OpenCV.ImgProc.GeometricImgTransform

The functions in this section perform various geometrical transformations of 2D images. They do not change the image content but deform the pixel grid and map this deformed grid to the destination image. In fact, to avoid sampling artifacts, the mapping is done in the reverse order, from destination to the source. That is, for each pixel (x,y) of the destination image, the functions compute coordinates of the corresponding "donor" pixel in the source image and copy the pixel value:

dst(x,y) = src(fx(x,y), fy(x,y))

In case when you specify the forward mapping <gx,gy> : src -> dst, the OpenCV functions first compute the corresponding inverse mapping <fx,fy>:dst->src and then use the above formula.

The actual implementations of the geometrical transformations, from the most generic remap and to the simplest and the fastest resize, need to solve two main problems with the above formula:

• Extrapolation of non-existing pixels. Similarly to the filtering functions described in the previous section, for some (x,y), either one of fx(x,y), or fy(x,y), or both of them may fall outside of the image. In this case, an extrapolation method needs to be used. OpenCV provides the same selection of extrapolation methods as in the filtering functions. In addition, it provides the method BorderTransparent. This means that the corresponding pixels in the destination image will not be modified at all.
• Interpolation of pixel values. Usually fx(x,y) and fy(x,y) are floating-point numbers. This means that <fx,fy> can be either an affine or perspective transformation, or radial lens distortion correction, and so on. So, a pixel value at fractional coordinates needs to be retrieved. In the simplest case, the coordinates can be just rounded to the nearest integer coordinates and the corresponding pixel can be used. This is called a nearest-neighbor interpolation. However, a better result can be achieved by using more sophisticated interpolation methods , where a polynomial function is fit into some neighborhood of the computed pixel (fx(x,y),fy(x,y)), and then the value of the polynomial at (fx(x,y),fy(x,y)) is taken as the interpolated pixel value. In OpenCV, you can choose between several interpolation methods. See resize for details.

Documentation

data ResizeAbsRel

Constructors

ResizeAbs Size2i

Resize to an absolute size.

ResizeRel (V2 Double)

Resize with relative factors for both the width and the height.

Instances

Show ResizeAbsRel

Methods

showsPrec :: Int -> ResizeAbsRel -> ShowS

show :: ResizeAbsRel -> String

showList :: [ResizeAbsRel] -> ShowS

resize :: ResizeAbsRel -> InterpolationMethod -> Mat (S '[height, width]) channels depth -> CvExcept (Mat (S '[D, D]) channels depth)

Resizes an image

To shrink an image, it will generally look best with InterArea interpolation, whereas to enlarge an image, it will generally look best with InterCubic (slow) or InterLinear (faster but still looks OK).

Example:

resizeInterAreaImg :: Mat ('S ['D, 'D]) ('S 3) ('S Word8)
resizeInterAreaImg = exceptError $
    withMatM (h ::: w + (w `div` 2) ::: Z)
             (Proxy :: Proxy 3)
             (Proxy :: Proxy Word8)
             transparent $ \imgM -> do
      birds_resized <-
        pureExcept $ resize (ResizeRel $ pure 0.5) InterArea birds_768x512
      matCopyToM imgM (V2 0 0) birds_768x512 Nothing
      matCopyToM imgM (V2 w 0) birds_resized Nothing
      lift $ arrowedLine imgM (V2 startX y) (V2 pointX y) red 4 LineType_8 0 0.15
  where
    [h, w] = miShape $ matInfo birds_768x512
    startX = round $ fromIntegral w * (0.95 :: Double)
    pointX = round $ fromIntegral w * (1.05 :: Double)
    y = h `div` 4

OpenCV Sphinx doc

warpAffine

Arguments

:: Mat (S '[height, width]) channels depth

Source image.

-> Mat (ShapeT '[2, 3]) (S 1) (S Double)

Affine transformation matrix.

-> InterpolationMethod

-> Bool

Perform the inverse transformation.

-> Bool

Fill outliers.

-> BorderMode

Pixel extrapolation method.

-> CvExcept (Mat (S '[height, width]) channels depth)

Transformed source image.

Applies an affine transformation to an image

Example:

rotateBirds :: Mat (ShapeT [2, 3]) ('S 1) ('S Double)
rotateBirds = getRotationMatrix2D (V2 256 170 :: V2 CFloat) 45 0.75

warpAffineImg :: Birds_512x341
warpAffineImg = exceptError $
    warpAffine birds_512x341 rotateBirds InterArea False False (BorderConstant black)

warpAffineInvImg :: Birds_512x341
warpAffineInvImg = exceptError $
    warpAffine warpAffineImg rotateBirds InterCubic True False (BorderConstant black)

OpenCV Sphinx doc

warpPerspective

Arguments

:: Mat (S '[height, width]) channels depth

Source image.

-> Mat (ShapeT '[3, 3]) (S 1) (S Double)

Perspective transformation matrix.

-> InterpolationMethod

-> Bool

Perform the inverse transformation.

-> Bool

Fill outliers.

-> BorderMode

Pixel extrapolation method.

-> CvExcept (Mat (S '[height, width]) channels depth)

Transformed source image.

Applies a perspective transformation to an image

OpenCV Sphinx doc

invertAffineTransform

Arguments

:: Mat (ShapeT '[2, 3]) (S 1) depth

-> CvExcept (Mat (ShapeT '[2, 3]) (S 1) depth)

Inverts an affine transformation

OpenCV Sphinx doc

getPerspectiveTransform

Arguments

:: IsPoint2 point2 CFloat

=> Vector (point2 CFloat)

Array of 4 floating-point Points representing 4 vertices in source image

-> Vector (point2 CFloat)

Array of 4 floating-point Points representing 4 vertices in destination image

-> Mat (ShapeT '[3, 3]) (S 1) (S Double)

The output perspective transformation, 3x3 floating-point-matrix.

Calculates a perspective transformation matrix for 2D perspective transform

OpenCV Sphinx doc

getRotationMatrix2D

Arguments

:: IsPoint2 point2 CFloat

=> point2 CFloat

Center of the rotation in the source image.

-> Double

Rotation angle in degrees. Positive values mean counter-clockwise rotation (the coordinate origin is assumed to be the top-left corner).

-> Double

Isotropic scale factor.

-> Mat (ShapeT '[2, 3]) (S 1) (S Double)

The output affine transformation, 2x3 floating-point matrix.

Calculates an affine matrix of 2D rotation

OpenCV Sphinx doc

remap

Arguments

:: Mat (S '[inputHeight, inputWidth]) inputChannels inputDepth

Source image.

-> Mat (S '[outputHeight, outputWidth]) (S 2) (S Float)

A map of (x, y) points.

-> InterpolationMethod

Interpolation method to use. Note that InterArea is not supported by this function.

-> BorderMode

-> CvExcept (Mat (S '[outputHeight, outputWidth]) inputChannels inputDepth)

Applies a generic geometrical transformation to an image.

The function remap transforms the source image using the specified map:

dst(x,y) = src(map(x,y))

Example:

remapImg
  :: forall (width    :: Nat)
            (height   :: Nat)
            (channels :: Nat)
            (depth    :: *  )
   . (Mat ('S ['S height, 'S width]) ('S channels) ('S depth) ~ Birds_512x341)
  => Mat ('S ['S height, 'S width]) ('S channels) ('S depth)
remapImg = exceptError $ remap birds_512x341 transform InterLinear (BorderConstant black)
  where
    transform = exceptError $
                matFromFunc (Proxy :: Proxy [height, width])
                            (Proxy :: Proxy 2)
                            (Proxy :: Proxy Float)
                            exampleFunc

    exampleFunc [_y,  x] 0 = wobble x w
    exampleFunc [ y, _x] 1 = wobble y h
    exampleFunc _pos _channel = error "impossible"

    wobble :: Int -> Float -> Float
    wobble v s = let v' = fromIntegral v
                     n = v' / s
                 in v' + (s * 0.05 * sin (n * 2 * pi * 5))

    w = fromInteger $ natVal (Proxy :: Proxy width)
    h = fromInteger $ natVal (Proxy :: Proxy height)

OpenCV documentation

undistort

Arguments

:: (ToMat m33d, MatShape m33d ~ S '[S 3, S 3], ToMat distCoeffs, MatShape distCoeffs `In` '[S '[S 4, S 1], S '[S 5, S 1], S '[S 8, S 1], S '[S 12, S 1], S '[S 14, S 1]])

=> Mat (S '[h, w]) c d

The source image to undistort.

-> m33d

The 3x3 matrix of intrinsic parameters.

-> distCoeffs

The distortion coefficients (k1,k2,p1,p2[,k3[,k4,k5,k6[,s1,s2,s3,s4[,τx,τy]]]]) of 4, 5, 8, 12 or 14 elements.

-> Mat (S '[h, w]) c d

The function transforms an image to compensate radial and tangential lens distortion.

Those pixels in the destination image, for which there is no correspondent pixels in the source image, are filled with zeros (black color).

The camera matrix and the distortion parameters can be determined using calibrateCamera . If the resolution of images is different from the resolution used at the calibration stage, f_x, f_y, c_x and c_y need to be scaled accordingly, while the distortion coefficients remain the same.

Example:

undistortImg
  :: forall (width    :: Nat)
            (height   :: Nat)
            (channels :: Nat)
            (depth    :: *  )
   . (Mat ('S ['S height, 'S width]) ('S channels) ('S depth) ~ Birds_512x341)
  => Mat ('S ['S height, 'S width]) ('S channels) ('S depth)
undistortImg = undistort birds_512x341 intrinsics coefficients
  where intrinsics :: M33 Float
        intrinsics =
          V3 (V3 15840.8      0      2049)
             (V3     0    15830.3    1097)
             (V3     0        0         1)

        coefficients :: Matx51d
        coefficients = unsafePerformIO $
          newMatx51d
            (-2.239145913492247)
             13.674526561736648
              3.650187848850095e-2
            (-2.0042015752853796e-2)
            (-0.44790921357620456)