Bilinear interpolation: Difference between revisions
m (Fixed mistake in color blerp) |
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int red = (int)Blerp(c00.R, c10.R, c01.R, c11.R, gx - gxi, gy - gyi); |
int red = (int)Blerp(c00.R, c10.R, c01.R, c11.R, gx - gxi, gy - gyi); |
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int green = (int)Blerp(c00.G, c10.G, c01.G, c11. |
int green = (int)Blerp(c00.G, c10.G, c01.G, c11.G, gx - gxi, gy - gyi); |
||
int blue = (int)Blerp(c00.B, c10.B, c01.B, c11. |
int blue = (int)Blerp(c00.B, c10.B, c01.B, c11.B, gx - gxi, gy - gyi); |
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Color rgb = Color.FromArgb(red, green, blue); |
Color rgb = Color.FromArgb(red, green, blue); |
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newImage.SetPixel(x, y, rgb); |
newImage.SetPixel(x, y, rgb); |
||
Revision as of 09:04, 25 March 2019
Bilinear interpolation is linear interpolation in 2 dimensions, and is typically used for image scaling and for 2D finite element analysis.
- Task
Open an image file, enlarge it by 60% using bilinear interpolation, then either display the result or save the result to a file.
C
<lang c>#include <stdint.h> typedef struct {
uint32_t *pixels; unsigned int w; unsigned int h;
} image_t;
- define getByte(value, n) (value >> (n*8) & 0xFF)
uint32_t getpixel(image_t *image, unsigned int x, unsigned int y){
return image->pixels[(y*image->w)+x];
} float lerp(float s, float e, float t){return s+(e-s)*t;} float blerp(float c00, float c10, float c01, float c11, float tx, float ty){
return lerp(lerp(c00, c10, tx), lerp(c01, c11, tx), ty);
} void putpixel(image_t *image, unsigned int x, unsigned int y, uint32_t color){
image->pixels[(y*image->w) + x] = color;
} void scale(image_t *src, image_t *dst, float scalex, float scaley){
int newWidth = (int)src->w*scalex;
int newHeight= (int)src->h*scaley;
int x, y;
for(x= 0, y=0; y < newHeight; x++){
if(x > newWidth){
x = 0; y++;
}
float gx = x / (float)(newWidth) * (src->w-1);
float gy = y / (float)(newHeight) * (src->h-1);
int gxi = (int)gx;
int gyi = (int)gy;
uint32_t result=0;
uint32_t c00 = getpixel(src, gxi, gyi);
uint32_t c10 = getpixel(src, gxi+1, gyi);
uint32_t c01 = getpixel(src, gxi, gyi+1);
uint32_t c11 = getpixel(src, gxi+1, gyi+1);
uint8_t i;
for(i = 0; i < 3; i++){
//((uint8_t*)&result)[i] = blerp( ((uint8_t*)&c00)[i], ((uint8_t*)&c10)[i], ((uint8_t*)&c01)[i], ((uint8_t*)&c11)[i], gxi - gx, gyi - gy); // this is shady
result |= (uint8_t)blerp(getByte(c00, i), getByte(c10, i), getByte(c01, i), getByte(c11, i), gx - gxi, gy -gyi) << (8*i);
}
putpixel(dst,x, y, result);
}
}</lang>
C#
Seems to have some artifacting in the output, but the image is at least recognizable. <lang csharp>using System; using System.Drawing;
namespace BilinearInterpolation {
class Program {
private static float Lerp(float s, float e, float t) {
return s + (e - s) * t;
}
private static float Blerp(float c00, float c10, float c01, float c11, float tx, float ty) {
return Lerp(Lerp(c00, c10, tx), Lerp(c01, c11, tx), ty);
}
private static Image Scale(Bitmap self, float scaleX, float scaleY) {
int newWidth = (int)(self.Width * scaleX);
int newHeight = (int)(self.Height * scaleY);
Bitmap newImage = new Bitmap(newWidth, newHeight, self.PixelFormat);
for (int x = 0; x < newWidth; x++) {
for (int y = 0; y < newHeight; y++) {
float gx = ((float)x) / newWidth * (self.Width - 1);
float gy = ((float)y) / newHeight * (self.Height - 1);
int gxi = (int)gx;
int gyi = (int)gy;
Color c00 = self.GetPixel(gxi, gyi);
Color c10 = self.GetPixel(gxi + 1, gyi);
Color c01 = self.GetPixel(gxi, gyi + 1);
Color c11 = self.GetPixel(gxi + 1, gyi + 1);
int red = (int)Blerp(c00.R, c10.R, c01.R, c11.R, gx - gxi, gy - gyi);
int green = (int)Blerp(c00.G, c10.G, c01.G, c11.G, gx - gxi, gy - gyi);
int blue = (int)Blerp(c00.B, c10.B, c01.B, c11.B, gx - gxi, gy - gyi);
Color rgb = Color.FromArgb(red, green, blue);
newImage.SetPixel(x, y, rgb);
}
}
return newImage;
}
static void Main(string[] args) {
Image newImage = Image.FromFile("Lenna100.jpg");
if (newImage is Bitmap oi) {
Image result = Scale(oi, 1.6f, 1.6f);
result.Save("Lenna100_larger.jpg");
} else {
Console.WriteLine("Could not open the source file.");
}
}
}
}</lang>
D
This uses the module from the Grayscale Image task.
<lang d>import grayscale_image;
/// Currently this accepts only a Grayscale image, for simplicity. Image!Gray rescaleGray(in Image!Gray src, in float scaleX, in float scaleY) pure nothrow @safe in {
assert(src !is null, "Input Image is null."); assert(src.nx > 1 && src.ny > 1, "Minimal input image size is 2x2."); assert(cast(uint)(src.nx * scaleX) > 0, "Output image width must be > 0."); assert(cast(uint)(src.ny * scaleY) > 0, "Output image height must be > 0.");
} body {
alias FP = float;
static FP lerp(in FP s, in FP e, in FP t) pure nothrow @safe @nogc {
return s + (e - s) * t;
}
static FP blerp(in FP c00, in FP c10, in FP c01, in FP c11,
in FP tx, in FP ty) pure nothrow @safe @nogc {
return lerp(lerp(c00, c10, tx), lerp(c01, c11, tx), ty);
}
immutable newWidth = cast(uint)(src.nx * scaleX); immutable newHeight = cast(uint)(src.ny * scaleY); auto result = new Image!Gray(newWidth, newHeight, true);
foreach (immutable y; 0 .. newHeight)
foreach (immutable x; 0 .. newWidth) {
immutable FP gx = x / FP(newWidth) * (src.nx - 1);
immutable FP gy = y / FP(newHeight) * (src.ny - 1);
immutable gxi = cast(uint)gx;
immutable gyi = cast(uint)gy;
immutable c00 = src[gxi, gyi ];
immutable c10 = src[gxi + 1, gyi ];
immutable c01 = src[gxi, gyi + 1];
immutable c11 = src[gxi + 1, gyi + 1];
immutable pixel = blerp(c00, c10, c01, c11, gx - gxi, gy - gyi);
result[x, y] = Gray(cast(ubyte)pixel);
}
return result;
}
void main() {
const im = loadPGM!Gray(null, "lena.pgm");
im.rescaleGray(0.3, 0.1).savePGM("lena_smaller.pgm");
im.rescaleGray(1.3, 1.8).savePGM("lena_larger.pgm");
}</lang>
F#
<lang fsharp>open System open System.Drawing
let lerp (s:float) (e:float) (t:float) =
s + (e - s) * t
let blerp c00 c10 c01 c11 tx ty =
lerp (lerp c00 c10 tx) (lerp c01 c11 tx) ty
let scale (self:Bitmap) (scaleX:float) (scaleY:float) =
let newWidth = int ((float self.Width) * scaleX)
let newHeight = int ((float self.Height) * scaleY)
let newImage = new Bitmap(newWidth, newHeight, self.PixelFormat)
for x in 0..newWidth-1 do
for y in 0..newHeight-1 do
let gx = (float x) / (float newWidth) * (float (self.Width - 1))
let gy = (float y) / (float newHeight) * (float (self.Height - 1))
let gxi = int gx
let gyi = int gy
let c00 = self.GetPixel(gxi, gyi)
let c10 = self.GetPixel(gxi + 1, gyi)
let c01 = self.GetPixel(gxi, gyi + 1)
let c11 = self.GetPixel(gxi + 1, gyi + 1)
let red = int (blerp (float c00.R) (float c10.R) (float c01.R) (float c11.R) (gx - (float gxi)) (gy - (float gyi)))
let green = int (blerp (float c00.G) (float c10.G) (float c01.G) (float c11.G) (gx - (float gxi)) (gy - (float gyi)))
let blue = int (blerp (float c00.B) (float c10.B) (float c01.B) (float c11.B) (gx - (float gxi)) (gy - (float gyi)))
let rgb = Color.FromArgb(red, green, blue)
newImage.SetPixel(x, y, rgb)
newImage
// Taken from https://stackoverflow.com/a/2362114 let castAs<'T when 'T : null> (o:obj) =
match o with | :? 'T as res -> res | _ -> Unchecked.defaultof<'T>
[<EntryPoint>] let main _ =
let newImage = Image.FromFile("Lenna100.jpg")
let oi = castAs<Bitmap>(newImage)
if oi = null then
Console.WriteLine("Could not open the source file.")
else
let result = scale oi 1.6 1.6
result.Save("Lenna100_larger.jpg")
0 // return an integer exit code</lang>
Go
(and also just using
draw.BiLinear
from the golang.org/x/image/draw pacakge).
<lang Go>package main
import ( "image" "image/color" "image/jpeg" "log" "math" "os"
"golang.org/x/image/draw" )
func scale(dst draw.Image, src image.Image) { sr := src.Bounds() dr := dst.Bounds() mx := float64(sr.Dx()-1) / float64(dr.Dx()) my := float64(sr.Dy()-1) / float64(dr.Dy()) for x := dr.Min.X; x < dr.Max.X; x++ { for y := dr.Min.Y; y < dr.Max.Y; y++ { gx, tx := math.Modf(float64(x) * mx) gy, ty := math.Modf(float64(y) * my) srcX, srcY := int(gx), int(gy) r00, g00, b00, a00 := src.At(srcX, srcY).RGBA() r10, g10, b10, a10 := src.At(srcX+1, srcY).RGBA() r01, g01, b01, a01 := src.At(srcX, srcY+1).RGBA() r11, g11, b11, a11 := src.At(srcX+1, srcY+1).RGBA() result := color.RGBA64{ R: blerp(r00, r10, r01, r11, tx, ty), G: blerp(g00, g10, g01, g11, tx, ty), B: blerp(b00, b10, b01, b11, tx, ty), A: blerp(a00, a10, a01, a11, tx, ty), } dst.Set(x, y, result) } } }
func lerp(s, e, t float64) float64 { return s + (e-s)*t } func blerp(c00, c10, c01, c11 uint32, tx, ty float64) uint16 { return uint16(lerp( lerp(float64(c00), float64(c10), tx), lerp(float64(c01), float64(c11), tx), ty, )) }
func main() { src, err := readImage("Lenna100.jpg") if err != nil { log.Fatal(err) } sr := src.Bounds() dr := image.Rect(0, 0, sr.Dx()*16/10, sr.Dy()*16/10) dst := image.NewRGBA(dr)
// Using the above bilinear interpolation code: scale(dst, src) err = writeJPEG(dst, "Lenna100_larger.jpg") if err != nil { log.Fatal(err) }
// Using the golang.org/x/image/draw package // (which also provides other iterpolators). draw.BiLinear.Scale(dst, dr, src, sr, draw.Src, nil) err = writeJPEG(dst, "Lenna100_larger.draw.jpg") if err != nil { log.Fatal(err) } }
func readImage(filename string) (image.Image, error) { f, err := os.Open(filename) if err != nil { return nil, err } defer f.Close() // nolint: errcheck m, _, err := image.Decode(f) return m, err }
func writeJPEG(m image.Image, filename string) error { f, err := os.Create(filename) if err != nil { return err } err = jpeg.Encode(f, m, nil) if cerr := f.Close(); err == nil { err = cerr } return err }</lang>
J
<lang J> Note 'FEA'
Here we develop a general method to generate isoparametric interpolants.
The interpolant is the dot product of the four shape function values evaluated at the coordinates within the element with the known values at the nodes. The sum of four shape functions of two variables (xi, eta) is 1 at each of four nodes. Let the base element have nodal coordinates (xi, eta) of +/-1.
2 3 (1,1) +---------------+ | | | | | (0,0) | | * | | | | | | | +---------------+ 0 1
determine f0(xi,eta), ..., f3(xi,eta). f0(-1,-1) = 1, f0(all other corners) is 0. f1( 1,-1) = 1, f1(all other corners) is 0. ...
Choose a shape function. Use shape functions C0 + C1*xi + C2*eta + C3*xi*eta . Given (xi,eta) as the vector y form a vector of the coefficients of the constants (1, xi, eta, and their product)
shape_function =: 1 , {. , {: , */
CORNERS NB. are the ordered coordinates of the corners
_1 _1
1 _1
_1 1
1 1
(=i.4) NB. rows of the identity matrix are the values of each shape functions at each corner
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
(=i.4x) %. shape_function"1 x: CORNERS NB. Compute the values of the constants as rational numbers.
1r4 1r4 1r4 1r4
_1r4 1r4 _1r4 1r4
_1r4 _1r4 1r4 1r4
1r4 _1r4 _1r4 1r4
This method extends to higher order interpolants having more nodes or to other dimensions.
)
mp =: +/ .* NB. matrix product
CORNERS =: 21 A.-.+:#:i.4 shape_function =: 1 , ] , */ COEFFICIENTS =: (=i.4) %. shape_function"1 CORNERS shape_functions =: COEFFICIENTS mp~ shape_function interpolate =: mp shape_functions </lang>
Note 'demonstrate the interpolant with a saddle' lower left has value 1, lower right: 2 upper left: 2.2 upper right: 0.7 ) require'viewmat' GRID =: |.,~"0/~(%~i:)100 SADDLE =: 1 2 2.2 0.7 interpolate"_ 1 GRID viewmat SADDLE assert 0.7 2.2 -: (<./ , >./) , SADDLE
File:J bilinear interpolant.jpg
Let n mean shape function, C mean constants, i mean interpolant, and the three digits meaning dimensionality, number of corners, and (in base 36) the number of nodes we construct various linear and quadratic interpolants in 1, 2, and 3 dimensions as <lang J> Note 'Some elemental information'
Node order 1D:
0 2 1
2D:
2 7 3
5 8 6 Node 8 at origin, Node 3 at (1,1)
0 4 1
Names for shape functions and constants: n249: n means shape function, 2 dimensions, 4 corners (quadrilateral), 9 nodes C244: C constants for 2 dimensions, 4 corners (quadrilateral), 4 nodes
3D At z = _1 z = 1 z = 0 2 b 3 6 j 7 e o f
9 k a h p i m q n
0 8 1 4 g 5 c l d
) mp =: ($: |:) : (+/ .*) NB. A Atranspose : matrix product A B identity =: =@:i. NB. generate identity matrix
NB. 1D
NB. master nodes
N1 =: ,._1 1 0x
NB. form of shape functions
n122 =: 1 , ]
n123 =: [: , ^/&(i.3)
NB. constants
C122 =: x:inv@:(x:@:identity@:# %. n122"1)2{.N1
C123 =: x:inv@:(x:@:identity@:# %. n123"1)3{.N1
NB. interpolants
i122 =: mp (C122 mp~ n122)
i123 =: mp (C123 mp~ n123)
NB. 2D
NB. nodes are arranged 4&{. are the corners, 8&{. the corners and edges, ] include the center.
N2 =: 336330 A.-.3x#.inv i.*:3 NB. 336330 (-: A.) 8 2 6 0 5 7 1 3 4
NB. terms of shape functions n244 =: [: , [: *// ^/&(i.2) NB. all linear combinations n248 =: }:@:n249 NB. exclude (xi eta)^2 n249 =: [: , [: *// ^/&(i.3) NB. all quadratic combinations
NB. constants C244 =: x:inv@:(x:@:identity@:# %. n244"1)4{.N2 NB. serendipity C248 =: x:inv@:(x:@:identity@:# %. n248"1)8{.N2 NB. serendipity C249 =: x:inv@:(x:@:identity@:# %. n249"1)9{.N2 NB. non-serendipity
NB. interpolants i244 =: mp (C244 mp~ n244) i248 =: mp (C248 mp~ n248) i249 =: mp (C249 mp~ n249)
NB. 3D N3 =: 267337661061030402017459663x A.<:3#.inv i.3^3 NB. 267337661061030402017459663x (-: A.) 0 18 6 24 2 20 8 26 9 3 21 15 1 19 7 25 11 5 23 17 12 10 4 22 16 14 13 NB. corners n388 =: [: , [: *// 1 , ] NB. all linear combinations
Note 'simplification not yet apparent to me'
combinations =: 4 : 0
if. x e. 0 1 do. z=.<((x!y),x)$ i.y
else. t=. |.(<.@-:)^:(i.<. 2^.x)x
z=.({.t) ([:(,.&.><@;\.)/ >:@-~[\i.@]) ({.t)+y-x
for_j. 2[\t do.
z=.([ ;@:(<"1@[ (,"1 ({.j)+])&.> ])&.> <@;\.({&.><)~ (1+({.j)-~{:"1)&.>) z
if. 2|{:j do. z=.(i.1+y-x)(,.>:)&.> <@;\.z end.
end.
end.
;z
NB.)
n38k =: 1 , ] , */"1@:((2 combinations 3)&{) , *: , (1&, * */) , ,@:(*:@:|. (*"0 1) (2 combinations 3)&{) NB. include mid-edge nodes
) n38q =: }:@:n38r NB. include mid-face nodes, all quadratic combinations but (xyz)^2 n38r =: [: , [: *// ^/&(i.3) NB. now this is simple! 3*3*3 nodal grid. C388 =: x:inv@:(x:@:identity@:# %. n388"1)8{.N3 NB.C38k =: x:inv@:(x:@:identity@:# %. n38k"1)36bk{.N3 C38q =: x:inv@:(x:@:identity@:# %. x:@:n38q"1)36bq{.N3 C38r =: x:inv@:(x:@:identity@:# %. x:@:n38r"1)36br{.N3 i388 =: mp (C388 mp~ n388) NB.i38k =: mp (C38k mp~ n38k) i38q =: mp (C38r mp~ n38r) i38r =: mp (C38r mp~ n38r) </lang>
Java
<lang Java>import javax.imageio.ImageIO; import java.awt.image.BufferedImage; import java.io.File; import java.io.IOException;
public class BilinearInterpolation {
/* gets the 'n'th byte of a 4-byte integer */
private static int get(int self, int n) {
return (self >> (n * 8)) & 0xFF;
}
private static float lerp(float s, float e, float t) {
return s + (e - s) * t;
}
private static float blerp(final Float c00, float c10, float c01, float c11, float tx, float ty) {
return lerp(lerp(c00, c10, tx), lerp(c01, c11, tx), ty);
}
private static BufferedImage scale(BufferedImage self, float scaleX, float scaleY) {
int newWidth = (int) (self.getWidth() * scaleX);
int newHeight = (int) (self.getHeight() * scaleY);
BufferedImage newImage = new BufferedImage(newWidth, newHeight, self.getType());
for (int x = 0; x < newWidth; ++x) {
for (int y = 0; y < newHeight; ++y) {
float gx = ((float) x) / newWidth * (self.getWidth() - 1);
float gy = ((float) y) / newHeight * (self.getHeight() - 1);
int gxi = (int) gx;
int gyi = (int) gy;
int rgb = 0;
int c00 = self.getRGB(gxi, gyi);
int c10 = self.getRGB(gxi + 1, gyi);
int c01 = self.getRGB(gxi, gyi + 1);
int c11 = self.getRGB(gxi + 1, gyi + 1);
for (int i = 0; i <= 2; ++i) {
float b00 = get(c00, i);
float b10 = get(c10, i);
float b01 = get(c01, i);
float b11 = get(c11, i);
int ble = ((int) blerp(b00, b10, b01, b11, gx - gxi, gy - gyi)) << (8 * i);
rgb = rgb | ble;
}
newImage.setRGB(x, y, rgb);
}
}
return newImage;
}
public static void main(String[] args) throws IOException {
File lenna = new File("Lenna100.jpg");
BufferedImage image = ImageIO.read(lenna);
BufferedImage image2 = scale(image, 1.6f, 1.6f);
File lenna2 = new File("Lenna100_larger.jpg");
ImageIO.write(image2, "jpg", lenna2);
}
}</lang>
Julia
<lang julia>using Images, FileIO, Interpolations
function enlarge(A::Matrix, factor::AbstractFloat)
lx, ly = size(A) nx, ny = round.(Int, factor .* (lx, ly)) vx, vy = linspace(1, lx, nx), linspace(1, ly, ny) itp = interpolate(A, BSpline(Linear()), OnGrid()) return itp[vx, vy]
end
A = load("data/lenna100.jpg") |> Matrix{RGB{Float64}}; Alarge = enlarge(A, 1.6); save("data/lennaenlarged.jpg", Alarge)</lang>
Kotlin
<lang scala>// version 1.2.21
import java.io.File import java.awt.image.BufferedImage import javax.imageio.ImageIO
/* gets the 'n'th byte of a 4-byte integer */ operator fun Int.get(n: Int) = (this shr (n * 8)) and 0xFF
fun lerp(s: Float, e: Float, t: Float) = s + (e - s) * t
fun blerp(c00: Float, c10: Float, c01: Float, c11: Float, tx: Float, ty: Float) =
lerp(lerp(c00, c10, tx), lerp(c01,c11, tx), ty)
fun BufferedImage.scale(scaleX: Float, scaleY: Float): BufferedImage {
val newWidth = (width * scaleX).toInt()
val newHeight = (height * scaleY).toInt()
val newImage = BufferedImage(newWidth, newHeight, type)
for (x in 0 until newWidth) {
for (y in 0 until newHeight) {
val gx = x.toFloat() / newWidth * (width - 1)
val gy = y.toFloat() / newHeight * (height - 1)
val gxi = gx.toInt()
val gyi = gy.toInt()
var rgb = 0
val c00 = getRGB(gxi, gyi)
val c10 = getRGB(gxi + 1, gyi)
val c01 = getRGB(gxi, gyi + 1)
val c11 = getRGB(gxi + 1, gyi + 1)
for (i in 0..2) {
val b00 = c00[i].toFloat()
val b10 = c10[i].toFloat()
val b01 = c01[i].toFloat()
val b11 = c11[i].toFloat()
val ble = blerp(b00, b10, b01, b11, gx - gxi, gy - gyi).toInt() shl (8 * i)
rgb = rgb or ble
}
newImage.setRGB(x, y, rgb)
}
}
return newImage
}
fun main(args: Array<String>) {
val lenna = File("Lenna100.jpg") // from the Percentage difference between images task
val image = ImageIO.read(lenna)
val image2 = image.scale(1.6f, 1.6f)
val lenna2 = File("Lenna100_larger.jpg")
ImageIO.write(image2, "jpg", lenna2)
}</lang>
Perl 6
<lang perl6>#!/usr/bin/env perl6
use v6; use GD::Raw;
- Reference:
- https://github.com/dagurval/perl6-gd-raw
my $fh1 = fopen('./Lenna100.jpg', "rb") or die; my $img1 = gdImageCreateFromJpeg($fh1);
my $fh2 = fopen('./Lenna100-larger.jpg',"wb") or die;
my $img1X = gdImageSX($img1); my $img1Y = gdImageSY($img1);
my $NewX = $img1X * 1.6; my $NewY = $img1Y * 1.6;
gdImageSetInterpolationMethod($img1, +GD_BILINEAR_FIXED);
my $img2 = gdImageScale($img1, $NewX.ceiling, $NewY.ceiling);
gdImageJpeg($img2,$fh2,-1);
gdImageDestroy($img1); gdImageDestroy($img2);
fclose($fh1); fclose($fh2); </lang>
- Output:
file Lenna100* Lenna100.jpg: JPEG image data, JFIF standard 1.01, resolution (DPI), density 72x72, segment length 16, baseline, precision 8, 512x512, frames 3 Lenna100-larger.jpg: JPEG image data, JFIF standard 1.01, resolution (DPI), density 96x96, segment length 16, comment: "CREATOR: gd-jpeg v1.0 (using IJG JPEG v80), default quality", baseline, precision 8, 820x820, frames 3
Phix
Gui app with slider for between 2 and 200% scaling. Various bits of this code scavenged from C#/Go/Kotlin/Wikipedia. <lang Phix>-- demo\rosetta\Bilinear_interpolation.exw include pGUI.e
function interpolate(atom s, e, f) -- -- s,e are the start and end values (one original pixel apart), -- f is a fraction of some point between them, 0(==s)..1(==e). -- eg s=91 (f=0.2) e=101, we want 0.8 of the 91 + 0.2 of 101, -- aka if f is 4 times closer to s than e, we want 4 times as -- much of s as we want of e, with sum(fractions_taken)==1. --
return s + (e-s)*f -- aka s*(1-f) + e*f
end function
function bilinear(integer c00, c10, c01, c11, atom fx, fy) -- -- for some output pixel, we have calculated the exact point -- on the original, and extracted the four pixels surrounding -- that, with fx,fy as the fractional x,y part of the 1x1 box. -- Like a capital H, we want some fraction on the left and the -- same on the right, then some fraction along the horizontal. -- It would be equivalent to do top/bottom then the vertical, -- which is handy since I am no longer certain which of those -- the following actually does, especially since we got the -- pixels from original[y,x] rather than original[x,y], and -- imImage and IupImage have {0,0} in different corners - but -- the output looks pretty good, and I think you would easily -- notice were this even slightly wrong, and in fact an early -- accidental typo of r10/r01 indeed proved very evident. --
atom left = interpolate(c00,c10,fx),
right = interpolate(c01,c11,fx)
return floor(interpolate(left,right,fy))
end function
function scale_image(imImage img, atom scaleX, scaleY) integer width = im_width(img),
height = im_height(img),
new_width = floor(width * scaleX)-1,
new_height = floor(height * scaleY)-1
atom mx = (width-1)/new_width,
my = (height-1)/new_height
sequence original = repeat(repeat(0,width),height) sequence new_image = repeat(repeat(0,new_width),new_height)
-- Extract the original pixels from the image [about
-- twice as fast as 4*im_pixel() in the main loop.]
for y=height-1 to 0 by -1 do
for x=0 to width-1 do
original[height-y,x+1] = im_pixel(img, x, y)
end for
end for
for x=0 to new_width-1 do
for y=0 to new_height-1 do
atom ax = x*mx, -- map onto original
ay = y*my
integer ix = floor(ax), -- top left
iy = floor(ay)
ax -= ix -- fraction of the 1x1 box
ay -= iy
integer {r00,g00,b00} = original[iy+1,ix+1],
{r10,g10,b10} = original[iy+1,ix+2],
{r01,g01,b01} = original[iy+2,ix+1],
{r11,g11,b11} = original[iy+2,ix+2],
r = bilinear(r00,r10,r01,r11,ax,ay),
g = bilinear(g00,g10,g01,g11,ax,ay),
b = bilinear(b00,b10,b01,b11,ax,ay)
new_image[y+1,x+1] = {r,g,b}
end for
end for
new_image = flatten(new_image) -- (as needed by IupImageRGB)
Ihandle new_img = IupImageRGB(new_width, new_height, new_image)
return new_img
end function
IupOpen()
constant w = machine_word() atom pError = allocate(w) imImage im1 = imFileImageLoadBitmap("Lena.ppm",0,pError) if im1=NULL then
?{"error opening image",peekNS(pError,w,1)}
{} = wait_key()
abort(0)
end if
Ihandle dlg,
scale = IupValuator(NULL,"MIN=2,MAX=200,VALUE=160"),
redraw = IupButton("redraw (160%)")
Ihandln image1 = IupImageFromImImage(im1),
image2 = scale_image(im1,1.6,1.6),
label1 = IupLabel(),
label2 = IupLabel()
IupSetAttributeHandle(label1, "IMAGE", image1) IupSetAttributeHandle(label2, "IMAGE", image2)
function valuechanged_cb(Ihandle /*scale*/)
atom v = IupGetDouble(scale,"VALUE")
IupSetStrAttribute(redraw,"TITLE","redraw (%d%%)",{v})
return IUP_DEFAULT
end function IupSetCallback(scale,"VALUECHANGED_CB",Icallback("valuechanged_cb"))
function redraw_cb(Ihandle /*redraw*/)
IupSetAttributeHandle(label2, "IMAGE", NULL) IupDestroy(image2) atom v = IupGetDouble(scale,"VALUE")/100 image2 = scale_image(im1,v,v) IupSetAttributeHandle(label2, "IMAGE", image2) IupSetAttribute(dlg,"SIZE",NULL) IupRefresh(dlg) return IUP_DEFAULT
end function IupSetCallback(redraw,"ACTION",Icallback("redraw_cb"))
dlg = IupDialog(IupVbox({IupHbox({scale, redraw}),
IupHbox({label1, label2})}))
IupSetAttribute(dlg, "TITLE", "Bilinear interpolation") IupCloseOnEscape(dlg) IupShow(dlg)
IupMainLoop() IupClose()</lang>
Python
Of course, it is much faster to use PIL, Pillow or SciPy to resize an image than to rely on this code.
<lang python>#!/bin/python import numpy as np from scipy.misc import imread, imshow from scipy import ndimage
def GetBilinearPixel(imArr, posX, posY): out = []
#Get integer and fractional parts of numbers modXi = int(posX) modYi = int(posY) modXf = posX - modXi modYf = posY - modYi modXiPlusOneLim = min(modXi+1,imArr.shape[1]-1) modYiPlusOneLim = min(modYi+1,imArr.shape[0]-1)
#Get pixels in four corners for chan in range(imArr.shape[2]): bl = imArr[modYi, modXi, chan] br = imArr[modYi, modXiPlusOneLim, chan] tl = imArr[modYiPlusOneLim, modXi, chan] tr = imArr[modYiPlusOneLim, modXiPlusOneLim, chan]
#Calculate interpolation b = modXf * br + (1. - modXf) * bl t = modXf * tr + (1. - modXf) * tl pxf = modYf * t + (1. - modYf) * b out.append(int(pxf+0.5))
return out
if __name__=="__main__":
im = imread("test.jpg", mode="RGB") enlargedShape = list(map(int, [im.shape[0]*1.6, im.shape[1]*1.6, im.shape[2]])) enlargedImg = np.empty(enlargedShape, dtype=np.uint8) rowScale = float(im.shape[0]) / float(enlargedImg.shape[0]) colScale = float(im.shape[1]) / float(enlargedImg.shape[1])
for r in range(enlargedImg.shape[0]): for c in range(enlargedImg.shape[1]): orir = r * rowScale #Find position in original image oric = c * colScale enlargedImg[r, c] = GetBilinearPixel(im, oric, orir)
imshow(enlargedImg) </lang>
Racket
This mimics the Wikipedia example. <lang racket>#lang racket (require images/flomap)
(define fm
(draw-flomap
(λ (dc)
(define (pixel x y color)
(send dc set-pen color 1 'solid)
(send dc draw-point (+ x .5) (+ y 0.5)))
(send dc set-alpha 1)
(pixel 0 0 "blue")
(pixel 0 1 "red")
(pixel 1 0 "red")
(pixel 1 1 "green"))
2 2))
(flomap->bitmap
(build-flomap
4 250 250
(λ (k x y)
(flomap-bilinear-ref
fm k (+ 1/2 (/ x 250)) (+ 1/2 (/ y 250))))))</lang>
Scala
Imperative solution
<lang Scala>import java.awt.image.BufferedImage import java.io.{File, IOException}
import javax.imageio.ImageIO
object BilinearInterpolation {
@throws[IOException]
def main(args: Array[String]): Unit = {
val lenna = new File("Lenna100.jpg")
val image = ImageIO.read(lenna)
val image2 = scale(image, 1.6f, 1.6f)
val lenna2 = new File("Lenna100_larger.jpg")
ImageIO.write(image2, "jpg", lenna2)
}
private def scale(self: BufferedImage, scaleX: Float, scaleY: Float) = {
val newWidth = (self.getWidth * scaleX).toInt
val newHeight = (self.getHeight * scaleY).toInt
val newImage = new BufferedImage(newWidth, newHeight, self.getType)
var x = 0
while (x < newWidth) {
var y = 0
while (y < newHeight) {
val gx = x.toFloat / newWidth * (self.getWidth - 1)
val gy = y.toFloat / newHeight * (self.getHeight - 1)
val gxi = gx.toInt
val gyi = gy.toInt
var rgb = 0
val c00 = self.getRGB(gxi, gyi)
val c10 = self.getRGB(gxi + 1, gyi)
val c01 = self.getRGB(gxi, gyi + 1)
val c11 = self.getRGB(gxi + 1, gyi + 1)
var i = 0
while (i <= 2) {
val b00 = get(c00, i)
val b10 = get(c10, i)
val b01 = get(c01, i)
val b11 = get(c11, i)
val ble = blerp(b00, b10, b01, b11, gx - gxi, gy - gyi).toInt << (8 * i)
rgb = rgb | ble
i += 1
}
newImage.setRGB(x, y, rgb)
y += 1
}
x += 1
}
newImage
}
/* gets the 'n'th byte of a 4-byte integer */ private def get(self: Int, n: Int) = (self >> (n * 8)) & 0xFF
private def blerp(c00: Float, c10: Float, c01: Float, c11: Float, tx: Float, ty: Float) = lerp(lerp(c00, c10, tx), lerp(c01, c11, tx), ty)
private def lerp(s: Float, e: Float, t: Float) = s + (e - s) * t
}</lang>
Sidef
<lang ruby>require('Imager')
func scale(img, scaleX, scaleY) {
var (width, height) = (img.getwidth, img.getheight) var (newWidth, newHeight) = (int(width*scaleX), int(height*scaleY))
var out = %O<Imager>.new(xsize => newWidth, ysize => newHeight)
var lerp = { |s, e, t|
s + t*(e-s)
}
var blerp = { |c00, c10, c01, c11, tx, ty|
lerp(lerp(c00, c10, tx), lerp(c01, c11, tx), ty)
}
for x,y in (^newWidth ~X ^newHeight) {
var gxf = (x/newWidth * (width - 1))
var gyf = (y/newHeight * (height - 1))
var gx = gxf.int
var gy = gyf.int
var *c00 = img.getpixel(x => gx, y => gy ).rgba
var *c10 = img.getpixel(x => gx+1, y => gy ).rgba
var *c01 = img.getpixel(x => gx, y => gy+1).rgba
var *c11 = img.getpixel(x => gx+1, y => gy+1).rgba
var rgb = 3.of { |i|
blerp(c00[i], c10[i], c01[i], c11[i], gxf - gx, gyf - gy).int
}
out.setpixel(x => x, y => y, color => rgb) }
return out
}
var img = %O<Imager>.new(file => "input.png") var out = scale(img, 1.6, 1.6) out.write(file => "output.png")</lang>
Tcl
This uses the polynomial expansion described in wikipedia, and draws the same example as illustrated in that page with a different pallette. It's not particularly fast - about 300ms for a 200x200 surface on an arbitrary machine.
The script below will show the computed image in a GUI frame, and present a button to save it.
<lang Tcl> package require Tk
proc pixel {f} {
if {$f < 0} {
error "why is $f?"
}
set i [expr {0xff & entier(0xff*$f)}]
format #%02x%02x%02x $i [expr {255-$i}] 127
}
proc bilerp {im O X Y XY} {
set w [image width $im]
set h [image height $im]
set dx [expr {1.0/$w}]
set dy [expr {1.0/$h}]
set a0 $O
set a1 [expr {$X - $O}]
set a2 [expr {$Y - $O}]
set a3 [expr {$O + $XY - ($X + $Y)}]
for {set y 0} {$y < $h} {incr y} {
for {set x 0} {$x < $w} {incr x} {
set i [expr {$x * $dx}]
set j [expr {$y * $dy}]
set xv [expr {$a0 + $a1*$i + $a2*$j + $a3*$i*$j}]
set y [expr {$h - $y}] ;# invert for screen coords
$im put [pixel $xv] -to $x $y
}
}
}
proc save {im} {
set fn [tk_getSaveFile -defaultextension png]
if {$fn eq ""} return
set fd [open $fn wb]
puts -nonewline $fd [$im data -format png]
close $fd
tk_messageBox -message "Saved as $fn!"
}
set im [image create photo -width 200 -height 200] puts [time {bilerp $im 0 1 1 0.5} 1] pack [label .l1 -image $im] pack [button .b -text "save" -command [list save $im]]
</lang>
zkl
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl.
Not fast enough to be called slow. <lang zkl>fcn lerp(s,e,t){ s + (e-s)*t; } fcn blerp(c00,c10,c01,c11, tx,ty){ lerp(lerp(c00,c10,tx), lerp(c01,c11,tx),ty) } fcn scale(src, scaleX,scaleY){
newWidth,newHeight := Int(scaleX*src.w), Int(scaleY*src.h);
dst:=PPM(newWidth,newHeight);
foreach y,x in ([0.0..newHeight-1],[0.0..newWidth-1]){
gx:=x/newWidth *(src.w-1);
gy:=y/newHeight *(src.h-1);
gxi,gyi:=Int(gx), Int(gy);
// cxy=RGB, cxy.toBigEndian(3)-->(R,G,B)
c00,c10 := src[gxi,gyi].toBigEndian(3), src[gxi+1,gyi].toBigEndian(3);
c01 := src[gxi,gyi+1] .toBigEndian(3);
c11 := src[gxi+1,gyi+1].toBigEndian(3);
dst[x,y] = (3).pump(Data(), // Data is a byte bucket
'wrap(i){ blerp(c00[i],c10[i],c01[i],c11[i], gx-gxi, gy-gyi) })
.toBigEndian(0,3);
} dst
}</lang> <lang zkl>img:=PPM.readPPMFile("lena.ppm"); img2:=scale(img,1.5,1.5); img2.write(File("lena1.5.ppm","wb")); scale(img,0.5,0.5).write(File("lena.5.ppm","wb"));</lang>
- Output:
