>      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                                                             & None:Make a 2D windowed array from two others, one to produce the elements in the internal region, and one to produce elements in the border region. The two arrays must have the same extent.Extent of array.Window points.Array for internal elements.Array for border elements. (c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNoneTA class with a set of convenient functions that allow for changing precision of channels within pixels, while scaling the values to keep them in an appropriate range.2let rgb = PixelRGB 0.0 0.5 1.0 :: Pixel RGB DoubletoWord8 <$> rgb<RGB:(0|128|255)>toWord16 <$> rgb<RGB:(0|32768|65535)>Values are scaled to [0, 255] range.Values are scaled to  [0, 65535] range.Values are scaled to [0, 4294967295] range.Values are scaled to [0, 18446744073709551615] range.Values are scaled to  [0.0, 1.0] range.Values are scaled to  [0.0, 1.0] range.Values are scaled from  [0.0, 1.0] range.Lower the precisionIncrease the precision9Convert to fractional with value less than or equal to 1.@Convert to integral streaching it's value up to a maximum value.Clamp a value to [0, 1] range.;Discards imaginary part and changes precision of real part.Values between  [0.0, 1.0]Values between  [0.0, 1.0]Values between [0, 9223372036854775807] on 64bitValues between [0, 9223372036854775807] Values between [0, 2147483647]!Values between  [0, 32767]"Values between [0, 127]#Values between [0, 18446744073709551615] on 64bit$Values between [0, 18446744073709551615]%Values between [0, 4294967295]&Values between  [0, 65535]]'Values between  [0, 255]] !"#$%&' !"#$%&'(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone$*9:;<=DRTF'Approach to be used near the borders during various transformations. Whenever a function needs information not only about a pixel of interest, but also about it's neighbours, it will go out of bounds around the image edges, hence is this set of approaches that can be used in such situtation.Fill in a constant pixel. ( outside | Image | outside (" 0) : 0 0 0 0 | 1 2 3 4 | 0 0 0 0 2Wrap around from the opposite border of the image. ' outside | Image | outside # : 1 2 3 4 | 1 2 3 4 | 1 2 3 4  Replicate the pixel at the edge. ' outside | Image | outside # : 1 1 1 1 | 1 2 3 4 | 4 4 4 4 Mirror like reflection. ' outside | Image | outside   : 4 3 2 1 | 1 2 3 4 | 4 3 2 1 !BAlso mirror like reflection, but without repeating the edge pixel. ' outside | Image | outside ! : 1 4 3 2 | 1 2 3 4 | 3 2 1 4 "Array representation that is actually has real data stored in memory, hence allowing for image indexing, forcing pixels into computed state etc.%Get a pixel at i-th and j -th location.Ylet grad_gray = makeImage (200, 200) (\(i, j) -> PixelY $ fromIntegral (i*j)) / (200*200)8index grad_gray (20, 30) == PixelY ((20*30) / (200*200))True&+Make sure that an image is fully evaluated.'1Fold an image from the left in a row major order.(2Fold an image from the right in a row major order.)TCreate an Image by supplying it's dimensions and a monadic pixel generating action.*Monading mapping over an image.+4Monading mapping over an image. Result is discarded.,Monadic folding.-%Monadic folding. Result is discarded.."Get dimensions of a mutable image./!Yield a mutable copy of an image.0$Yield an immutable copy of an image.1NCreate a mutable image with given dimensions. Pixels are likely uninitialized.2$Yield the pixel at a given location.3 Set a pixel at a given location.4Swap pixels at given locations.8NCreate an Image by supplying it's dimensions and a pixel generating function.:PCreate a scalar image, required for various operations on images with a scalar.;Retrieves a pixel at (0, 0) index. Useful together with F*, when arbitrary initial pixel is needed.<Map a function over a an image.=8Map an index aware function over each pixel in an image.>Zip two images with a function?+Zip two images with an index aware function@Traverse an imageATraverse two images.BTranspose an imageC#Backwards permutation of an image. DmConstruct an image from a nested rectangular shaped list of pixels. Length of an outer list will constitute m* rows, while the length of inner lists - nJ columns. All of the inner lists must be the same length and greater than 0.QfromLists [[PixelY (fromIntegral (i*j) / 60000) | j <- [1..300]] | i <- [1..200]])<Image VectorUnboxed Y (Double): 200x300> images/grad_fromLists.pngEIPerform matrix multiplication on two images. Inner dimensions must agree.F"Undirected reduction of an image. G>Undirected reduction of an image with an index aware function.HPixelwise equality function of two images. Images are considered distinct if either images' dimensions or at least one pair of corresponding pixels are not the same. Used in defining an in instance for the ( typeclass.I5 class does not enforce an image to be represented as concrete array of pixels in memory, but if at any time it is desired for the image to be brought to a computed state, this function can be used.JEach array has a sibling 6 array representation, which K Convert an image to a flattened 7+. For all current representations it is a O(1) opeartion.DtoVector $ makeImage (3, 2) (\(i, j) -> PixelY $ fromIntegral (i+j))XfromList [<Luma:(0.0)>,<Luma:(1.0)>,<Luma:(1.0)>,<Luma:(2.0)>,<Luma:(2.0)>,<Luma:(3.0)>]L'Construct a two dimensional image with m rows and n columns from a flat 7 of length k,. For all current representations it is a O(1) opeartion. Make sure that  m * n = k.NfromVector (200, 300) $ generate 60000 (\i -> PixelY $ fromIntegral i / 60000)<Image Vector Luma: 200x300> images/grad_fromVector.pngM,Base array like representation for an image.N9Required array specific constraints for an array element.O Underlying image representation.PGet dimensions of an image.)frog <- readImageRGB VU "images/frog.jpg"frog+<Image VectorUnboxed RGB (Double): 200x320> dims frog (200,320)Q)A color space that supports transparency.R3A corresponding opaque version of this color space.S-Get an alpha channel of a transparant pixel. T(Add an alpha channel to an opaque pixel. 1 addAlpha 0 (PixelHSI 1 2 3) == PixelHSIA 1 2 3 0ULConvert a transparent pixel to an opaque one by dropping the alpha channel. 0 dropAlpha (PixelRGBA 1 2 3 4) == PixelRGB 1 2 3XmConvert a Pixel to a representation suitable for storage as an unboxed element, usually a tuple of channels.Y6Convert from an elemnt representation back to a Pixel.ZLConstrut a Pixel by replicating the same value across all of the components.[ Retrieve Pixel's component value\Set Pixel's component value]9Map a channel aware function over all Pixel's components.^,Map a function over all Pixel's componenets._Zip two Pixels with a function.a'Right fold over all Pixel's components.b-Left strict fold over all Pixel's components.e>A Pixel family with a color space and a precision of elements.f9Exchange the underlying array representation of an image.gBorder handling function. If (i, j) location is within bounds, then supplied lookup function will be used, otherwise it will be handled according to a supplied border strategy.hOImage indexing function that returns a default pixel if index is out of bounds.ibImage indexing function that uses a special border resolutions strategy for out of bounds pixels.j%Image indexing function that returns ) if index is out of bounds, * px otherwise.k%2D to a flat vector index conversion.Note': There is an implicit assumption that j < nl#Flat vector to 2D index conversion.^ !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefNew representation of an image. Source image.gBorder handling strategy.Image dimensionsImage's indexing function.(i, j) location of a pixel lookup.hijkn columns(i, j) row, column indexFlat vector indexln columnsFlat vector index(i, j) row, column indexmnopqrstuvwxyZ! "#%(/0$2*1+4'3,-&).576@=<BF>HKLAC?8DE9:;GIJMONPQRSTUVWZXY[\]^_`abcdefghijklmZeVWXYZ[\]^_`abcdQRSTUMNOP56789:;<=>?@ABCDEFGHIJKL"#$%&'()*+,-./01234fhij !gklm !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxy(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone$*09:;<=DORT+Generic 7 representation. +,-./0123456LO/0+,+,21-.354/06(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone$*09:;<=DORT{ Storable 7 representation. {|789:;<=>O/08{|{|:97;=<8>(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone :<=DR?Unboxing of a e.@ABCDE?FAG@BC@DEA?(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone$*09:;<=DORT}Unboxed 7 representation. }~HIJKLMNOPO/0I}~}~KJHLNMIO(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone:<=Filter out Pixels from an image that do not satisfy the predicate and convert a result into a flat unboxed vector with indexed Pixels.Filter out Pixels from an image that do not satisfy the index aware predicate and convert a result into a flat unboxed vector with indexed Pixels. The predicate Source image The predicate Source imagekl{|}~}~{|lk(c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone$:Bilinear interpolation method.&Nearest Neighbor interpolation method.+Implementation for an interpolation method.CConstruct a new pixel by using information from neighboring pixels.QRQR(c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone$Downsample an image. Drop all rows and colums that satisfy the predicates. For example, in order to discard every 5th row and keep every even indexed column:*frog <- readImageRGB RPU "images/frog.jpg"7displayImage $ downsample ((0 ==) . (`mod` 5)) odd frog images/frog.jpg images/frog_downsampled.jpgUpsample an image by inserting rows and columns with zero valued pixels into an image. Supplied functions specify how many rows/columns shoud be inserted (before, after) a particular row/column. Returning a negative value in a tuple will result in an error. E.g. insert 2 columns before and 4 columns after every 10th column, while leaving rows count unchanged:*frog <- readImageRGB RPU "images/frog.jpg"_displayImage $ upsample (const (0, 0)) (\ k -> if k `mod` 10 == 0 then (2, 4) else (0, 0)) frog images/frog.jpg images/frog_upsampled.jpg0Downsample an image by discarding every odd row.3Downsample an image by discarding every odd column.VUpsample an image by inserting a row of back pixels after each row of a source image.\Upsample an image by inserting a column of back pixels after each column of a source image._Concatenate two images together into one. Both input images must have the same number of rows.bConcatenate two images together into one. Both input images must have the same number of columns.2Shift an image towards its bottom right corner by (delatM, deltaN)B rows and columns, while specifying a border resolution strategy.)frog <- readImageRGB VU "images/frog.jpg"KwriteImage "images/frog_translate_wrap.jpg" $ translate Wrap (50, 100) frogKwriteImage "images/frog_translate_edge.jpg" $ translate Edge (50, 100) frog images/frog.jpg  images/frog_translate_wrap.jpg images/frog_translate_edge.jpgChange the size of an image. Pixel values and positions will not change, except the ones outside the border, which are handled according to supplied resolution strategy. images/logo_40.pngvFor example, it can be used to make a tile from the image above, or simply scale the canvas and place it in a middle:-logo <- readImageRGBA VU "images/logo_40.png"5let incBy (fm, fn) = (rows logo * fm, cols logo * fn)HwriteImage "images/logo_tile.png" $ canvasSize Wrap (incBy (6, 10)) logoqwriteImage "images/logo_center.png" $ translate (Fill 0) (incBy (2, 3)) $ canvasSize (Fill 0) (incBy (5, 7)) logo images/logo_tile.png images/logo_center.png5Crop an image, i.e. retrieves a sub-image image with m rows and n columns. Make sure (i + m, j + n)Y is not greater than dimensions of a source image, otherwise it will result in an error.cPlace one image on top of a source image, starting at a particular location within a source image.Flip an image vertically.)frog <- readImageRGB VU "images/frog.jpg"/writeImage "images/frog_flipV.jpg" $ flipV frog images/frog.jpg images/frog_flipV.jpgFlip an image horizontally.)frog <- readImageRGB VU "images/frog.jpg"/writeImage "images/frog_flipH.jpg" $ flipH frog images/frog.jpg images/frog_flipH.jpg!Rotate an image clockwise by 90.)frog <- readImageRGB VU "images/frog.jpg"5writeImage "images/frog_rotate90.jpg" $ rotate90 frog images/frog.jpg images/frog_rotate90.jpgRotate an image by 180.)frog <- readImageRGB VU "images/frog.jpg"7writeImage "images/frog_rotate180.jpg" $ rotate180 frog images/frog.jpg images/frog_rotate180.jpg"Rotate an image clockwise by 270.)frog <- readImageRGB VU "images/frog.jpg"7writeImage "images/frog_rotate270.jpg" $ rotate270 frog images/frog.jpg images/frog_rotate270.jpg3Rotate an image clockwise by an angle  in radians.*frog <- readImageRGBA VU "images/frog.jpg"PwriteImage "images/frog_rotate330.png" $ rotate Bilinear (Fill 0) (11*pi/6) frog images/frog.jpg images/frog_rotate330.png.Resize an image using an interpolation method.)frog <- readImageRGB VU "images/frog.jpg"JwriteImage "images/frog_resize.jpg" $ resize Bilinear Edge (100, 640) frog images/frog_resize.jpg_Scale an image. Same as resize, except scaling factors are supplied instead of new dimensions.  scale   (0.5, 2) frog == resize   (100, 640) frogSPut an angle into  [0, 2*pi) range.T Make sure  sin' pi == 0 instead of  sin pi == 1.2246467991473532e-16U Make sure cos' (pi/2) == 0 instead of #cos (pi/2) == 6.123233995736766e-17 and cos' (3*pi/2) == 0 instead of 'cos (3*pi/2) == -1.8369701987210297e-16Rows predicateColumns predicate Source imageBorder resolution strategy4Number of rows and columns image will be shifted by.Border resolution strategyNew dimensions of the image Source image(i, j)+ starting index from within a source image.(m, n) dimensions of a new image. Source image.(i, j)+ starting index from within a source image..Image to be positioned above the source image. Source image.VInterpolation method to be usedBorder handling strategyAngle in radians Source image Rotated image/Interpolation method to be used during scaling.Border handling strategyDimensions of a result image. Source image. Result image./Interpolation method to be used during scaling.Border handling strategyPositive scaling factors. Source image.STUVSTU(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone 09:;<=DRT %YCbCr color space with Alpha channel.$Luma component (commonly denoted as Y') Blue difference chroma componentRed difference chroma componentAlpha component.NColor space is used to encode RGB information and is used in JPEG compression.$Luma component (commonly denoted as Y') Blue difference chroma componentRed difference chroma componentWXYZ[\]^_`abcdefg eXWYZ[\]^_`WabcdefgX(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone 09:;<=DRTLuma with Alpha channel.Luma Alpha channel0Luma or brightness, which is usually denoted as Y'.hijklmnopqrstuvwxyeihjklmnopqhrstuvwxyi(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone 09:;<=DRTThis is a single channel colorspace, that is designed to separate Gray level values from other types of colorspace, hence it is not convertible to or from, but rather is here to allow operation on arbirtary single channel images. If you are looking for a true grayscale colorspace  should be used instead.0Separate a Pixel into a list of components with 3 pixels containing every component from the pixel.toPixelsX (PixelRGB 4 5 6)[<X:(4)>,<X:(5)>,<X:(6)>]Combine a list of  pixels into a Pixel with a specified channel order. Not the most efficient way to construct a pixel, but might prove useful to someone.6fromPixelsX [(RedRGB, 3), (BlueRGB, 5), (GreenRGB, 4)]<RGB:(3.0|4.0|5.0)>@fromPixelsX $ zip (enumFrom RedRGB) (toPixelsX $ PixelRGB 4 5 6)<RGB:(4.0|5.0|6.0)>-Separate an image into a list of images with 8 pixels containing every channel from the source image.&frog <- readImageRGB "images/frog.jpg"6let [frog_red, frog_green, frog_blue] = toImagesX frog4writeImage "images/frog_red.png" $ toImageY frog_red8writeImage "images/frog_green.jpg" $ toImageY frog_green6writeImage "images/frog_blue.jpg" $ toImageY frog_blue images/frog_red.jpg  images/frog_green.jpg images/frog_blue.jpgCombine a list of images with Y pixels into an image of any color space, by supplying an order of color space channels.(For example here is a frog with swapped BlueRGB and GreenRGB channels.qwriteImage "images/frog_rbg.jpg" $ fromImagesX [(RedRGB, frog_red), (BlueRGB, frog_green), (GreenRGB, frog_blue)] images/frog.jpg images/frog_rbg.jpgIt is worth noting though, despite that separating image channels can be sometimes pretty useful, exactly the same effect as in example above can be achieved in a much simpler and a more efficient way:  <+ (\(PixelRGB r g b) -> PixelRGB r b g) frogz{|}~ez {|}~z(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone 09:;<=DRT3Red, Green and Blue color space with Alpha channel. Red, Green and Blue color space. e(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone 09:;<=DRT =Hue, Saturation and Intensity color space with Alpha channel.Hue Saturation IntensityAlpha*Hue, Saturation and Intensity color space.Hue Saturation  Intensity e(c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone: PConstrcut a complex pixel from two pixels representing real and imaginary parts.  PixelRGB 4 8 6  PixelRGB 7 1 1 == PixelRGB (4  7) (8  1) (6  1)*Extracts the real part of a complex pixel./Extracts the imaginary part of a complex pixel.BForm a complex pixel from polar components of magnitude and phase. t9 is a complex pixel with magnitude 1 and phase t (modulo 2*). The function  takes a complex pixel and returns a (magnitude, phase) pair of pixels in canonical form: the magnitude is nonnegative, and the phase in the range (-, ]1; if the magnitude is zero, then so is the phase.-The nonnegative magnitude of a complex pixel.+The phase of a complex pixel, in the range (-, ]2. If the magnitude is zero, then so is the phase.!The conjugate of a complex pixel.  6(c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone*:TFast Fourier TransformInverse Fast Fourier Transform Check if  is a power of two.ICompute the DFT of a matrix. Array dimensions must be powers of two else . (c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone: PConstruct a complex image from two images representing real and imaginary parts.)frog <- readImageRGB VU "images/frog.jpg" frog !+! 03<Image VectorUnboxed RGB (Complex Double): 200x320> frog !+! frog3<Image VectorUnboxed RGB (Complex Double): 200x320>*Extracts the real part of a complex image./Extracts the imaginary part of a complex image.BForm a complex image from polar components of magnitude and phase. t9 is a complex image with magnitude 1 and phase t (modulo 2*). The function polar' takes a complex image and returns a (magnitude, phase) pair of images in canonical form: the magnitude is nonnegative, and the phase in the range (-, ]1; if the magnitude is zero, then so is the phase.-The nonnegative magnitude of a complex image.+The phase of a complex image, in the range (-, ]2. If the magnitude is zero, then so is the phase.!The conjugate of a complex image.>Make a filter by using a function that works around a regular (x, y) coordinate system.&Apply a filter to an image created by . Dimensions of the filter. Both m and n have to be powers of 2, i.e. m == 2^k, where k is some integer. Source image.Filter. 6(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone 09:;<=DRT ?Cyan, Magenta, Yellow and Black color space with Alpha channel.CyanMagentaYellow Key (Black)Alpha ,Cyan, Magenta, Yellow and Black color space.CyanMagentaYellow Key (Black)e(c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone09:;<=DRT 1Under the hood, Binary pixels are represented as , but can only take values of 0 or 1.+Binary Color Space, also known as bi-tonal. Convert to a  pixel.Represents value  or 1? in binary. Often also called a foreground pixel of an object.Represents value  or 02 in binary. Often also called a background pixel. Convert a  to a PixelBin pixel.isOn (fromBool True)TrueTest if Pixel's value is .Test if Pixel's value is .Unboxing of a .Values: 0 and 1-e(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone$*09:;<=DRT;Repa Array representation, which is computed sequentially. 9Repa Array representation, which is computed in parallel.Combine two arrays, element-wise, with index aware operator. If the extent of the two array arguments differ, then the resulting array's extent is their intersection.&     O           (c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone$*09:;<=DRTSRepa Array representation backed by Storable Vector, which is computed in parallel.URepa Array representation backed by Storable Vector, which is computed sequentially.  !"#$%O/08  !#"$%!(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone$*09:;<=DRTRRepa Array representation backed by Unboxed Vector, which is computed in parallel.TRepa Array representation backed by Unboxed Vector, which is computed sequentially. &'()*+,-./O/0I'&(*)&+-,'./(c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone:<=?Create a sequential unboxed image from a 2D Repa delayed array.=Create a parallel unboxed image from a 2D Repa delayed array..Convert into Repa Unboxed array from an image. (c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone $9:;<=T#Conversion to - from another color space with Alpha channel.Convert to an  pixel.Conversion to  color space.Convert to an  pixel.Conversion to . Convert to a  pixel.Conversion to  color space. Convert to a  pixel.Conversion to - from another color space with Alpha channel.Convert to an  pixel.Conversion to  color space.Convert to an  pixel.Conversion to - from another color space with Alpha channel.Convert to an  pixel.Conversion to  color space.Convert to an  pixel.,Conversion to Luma from another color space. )Convert a pixel to Luma pixel with Alpha. Conversion to Luma color space. Convert a pixel to Luma pixel.  Convert to a  image. $Convert a Binary pixel to Luma pixel$Convert a Binary image to Luma imageYCheck weather two Pixels are equal within a tolerance. Useful for comparing pixels with 0 or 1 precision.Convert an image to Luma image.*Convert an image to Luma image with Alpha.Convert to an  image.Convert to an  image.Convert to an  image.Convert to an  image. Convert to a  image. Convert to a  image.Convert to an  image.Convert to an  image.~Computes Luma: + Y' = 0.299 * R' + 0.587 * G' + 0.114 * B'       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~{eXWihz     ye             !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~"(c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone 9:;<=DR *Image formats that can be written to file.Encode an image to 2.)Image formats that can be read from file.Decode an image from 2.Image file format. Helps in guessing image format using a file extension, as well as supplying format specific options during saving an image.@Options that can be used during writing an image in this format.-Default file extension for this image format.'Known extensions for this image format.Returns  if a file extension (ex. ".png") corresponds to this format.0Used during converting pixels between libraries.3456 3456#(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone $9:;<=DRT$Tagged Image File Format image with .tif or .tiff extension.6Truevision Graphics Adapter image with .tga extension.%Portable Network Graphics image with .png extension.,Joint Photographic Experts Group image with .jpg or .jpeg extension.High-dynamic-range image with .hdr or .pic extension.'Graphics Interchange Format image with .gif extension.Bitmap image with .bmp extension.$789:;<=>?@ABCDEFGHIJ"  :897<;>=@?BA7DCFE89HG:JI$(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone $9:;<=DRTxKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~xKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~%(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone $9:;<=DRTG G &(c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone 9:;<=DR#Netpbm: portable pixmap image with .ppm extension.$Netpbm: portable graymap image with .pgm extension.#Netpbm: portable bitmap image with .pbm extension.4     !"#$%&'()*+,-./01234567+     !"#$%&'()*+-,/.10325476'(c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone:JCorrelate an image with a kernel. Border resolution technique is required.PConvolution of an image using a kernel. Border resolution technique is required.Example using  ,https://en.wikipedia.org/wiki/Sobel_operatorSobel operator:(frog <- readImageY RPU "images/frog.jpg"Olet frogX = convolve Edge (fromLists [[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]]) frogOlet frogY = convolve Edge (fromLists [[-1,-2,-1], [ 0, 0, 0], [ 1, 2, 1]]) frog7displayImage $ normalize $ sqrt (frogX ^ 2 + frogY ^ 2) images/frogY.jpg images/frog_sobel.jpgKConvolve image's rows with a vector kernel represented by a list of pixels.NConvolve image's columns with a vector kernel represented by a list of pixels.%Approach to be used near the borders. Kernel image. Source image.(c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone$This function magnifies an image by a positive factor and draws a grid around the original pixels. It is here simply as useful inspection tool.)frog <- readImageRGB VU "images/frog.jpg"SwriteImage "images/frog_eye_grid.png" $ pixelGrid 10 $ crop (51, 112) (20, 20) frog images/frog.jpg images/frog_eye_grid.pngMagnification factor. Source image.%! % !(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone 9:;<=DRQA collection of all image formats that can be written to file using images with 1 precision pixels.CA collection of all image formats that can be read into HIP images.89C  :897? 89(c) Alexey Kuleshevich 2017BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone:T:External viewing application to use for displaying images.*Any custom viewer, which can be specified:FilePath# - to the actual viewer executable.[String]@ - command line arguments that will be passed to the executable.Int* - position index in the above list where : to an image should be injected This function will try to guess an image format from file's extension, then it will attempt to decode it as such. It will fall back onto the rest of the supported formats and will try to read them regarless of file's extension. Whenever image cannot be decoded, ;H containing all errors for each attempted format will be returned, and <T containing an image otherwise. Image will be read with a type signature specified:Nfrog <- readImage "images/frog.jpg" :: IO (Either String (Image VS RGB Word8))displayImage frog Just like ?, but will throw an exception if incorrect format is detected.dThis function allows for reading all supported image in their exact colorspace and precision. Only {1 image representation can be read natively, but  (r can be use later to switch to a different representation. For instance, "frog.jpg" image can be read into it's  colorspace with  precision:QreadImageExact JPG "images/frog.jpg" :: IO (Either String (Image VS YCbCr Word8))'Right <Image VS YCbCr (Word8): 200x320>lThe drawback here is that colorspace and precision has to match exactly, otherwise it will return an error:OreadImageExact JPG "images/frog.jpg" :: IO (Either String (Image VS RGB Word8))Left "JuicyPixel decoding error: Input image is in YCbCr8 (Pixel YCbCr Word8), cannot convert it to RGB8 (Pixel RGB Word8) colorspace."Any attempt to read an image in a color space, which is not supported by supplied format, will result in a compile error. Refer to + class for all images that can be decoded. Just like ?, but will throw an exception if incorrect format is detected. Just like s, this function will guess an output file format from the extension and write to file any image that is in one of , ,  or  color spaces with 1 precision. While doing necessary conversions the choice will be given to the most suited color space supported by the format. For instance, in case of a  format, an (O arr  1) would be written as RGBA16G, hence preserving transparency and using highest supported precision +. At the same time, writing that image in  format would save it in RGB8, since  is the highest precision > supports and it currently cannot be saved with transparency.3Write an image in a specific format, while supplying any format specific options. Precision and color space, that an image will be written as, is decided from image's type. Attempt to write image file in a format that does not support color space and precision combination will result in a compile error.An image is written as a .tiffo file into an operating system's temporary directory and passed as an argument to the external viewer program.;Displays an image file by calling an external image viewer.Makes a call to an external viewer that is set as a default image viewer by the OS. This is a non-blocking function call, so it might take some time before an image will appear.5Default viewer is inferred from the operating system. eog /tmp/hip/img.tiff (https://help.gnome.org/users/eog/stable/ Eye of GNOME .feh --fullscreen --auto-zoom /tmp/hip/img.tiff https://feh.finalrewind.org/FEH gpicview /tmp/hip/img.tiff %http://lxde.sourceforge.net/gpicview/GPicView gimp /tmp/hip/img.tiff https://www.gimp.org/GIMP=File path for an image4A file format that an image should be read as. See #g:4Supported Image FormatsLocation of an image.*Location where an image should be written.An image to write. 5A file format that an image should be saved in. See #g:4Supported Image Formats"A list of format specific options.*Location where an image should be written.TAn image to write. Can be a list of images in case of formats supporting animation.External viewer to useShould the call be blockingImage to displayImage to be displayedS  :897= (c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone$:T For now it is just a type synonym, but in the future it might become a custom data type with fields like title, width, heigth, etc.'A single channel histogram of an image.UVector containing pixel counts. Index of a vector serves as an original pixel value.:Name of the channel that will be displayed in the legend.Color of a plotted line..Get a pure colour representation of a channel.2Create a histogram per channel with 256 bins each.CGenerate a histogram with 256 bins for a single channel Gray image.'Write histograms into a PNG image file.)frog <- readImageRGB VU "images/frog.jpg"@writeHistograms "images/frog_histogram.svg" $ getHistograms frog images/frog_histogram.svgODisplay image histograms using an external program. Works in a similar way as .)frog <- readImageRGB VU "images/frog.jpg"&displayHistograms $ getHistograms frog>ODisplay image histograms using an external program. Works in a similar way as .>  > (c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone 9:;<=? contains a convenient set of functions for binary image construction, which is done by comparing either a single pixel with every pixel in an image or two same size images pointwise. For example:'frog <- readImageY VU "images/frog.jpg"1frog .==. PixelY 0 -- (or: PixelY 0 .==. frog)2frog .<. flipH frog -- (or: flipH frog .>. frog) Pixel wise AND operator on binary images.  Pixel wise OR operator on binary images.'Complement each pixel in a binary image?Construct a binary image using a predicate from a source image.BConstruct a binary image using a predicate from two source images.3Threshold a source image with an applicative pixel.+yield <- readImageRGB VU "images/yield.jpg"dwriteImageExact PNG [] "images/yield_bin.png" $ thresholdWith (PixelRGB (>0.55) (<0.6) (<0.5)) yield images/yield.jpg images/yield_bin.png?Compare two images with an applicative pixel. Works just like , but on two images.+Disjunction of all pixels in a Binary image+Conjunction of all pixels in a Binary imageErosion is defined as: {E = B " S = {m,n|S "B}gwriteImageExact PNG [] "images/figure_erode.png" $ pixelGrid 10 $ fromImageBinary $ erode struct figure images/figure.png eroded with  images/struct.png is images/figure_erode.pngDialation is defined as: {D = B " S = {m,n|S ")B"`"}kwriteImageExact PNG [] "images/figure_dialate.png" $ pixelGrid 10 $ fromImageBinary $ dialate struct figure images/figure.png dialated with  images/struct.png is images/figure_dialate.pngOpening is defined as: {B % S = (B " S) " S}ewriteImageExact PNG [] "images/figure_open.png" $ pixelGrid 10 $ fromImageBinary $ open struct figure images/figure.png opened with  images/struct.png is images/figure_open.pngClosing is defined as: {B % S = (B " S) " S}gwriteImageExact PNG [] "images/figure_close.png" $ pixelGrid 10 $ fromImageBinary $ close struct figure images/figure.png closed with  images/struct.png is images/figure_close.png Predicate Source image. PredicateFirst source image.Second source image.5Pixel containing a thresholding function per channel. Source image.2Pixel containing a comparing function per channel. First image. second image.Structuring element.Binary source image.Structuring element.Binary source image.Structuring element.Binary source image.Structuring element.Binary source image.44444432)(c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone  ! "#5OeXWihz{|}~     :8975"# !}~{| (c) Alexey Kuleshevich 2016BSD3%Alexey Kuleshevich <lehins@yandex.ru> experimental non-portableNone:>Create an image with a specified representation and pixels of 1, precision. Note, that it is essential for 14 precision pixels to keep values normalized in the [0, 1]= range in order for an image to be written to file properly.llet grad_gray = makeImageR VU (200, 200) (\(i, j) -> PixelY (fromIntegral i) / 200 * (fromIntegral j) / 200) Because all es and Os are installed into ?, above is equivalent to:^let grad_gray = makeImageR RPU (200, 200) (\(i, j) -> PixelY $ fromIntegral (i*j)) / (200*200)+writeImage "images/grad_gray.png" grad_gray&Creating color images is just as easy.~let grad_color = makeImageR VU (200, 200) (\(i, j) -> PixelRGB (fromIntegral i) (fromIntegral j) (fromIntegral (i + j))) / 400-writeImage "images/grad_color.png" grad_color images/grad_gray.png images/grad_color.png Read image as luma (brightness).Read image as luma with Alpha channel. Read image in RGB colorspace. "Read image in RGB colorspace with Alpha channel. #Get the number of rows in an image.)frog <- readImageRGB VU "images/frog.jpg"frog+<Image VectorUnboxed RGB (Double): 200x320> rows frog200 &Get the number of columns in an image.)frog <- readImageRGB VU "images/frog.jpg"frog+<Image VectorUnboxed RGB (Double): 200x320> cols frog320 Sum all pixels in the image.!Multiply all pixels in the image.(Retrieve the biggest pixel from an image)Retrieve the smallest pixel from an image,Scales all of the pixels to be in the range [0, 1].YCheck weather two images are equal within a tolerance. Useful for comparing images with 0 or 1 precision.Type restricted version of D9 that constructs an image using supplied representation.0Generates a nested list of pixels from an image.  img == fromLists (toLists img) Underlying image representation.(m rows, n& columns) - dimensions of a new image.A function that takes (i -th row, and jB-th column) as an argument and returns a pixel for that location.     Q  ! "#%5FECBA@?>=<D8OPeXWihzfhij{|}~     :897     #8D    P%jhi<=>?@ABCEF f     @*+,*+-*+.*+/01201301401501607807907:07;07<07=07>07>*?@*?A*BC D E F G H I J KLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~(          !!!! !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~"""""""""""################&&&&&&''''                                                   ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = >?@A*BC*BDEEFGHIJKLMNOPQRSTUVWXYZ[\]^_`a_`gbcdefghi_`jklmnopqrstuvwxyz{|}~stuvy{|}~stuvystuvy{|}~stuvy{|}~*?*stuvy{|}~??? sy*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B*B            !!!!!!!!!!??""" 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Graphics.Image.Processing.BinaryGraphics.Image%Graphics.Image.Interface.Repa.Helpers!Graphics.Image.Interface.Elevator'Graphics.Image.Interface.Vector.Generic(Graphics.Image.Interface.Vector.Storable(Graphics.Image.Interface.Vector.Unboxing'Graphics.Image.Interface.Vector.Unboxed'Graphics.Image.Processing.Interpolation#Graphics.Image.Processing.GeometricGraphics.Image.ColorSpace.YCbCrGraphics.Image.ColorSpace.YGraphics.Image.ColorSpace.XGraphics.Image.ColorSpace.LumaYGraphics.Image.ColorSpace.RGBGraphics.Image.ColorSpace.HSI!Graphics.Image.ColorSpace.Complex)Graphics.Image.Processing.Complex.FourierGraphics.Image.ColorSpace.CMYK Graphics.Image.ColorSpace.Binary%Graphics.Image.Interface.Repa.Generic&Graphics.Image.Interface.Repa.Storable%Graphics.Image.Interface.Repa.UnboxedGraphics.Image.IO.Base,Graphics.Image.IO.Formats.JuicyPixels.Common.Graphics.Image.IO.Formats.JuicyPixels.Readable.Graphics.Image.IO.Formats.JuicyPixels.Writable 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$fArrayRPcseD:R:ImageRPcse0$fBaseArrayRPcse $fArrayRScseD:R:ImageRScse0$fBaseArrayRScse$fShowRS$fShowRPPSImageSSImagefromRepaArrayStorablefromVectorStorable $fArrayRPScseD:R:ImageRPScse0$fBaseArrayRPScse $fArrayRSScseD:R:ImageRSScse0$fBaseArrayRSScse $fShowRPS $fShowRSSPUImageSUImage $fArrayRPUcseD:R:ImageRPUcse0$fBaseArrayRPUcse $fArrayRSUcseD:R:ImageRSUcse0$fBaseArrayRSUcse $fShowRPU $fShowRSUFloatDoublebytestring-0.10.8.1Data.ByteString.Lazy.Internal ByteString$fConvertiblePixelPixel$fConvertiblePixelPixel0$fConvertiblePixelPixel1$fConvertiblePixelPixel2 JPGQuality GIFAPalette GIFALooping GIFPaletteD:R:SaveOptionTIF0$fImageFormatTIFD:R:SaveOptionTGA0$fImageFormatTGAD:R:SaveOptionPNG0$fImageFormatPNGD:R:SaveOptionJPG0$fImageFormatJPGD:R:SaveOptionHDR0$fImageFormatHDRD:R:SaveOptionGIFA0$fImageFormatGIFAD:R:SaveOptionGIF0$fImageFormatGIFD:R:SaveOptionBMP0$fImageFormatBMP decodeGifsdecodeGifsDelaysjpImageToImageUnsafejpImageY8ToImagejpImageY16ToImagejpImageYA8ToImagejpImageYA16ToImagejpImageRGB8ToImagejpImageRGB16ToImagejpImageRGBFToImagejpImageRGBA8ToImagejpImageRGBA16ToImagejpImageYCbCr8ToImagejpImageCMYK8ToImagejpImageCMYK16ToImagejpDynamicImageToImage'jpDynamicImageToImage jpImageShowCSjpError jpCSError$fReadableImageTIF$fReadableImageTIF0$fReadableImageTIF1$fReadableImageTIF2$fReadableImageTGA$fReadableImageTGA0$fReadableImageTGA1$fReadableImageTGA2$fReadableImagePNG$fReadableImagePNG0$fReadableImagePNG1$fReadableImagePNG2$fReadableImageJPG$fReadableImageJPG0$fReadableImageJPG1$fReadableImageJPG2$fReadableImageHDR$fReadableImageHDR0$fReadableImageHDR1$fReadableImageHDR2$fReadable[]GIFA$fReadable[]GIFA0$fReadable[]GIFA1$fReadable[]GIFA2$fReadableImageGIF$fReadableImageGIF0$fReadableImageGIF1$fReadableImageGIF2$fReadableImageBMP$fReadableImageBMP0$fReadableImageBMP1$fReadableImageBMP2$fReadableImageTIF3$fReadableImageTIF4$fReadableImageTIF5$fReadableImageTIF6$fReadableImageTIF7$fReadableImageTIF8$fReadableImageTIF9$fReadableImageTIF10$fReadableImageTIF11$fReadableImageTIF12$fReadableImageTIF13$fReadableImageTGA3$fReadableImageTGA4$fReadableImageTGA5$fReadableImageTGA6$fReadableImagePNG3$fReadableImagePNG4$fReadableImagePNG5$fReadableImagePNG6$fReadableImagePNG7$fReadableImagePNG8$fReadableImagePNG9$fReadableImagePNG10$fReadableImagePNG11$fReadableImageJPG3$fReadableImageJPG4$fReadableImageJPG5$fReadableImageJPG6$fReadableImageJPG7$fReadableImageHDR3$fReadable[]GIFA3$fReadable[]GIFA4$fReadable[]GIFA5$fReadable[]GIFA6$fReadableImageGIF3$fReadableImageGIF4$fReadableImageBMP3$fReadableImageBMP4$fReadableImageBMP5$fReadableImageBMP6$fConvertiblePixelPixelCMYK16$fConvertiblePixelPixelCMYK8$fConvertiblePixelPixelYCbCr8$fConvertiblePixelPixelRGBA16$fConvertiblePixelPixelRGBA8$fConvertiblePixelPixelRGBF$fConvertiblePixelPixelRGB16$fConvertiblePixelPixelRGB8$fConvertiblePixelPixelYA16$fConvertiblePixelPixelYA8$fConvertiblePixelFloat$fConvertiblePixelWord32$fConvertiblePixelWord16$fConvertiblePixelWord8$fConvertiblePixelCMYK16Pixel$fConvertiblePixelCMYK8Pixel$fConvertiblePixelYCbCr8Pixel$fConvertiblePixelRGBA16Pixel$fConvertiblePixelRGBA8Pixel$fConvertiblePixelRGBFPixel$fConvertiblePixelRGB16Pixel$fConvertiblePixelRGB8Pixel$fConvertiblePixelYA16Pixel$fConvertiblePixelYA8Pixel$fConvertibleFloatPixel$fConvertibleWord32Pixel$fConvertibleWord16Pixel$fConvertibleWord8Pixel encodeGIF encodeGIFA encodeJPGimageToJPImage$fWritableImageTIF$fWritableImageTIF0$fWritableImageTIF1$fWritableImageTIF2$fWritableImageTIF3$fWritableImageTIF4$fWritableImageTIF5$fWritableImageTIF6$fWritableImageTIF7$fWritableImageTIF8$fWritableImageTIF9$fWritableImageTIF10$fWritableImageTIF11$fWritableImageTIF12$fWritableImageTIF13$fWritableImageTIF14$fWritableImageTIF15$fWritableImageTIF16$fWritableImageTGA$fWritableImageTGA0$fWritableImageTGA1$fWritableImageTGA2$fWritableImageTGA3$fWritableImageTGA4$fWritableImageTGA5$fWritableImageTGA6$fWritableImagePNG$fWritableImagePNG0$fWritableImagePNG1$fWritableImagePNG2$fWritableImagePNG3$fWritableImagePNG4$fWritableImagePNG5$fWritableImagePNG6$fWritableImagePNG7$fWritableImagePNG8$fWritableImagePNG9$fWritableImagePNG10$fWritableImagePNG11$fWritableImageJPG$fWritableImageJPG0$fWritableImageJPG1$fWritableImageJPG2$fWritableImageJPG3$fWritableImageJPG4$fWritableImageJPG5$fWritableImageJPG6$fWritableImageHDR$fWritableImageHDR0$fWritableImageHDR1$fWritableImageHDR2$fWritableImageHDR3$fWritable[]GIFA$fWritable[]GIFA0$fWritableImageGIF$fWritableImageGIF0$fWritableImageGIF1$fWritableImageGIF2$fWritableImageGIF3$fWritableImageBMP$fWritableImageBMP0$fWritableImageBMP1$fWritableImageBMP2$fWritableImageBMP3$fWritableImageBMP4$fWritableImageBMP5$fWritableImageBMP6pnmToImagesUsingpnmDataToImagemakeImageUnsafepnmDataPBMToImagepnmDataPGM8ToImagepnmDataPGM16ToImagepnmDataPPM8ToImagepnmDataPPM16ToImageppmToImageUsing decodePnmpnmError pnmCSError pnmShowData$fReadable[][]$fReadable[][]0$fReadable[][]1$fReadable[][]2$fReadable[][]3$fReadableImagePPM$fReadableImagePPM0$fReadableImagePGM$fReadableImagePGM0$fReadableImagePBM$fReadableImagePPM1$fReadableImagePPM2$fReadableImagePPM3$fReadableImagePPM4$fReadableImagePGM1$fReadableImagePBM0$fConvertiblePpmPixelRGB16Pixel$fConvertiblePpmPixelRGB8Pixel$fConvertiblePgmPixel16Pixel$fConvertiblePgmPixel8Pixel$fConvertiblePbmPixelPixelD:R:SaveOption[]0$fImageFormat[]D:R:SaveOption[]2$fImageFormat[]0D:R:SaveOption[]4$fImageFormat[]1D:R:SaveOptionPPM0$fImageFormatPPMD:R:SaveOptionPGM0$fImageFormatPGMD:R:SaveOptionPBM0$fImageFormatPBMD:R:SaveOptionOutputFormat0D:R:SaveOptionInputFormat0GHC.IOFilePath Data.EitherLeftRight guessFormatdisplayHistogramsUsingGHC.NumNum