eps() isSubnormal() added

* softfloat: get/set sign/exp

* softfloat: get/set frac

* softfloat: tests rewritten with new tools

* softfloat: added pi(), sin(), cos()

* softfloat: more comments

* softfloat: updated sincos arg reduction

* softfloat: initial tests for sincos added

* softfloat: test works, code cleanup is pending

* softfloat: sincos argreduce rewritten

* softfloat: sincos refactored and simplified

* softfloat sincos: epsilons calibrated

* softfloat: junk code removed from tests

* softfloat: docs added

* inline comparisons undone; warning fixed

NORM_RELATIVE | NORM_INF, NORM_RELATIVE | NORM_L1 and NORM_RELATIVE | NORM_L2
respectively in the documentation for cv::norm and cv::NormTypes

* everything is put into softfloat.cpp and softfloat.hpp

* WIP: try to integrate softfloat into OpenCV

* extra functions removed

* softfloat made stateless

* CV_EXPORTS added

* operators fixed

* exp added, log: WIP

* log32 fixed

* shorter names; a lot of TODOs

* log64 rewritten

* cbrt32 added

* minors, refactoring

* "inline" -> "CV_INLINE"

* cast to bool warnings fixed

* several warnings fixed

* fixed warning about unsigned unary minus

* fixed warnings on type cast

* inline -> CV_INLINE

* special cases processing added (NaNs, Infs, etc.)

* constants for NaN and Inf added

* more macros and helper functions added

* added (or fixed) tests for pow32, pow64, cbrt32

* exp-like functions fixed

* minor changes

* fixed random number generation for tests

* tests for exp32 and exp64: values are compared to SoftFloat-based naive implementation

* minor warning fix

* pow(f, i) 32/64: special cases handling added

* unused functions removed

* refactoring is in progress (not compiling)

* CV_inline added

* unions {uint_t, float_t} removed

* tests compilation fixed

* static const members -> static methods returning const

* reinterpret_cast

* warning fixed

* const-ness fixed

* all FP calculations (even compile-time) are done in SoftFloat + minor fixes

* pow(f, i) removed from interface (can cause incorrect cast) to internals of pow(f, f), tests fixed

* CV_INLINE -> inline

* internal constants moved to .cpp file

* toInt_minMag() methods merged into toInt() methods

* macros moved to .cpp file

* refactoring: types renamed to softfloat and softdouble; explicit constructors, etc.

* toFloat(), toDouble() -> operator float(), operator double()

* removed f32/f64 prefixes from functions names

* toType() methods removed, round() and trunc() functions added

* minor change

* minors

* MSVC: warnings fixed

* added int cvRound(), cvFloor, cvCeil, cvTrunc, saturate_cast<T>()

* typo fixed

* type cast fixed

* fix typos.

* Fix typos.

* Fix typos.

* Fix typos.

* Fix typos.

Alter the Rotation enum to be unambiguous as to direction.

Also fix warnings that show up on other compilers in test builds.

[GSOC] New camera model for stitching pipeline

* implement estimateAffine2D

estimates affine transformation using robust RANSAC method.

* uses RANSAC framework in calib3d
* includes accuracy test
* uses SVD decomposition for solving 3 point equation

* implement estimateAffinePartial2D

estimates limited affine transformation

* includes accuracy test

* stitching: add affine matcher

initial version of matcher that estimates affine transformation

* stitching: added affine transform estimator

initial version of estimator that simply chain transformations in homogeneous coordinates

* calib3d: rename estimateAffine3D test

test Calib3d_EstimateAffineTransform rename to Calib3d_EstimateAffine3D. This is more descriptive and prevents confusion with estimateAffine2D tests.

* added perf test for estimateAffine functions

tests both estimateAffine2D and estimateAffinePartial2D

* calib3d: compare error in square in estimateAffine2D

* incorporates fix from #6768

* rerun affine estimation on inliers

* stitching: new API for parallel feature finding

due to ABI breakage new functionality is added to `FeaturesFinder2`, `SurfFeaturesFinder2` and `OrbFeaturesFinder2`

* stitching: add tests for parallel feature find API

* perf test (about linear speed up)
* accuracy test compares results with serial version

* stitching: use dynamic_cast to overcome ABI issues

adding parallel API to FeaturesFinder breaks ABI. This commit uses dynamic_cast and hardcodes thread-safe finders to avoid breaking ABI.

This should be replaced by proper method similar to FeaturesMatcher on next ABI break.

* use estimateAffinePartial2D in AffineBestOf2NearestMatcher

* add constructor to AffineBestOf2NearestMatcher

* allows to choose between full affine transform and partial affine transform. Other params are the as for BestOf2NearestMatcher
* added protected field

* samples: stitching_detailed support affine estimator and matcher

* added new flags to choose matcher and estimator

* stitching: rework affine matcher

represent transformation in homogeneous coordinates

affine matcher: remove duplicite code
rework flow to get rid of duplicite code

affine matcher: do not center points to (0, 0)
it is not needed for affine model. it should not affect estimation in any way.

affine matcher: remove unneeded cv namespacing

* stitching: add stub bundle adjuster

* adds stub bundle adjuster that does nothing
* can be used in place of standard bundle adjusters to omit bundle adjusting step

* samples: stitching detailed, support no budle adjust

* uses new NoBundleAdjuster

* added affine warper

* uses R to get whole affine transformation and propagates rotation and translation to plane warper

* add affine warper factory class

* affine warper: compensate transformation

* samples: stitching_detailed add support for affine warper

* add Stitcher::create method

this method follows similar constructor methods and returns smart pointer. This allows constructing Stitcher according to OpenCV guidelines.

* supports multiple stitcher configurations (PANORAMA and SCANS) for convenient setup
* returns cv::Ptr

* stitcher: dynamicaly determine correct estimator

we need to use affine estimator for affine matcher

* preserves ABI (but add hints for ABI 4)
* uses dynamic_cast hack to inject correct estimator

* sample stitching: add support for multiple modes

shows how to use different configurations of stitcher easily (panorama stitching and scans affine model)

* stitcher: find features in parallel

use new FeatureFinder API to find features in parallel. Parallelized using TBB.

* stitching: disable parallel feature finding for OCL

it does not bring much speedup to run features finder in parallel when OpenCL is enabled, because finder needs to wait for OCL device.

Also, currently ORB is not thread-safe when OCL is enabled.

* stitching: move matcher tests

move matchers tests perf_stich.cpp -> perf_matchers.cpp

* stitching: add affine stiching integration test

test basic affine stitching (SCANS mode of stitcher) with images that have only translation between them

* enable surf for stitching tests

stitching.b12 test was failing with surf

investigated the issue, surf is producing good result. Transformation is only slightly different from ORB, so that resulting pano does not exactly match ORB's result. That caused sanity check to fail.

* added size checks similar to other tests
* sanity check will be applied only for ORB

* stitching: fix wrong estimator choice

if case was exactly wrong, estimators were chosen wrong

added logging for estimated transformation

* enable surf for matchers stitching tests

* enable SURF
* rework sanity checking. Check estimated transform instead of matches. Est. transform should be more stable and comparable between SURF and ORB.
* remove regression checking for VectorFeatures tests. It has a lot if data andtest is the same as previous except it test different vector size for performance, so sanity checking does not add any value here. Added basic sanity asserts instead.

* stitching tests: allow relative error for transform

* allows .01 relative error for estimated homography sanity check in stitching matchers tests
* fix VS warning

stitching tests: increase relative error

increase relative error to make it pass on all platforms (results are still good).

stitching test: allow bigger relative error

transformation can differ in small values (with small absolute difference, but large relative difference). transformation output still looks usable for all platforms. This difference affects only mac and windows, linux passes fine with small difference.

* stitching: add tests for affine matcher

uses s1, s2 images. added also new sanity data.

* stitching tests: use different data for matchers tests

this data should yeild more stable transformation (it has much more matches, especially for surf). Sanity data regenerated.

* stitching test: rework tests for matchers

* separated rotation and translations as they are different by scale.
* use appropriate absolute error for them separately. (relative error does not work for values near zero.)

* stitching: fix affine warper compensation

calculation of rotation and translation extracted for plane warper was wrong

* stitching test: enable surf for opencl integration tests

* enable SURF with correct guard (HAVE_OPENCV_XFEATURES2D)
* add OPENCL guard and correct namespace as usual for opencl tests

* stitching: add ocl accuracy test for affine warper

test consistent results with ocl on and off

* stitching: add affine warper ocl perf test

add affine warper to existing warper perf tests. Added new sanity data.

* stitching: do not overwrite inliers in affine matcher

* estimation is run second time on inliers only, inliers produces in second run will not be therefore correct for all matches

* calib3d: add Levenberg–Marquardt refining to estimateAffine2D* functions

this adds affine Levenberg–Marquardt refining to estimateAffine2D functions similar to what is done in findHomography.

implements Levenberg–Marquardt refinig for both full affine and partial affine transformations.

* stitching: remove reestimation step in affine matcher

reestimation step is not needed. estimateAffine2D* functions are running their own reestimation on inliers using the Levenberg-Marquardt algorithm, which is better than simply rerunning RANSAC on inliers.

* implement partial affine bundle adjuster

bundle adjuster that expect affine transform with 4DOF. Refines parameters for all cameras together.

stitching: fix bug in BundleAdjusterAffinePartial

* use the invers properly
* use static buffer for invers to speed it up

* samples: add affine bundle adjuster option to stitching_detailed

* add support for using affine bundle adjuster with 4DOF
* improve logging of initial intristics

* sttiching: add affine bundle adjuster test

* fix build warnings

* stitching: increase limit on sanity check

prevents spurious test failures on mac. values are still pretty fine.

* stitching: set affine bundle adjuster for SCANS mode

* fix bug with AffineBestOf2NearestMatcher (we want to select affine partial mode)
* select right bundle adjuster

* stitching: increase error bound for matcher tests

* this prevents failure on mac. tranformation is still ok.

* stitching: implement affine bundle adjuster

* implements affine bundle adjuster that is using full affine transform
* existing test case modified to test both affinePartial an full affine bundle adjuster

* add stitching tutorial

* show basic usage of stitching api (Stitcher class)

* stitching: add more integration test for affine stitching

* added new datasets to existing testcase
* removed unused include

* calib3d: move `haveCollinearPoints` to common header

* added comment to make that this also checks too close points

* calib3d: redone checkSubset for estimateAffine* callback

* use common function to check collinearity
* this also ensures that point will not be too close to each other

* calib3d: change estimateAffine* functions API

* more similar to `findHomography`, `findFundamentalMat`, `findEssentialMat` and similar
* follows standard recommended semantic INPUTS, OUTPUTS, FLAGS
* allows to disable refining
* supported LMEDS robust method (tests yet to come) along with RANSAC
* extended docs with some tips

* calib3d: rewrite estimateAffine2D test

* rewrite in googletest style
* parametrize to test both robust methods (RANSAC and LMEDS)
* get rid of boilerplate

* calib3d: rework estimateAffinePartial2D test

* rework in googletest style
* add testing for LMEDS

* calib3d: rework estimateAffine*2D perf test

* test for LMEDS speed
* test with/without Levenberg-Marquart
* remove sanity checking (this is covered by accuracy tests)

* calib3d: improve estimateAffine*2D tests

* test transformations in loop
* improves test by testing more potential transformations

* calib3d: rewrite kernels for estimateAffine*2D functions

* use analytical solution instead of SVD
* this version is faster especially for smaller amount of points

* calib3d: tune up perf of estimateAffine*2D functions

* avoid copying inliers
* avoid converting input points if not necessary
* check only `from` point for collinearity, as `to` does not affect stability of transform

* tutorials: add commands examples to stitching tutorials

* add some examples how to run stitcher sample code
* mention stitching_detailed.cpp

* calib3d: change computeError for estimateAffine*2D

* do error computing in floats instead of doubles

this have required precision + we were storing the result in float anyway. This make code faster and allows auto-vectorization by smart compilers.

* documentation: mention estimateAffine*2D function

* refer to new functions on appropriate places
* prefer estimateAffine*2D over estimateRigidTransform

* stitching: add camera models documentations

* mention camera models in module documentation to give user a better overview and reduce confusion

  * raise an error when wrong bit depth passed
  * raise an build error when wrong depth is specified for cvtScaleHalf_
  * remove unnecessary safe check in cvtScaleHalf_
  * use intrinsic instead of direct pointer access
  * update the explanation

  * update the comment to real header

  * remove useHW option
  * update test

  * check compiler support
  * check HW support before executing
  * add test doing round trip conversion from / to FP32
  * treat array correctly if size is not multiple of 4
  * add declaration to prevent warning
  * make it possible to enable fp16 on 32bit ARM
  * let the conversion possible on non-supported HW, too.
  * add test using both HW and SW implementation

Added a writeFormat() method to Algorithm which must be called by the
write() method of derived classes.

1) fix multichannel support
2) remove useless bad_value, read value from original Mat directly
3) add more tests
4) fix docs for cvCeil and checkRange