Fourier-Bessel improvements.

BlurHash.xcodeproj/project.pbxproj

@@ -25,6 +25,7 @@
 		1B49CD271EC47243006F8E7D /* Encode.swift in Sources */ = {isa = PBXBuildFile; fileRef = 1B49CD261EC47243006F8E7D /* Encode.swift */; };
 		1B49CD291EC4724C006F8E7D /* Decode.swift in Sources */ = {isa = PBXBuildFile; fileRef = 1B49CD281EC4724C006F8E7D /* Decode.swift */; };
 		1B787C901EC4A29C00F167D3 /* StringExtension.swift in Sources */ = {isa = PBXBuildFile; fileRef = 1B787C8F1EC4A29C00F167D3 /* StringExtension.swift */; };
+		1BED97AA1F75488E00255036 /* pic6.png in Resources */ = {isa = PBXBuildFile; fileRef = 1BED97A91F75486400255036 /* pic6.png */; };
 /* End PBXBuildFile section */
 
 /* Begin PBXContainerItemProxy section */
@@ -90,6 +91,7 @@
 		1B49CD261EC47243006F8E7D /* Encode.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Encode.swift; sourceTree = "<group>"; };
 		1B49CD281EC4724C006F8E7D /* Decode.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Decode.swift; sourceTree = "<group>"; };
 		1B787C8F1EC4A29C00F167D3 /* StringExtension.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = StringExtension.swift; sourceTree = "<group>"; };
+		1BED97A91F75486400255036 /* pic6.png */ = {isa = PBXFileReference; lastKnownFileType = image.png; name = pic6.png; path = ../../../Downloads/pic6.png; sourceTree = "<group>"; };
 /* End PBXFileReference section */
 
 /* Begin PBXFrameworksBuildPhase section */
@@ -140,6 +142,7 @@
 				1B0A25261EC5EAB000F25F08 /* pic3.png */,
 				1B0A25271EC5EAB000F25F08 /* pic4.png */,
 				1B0A25281EC5EAB000F25F08 /* pic5.png */,
+				1BED97A91F75486400255036 /* pic6.png */,
 			);
 			name = Images;
 			sourceTree = "<group>";
@@ -335,6 +338,7 @@
 			files = (
 				1B0A25291EC5EAB000F25F08 /* pic1.png in Resources */,
 				1B0A252A1EC5EAB000F25F08 /* pic2.png in Resources */,
+				1BED97AA1F75488E00255036 /* pic6.png in Resources */,
 				1B0A252B1EC5EAB000F25F08 /* pic3.png in Resources */,
 				1B0A252C1EC5EAB000F25F08 /* pic4.png in Resources */,
 				1B0A252D1EC5EAB000F25F08 /* pic5.png in Resources */,
@@ -627,6 +631,7 @@
 				1B2BA1C31F0E5EC6006057C1 /* Release */,
 			);
 			defaultConfigurationIsVisible = 0;
+			defaultConfigurationName = Release;
 		};
 		1B49CD151EC4721A006F8E7D /* Build configuration list for PBXProject "BlurHash" */ = {
 			isa = XCConfigurationList;

BlurHashTest/Base.lproj/Main.storyboard

@@ -1,15 +1,20 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="12120" systemVersion="16C67" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" useTraitCollections="YES" colorMatched="YES" initialViewController="BYZ-38-t0r">
+<document type="com.apple.InterfaceBuilder3.CocoaTouch.Storyboard.XIB" version="3.0" toolsVersion="13196" targetRuntime="iOS.CocoaTouch" propertyAccessControl="none" useAutolayout="YES" useTraitCollections="YES" colorMatched="YES" initialViewController="BYZ-38-t0r">
     <device id="retina4_7" orientation="portrait">
         <adaptation id="fullscreen"/>
     </device>
     <dependencies>
         <deployment identifier="iOS"/>
-        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="12088"/>
+        <plugIn identifier="com.apple.InterfaceBuilder.IBCocoaTouchPlugin" version="13173"/>
         <capability name="Constraints to layout margins" minToolsVersion="6.0"/>
         <capability name="Constraints with non-1.0 multipliers" minToolsVersion="5.1"/>
         <capability name="documents saved in the Xcode 8 format" minToolsVersion="8.0"/>
     </dependencies>
+    <customFonts key="customFonts">
+        <array key="Courier.ttc">
+            <string>Courier</string>
+        </array>
+    </customFonts>
     <scenes>
         <!--View Controller-->
         <scene sceneID="tne-QT-ifu">
@@ -23,7 +28,7 @@
                         <rect key="frame" x="0.0" y="0.0" width="375" height="667"/>
                         <autoresizingMask key="autoresizingMask" widthSizable="YES" heightSizable="YES"/>
                         <subviews>
-                            <imageView contentMode="scaleToFill" horizontalHuggingPriority="251" verticalHuggingPriority="251" placeholderIntrinsicWidth="240" placeholderIntrinsicHeight="128" translatesAutoresizingMaskIntoConstraints="NO" id="P5Q-KT-MGh">
+                            <imageView contentMode="scaleAspectFit" horizontalHuggingPriority="251" verticalHuggingPriority="251" placeholderIntrinsicWidth="240" placeholderIntrinsicHeight="128" translatesAutoresizingMaskIntoConstraints="NO" id="P5Q-KT-MGh">
                                 <rect key="frame" x="67" y="52" width="240" height="128"/>
                                 <gestureRecognizers/>
                                 <connections>

BlurHashTest/ViewController.swift

@@ -9,6 +9,7 @@ class ViewController: UIViewController {
     @IBOutlet weak var yComponentsLabel: UILabel?
 
     let images: [UIImage] = [
+        UIImage(named: "pic6.png")!,
         UIImage(named: "pic2.png")!,
         UIImage(named: "pic1.png")!,
         UIImage(named: "pic3.png")!,
@@ -34,7 +35,7 @@ class ViewController: UIViewController {
     }
 
     @IBAction func xPlusTapped() {
-        if xComponents < 8 {
+        if xComponents < 10 {
             xComponents += 1
             updateEncode()
             updateDecode()
@@ -50,7 +51,7 @@ class ViewController: UIViewController {
     }
 
     @IBAction func yPlusTapped() {
-        if yComponents < 8 {
+        if yComponents < 5 {
             yComponents += 1
             updateEncode()
             updateDecode()
@@ -80,7 +81,11 @@ class ViewController: UIViewController {
     }
 
     func updateDecode() {
-        let blurImage = UIImage(blurHash: blurHash, size: CGSize(width: 32, height: 32), punch: punch)
+        guard let image = originalImageView?.image else { return }
+        let blurImage = UIImage(blurHash: blurHash, size: CGSize(
+        width: Int(ceil(32 * sqrt(image.size.width / image.size.height))),
+        height: Int(ceil(32 * sqrt(image.size.height / image.size.width)))),
+        punch: punch)
 
         blurImageView?.image = blurImage
     }

Swift/Decode.swift

@@ -6,15 +6,15 @@ extension UIImage {
         guard string.length >= 6 else { return nil }
 
         let sizeFlag = string.substring(with: NSRange(location: 0, length: 1)).decode64()
-        let numY = (sizeFlag >> 3) + 1
-        let numX = (sizeFlag & 7) + 1
+        let numY = (sizeFlag / 10) + 1
+        let numX = (sizeFlag % 10) + 1
 
         let quantisedMaximumValue = string.substring(with: NSRange(location: 1, length: 1)).decode64()
         let maximumValue = Float(quantisedMaximumValue + 1) / 128
 
         guard string.length == 4 + 2 * numX * numY else { return nil }
 
-        let colours: [(Float, Float, Float)] = (0 ..< numX * numY).map { i in
+        var colours: [(Float, Float, Float)] = (0 ..< numX * numY).map { i in
             if i == 0 {
                 let value = string.substring(with: NSRange(location: 2, length: 4)).decode64()
                 return decodeDC(value)
@@ -28,6 +28,7 @@ extension UIImage {
         let height = Int(size.height)
         let bytesPerRow = width * 3
         guard let data = CFDataCreateMutable(kCFAllocatorDefault, bytesPerRow * height) else { return nil }
+        CFDataSetLength(data, bytesPerRow * height)
         guard let pixels = CFDataGetMutableBytePtr(data) else { return nil }
 
         for y in 0 ..< height {
@@ -36,10 +37,19 @@ extension UIImage {
                 var g: Float = 0
                 var b: Float = 0
 
-                for j in 0 ..< numY {
-                    for i in 0 ..< numX {
-                        let basis = cos(Float.pi * Float(x) * Float(i) / Float(width)) * cos(Float.pi * Float(y) * Float(j) / Float(height))
-                        let colour = colours[i + j * numX]
+                for q in 0 ..< numY {
+                    for k in 0 ..< numX {
+                        let fx = Double(x) - Double(width) / 2
+                        let fy = Double(y) - Double(height) / 2
+                        let rr = sqrt(fx * fx + fy * fy) / (Double(width) / 2)
+                        let omega = atan2(fy, fx)
+                        let K = (k + 1) / 2
+                        let Rkq = UIImage.Rqk[q][K]
+                        let isCosine = k % 2 == 0
+                        //let normalisation = Rkq == 0 ? 1 : sqrt(Double.pi)
+                        let basis = Float(/*normalisation * */jn(K, Rkq * rr) * (isCosine ? cos(omega * Double(K)) : sin(omega * Double(K))))
+
+                        let colour = colours[k + q * numX]
                         r += colour.0 * basis
                         g += colour.1 * basis
                         b += colour.2 * basis
@@ -79,9 +89,9 @@ func decodeAC(_ value: Int, maximumValue: Float) -> (Float, Float, Float) {
     let quantB = value & 15
 
     let rgb = (
-        signPow((Float(quantR) - 8) / 8, 3.0) * maximumValue * 2,
-        signPow((Float(quantG) - 8) / 8, 3.0) * maximumValue * 2,
-        signPow((Float(quantB) - 8) / 8, 3.0) * maximumValue * 2
+        signPow((Float(quantR) - 8) / 7, 3.0) * maximumValue * 2,
+        signPow((Float(quantG) - 8) / 7, 3.0) * maximumValue * 2,
+        signPow((Float(quantB) - 8) / 7, 3.0) * maximumValue * 2
     )
 
     return rgb

Swift/Encode.swift

@@ -1,9 +1,29 @@
 import UIKit
 
 extension UIImage {
+    static let Rqk: [[Double]] = [
+        // TODO:
+        // http://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlx
+        // http://www.math.usm.edu/lambers/mat415/lecture15.pdf
+
+        [0, 1.8412, 3.0542, 4.2012, 5.3175, 6.4156],
+        [3.8317, 5.3314, 6.7061, 8.0152, 9.2824, 10.5199],
+        [7.0156, 8.5363, 9.9695, 11.3459, 12.6819, 13.9872],
+        [10.1735, 11.7060, 13.1704, 14.5858, 15.9641, 17.3128],
+        [13.3237, 14.8636, 16.3475, 17.7887, 19.1960, 20.5755],
+
+/*        [2.4048, 3.8317, 5.1356, 6.3802, 7.5883, 8.7715],
+        [5.5201, 7.0156, 8.4172, 9.7610, 11.0647, 12.3386],
+        [8.6537, 10.1735, 11.6198, 13.0152, 14.3725, 15.7002],
+        [11.7915, 13.3237, 14.7960, 16.2235, 17.6160, 18.9801],
+        [14.9309, 16.4706, 17.9598, 19.4094, 20.8269, 22.2178],*/
+    ]
+
+    // https://lmb.informatik.uni-freiburg.de/Publications/2008/WRB08/wa_report01_08.pdf
+
     public func blurHash(components: (Int, Int)) -> String? {
-        guard components.0 >= 1, components.0 <= 8,
-        components.1 >= 1, components.1 <= 8,
+        guard components.0 >= 1, components.0 <= 10,
+        components.1 >= 1, components.1 <= 5,
         cgImage?.colorSpace?.numberOfComponents == 3,
         cgImage?.bitsPerPixel == 24 || cgImage?.bitsPerPixel == 32 else { return nil }
 
@@ -17,12 +37,24 @@ extension UIImage {
         let bytesPerRow = cgImage.bytesPerRow
 
         var factors: [(Float, Float, Float)] = []
-        for y in 0 ..< components.1 {
-            for x in 0 ..< components.0 {
+
+        for q in 0 ..< components.1 {
+            for k in 0 ..< components.0 {
                 let factor = multiplyBasisFunction(pixels: pixels, width: width, height: height, bytesPerRow: bytesPerRow, bytesPerPixel: cgImage.bitsPerPixel / 8, pixelOffset: 0) {
-                    cos(Float.pi * Float(x) * $0 / Float(width)) * cos(Float.pi * Float(y) * $1 / Float(height))
+                    let fx = Double($0) - Double(width) / 2
+                    let fy = Double($1) - Double(height) / 2
+                    let r = sqrt(fx * fx + fy * fy) / (Double(width) / 2)
+                    let omega = atan2(fy, fx)
+                    guard r < 1 else { return 0 }
+                    let K = (k + 1) / 2
+                    let Rkq = UIImage.Rqk[q][K]
+                    let isCosine = k % 2 == 0
+                    return Float(/**/jn(K, Rkq * r) * (isCosine ? cos(omega * Double(K)) : sin(omega * Double(K))))
                 }
-                factors.append(factor)
+                let normalisation: Float = q == 0 && k == 0 ? 1 : 0.5
+                let normalisedFactor = (factor.0 * normalisation, factor.1 * normalisation, factor.2 * normalisation)
+print("\(q) \(k): \(normalisedFactor)")
+                factors.append(normalisedFactor)
             }
         }
 
@@ -31,12 +63,12 @@ extension UIImage {
 
         var hash = ""
 
-        let sizeFlag = (components.0 - 1) + ((components.1 - 1) << 3)
+        let sizeFlag = (components.0 - 1) + ((components.1 - 1) * 10)
         hash += sizeFlag.encode64(length: 1)
 
         let maximumValue: Float
         if ac.count > 0 {
-            let actualMaximumValue = ac.map({ max($0.0, $0.1, $0.2) }).max()!
+            let actualMaximumValue = ac.flatMap({ [abs($0.0), abs($0.1), abs($0.2)] }).max()!
             let quantisedMaximumValue = Int(max(0, min(63, floor(actualMaximumValue * 128 - 0.5))))
             maximumValue = Float(quantisedMaximumValue + 1) / 128
             hash += quantisedMaximumValue.encode64(length: 1)
@@ -60,18 +92,18 @@ extension UIImage {
         var b: Float = 0
 
         let buffer = UnsafeBufferPointer(start: pixels, count: height * bytesPerRow)
+        var scale: Float = 0
 
         for x in 0 ..< width {
             for y in 0 ..< height {
                 let basis = basisFunction(Float(x), Float(y))
-                r += basis * sRGBToLinear(buffer[bytesPerPixel * x + pixelOffset + 0 + y * bytesPerRow])
-                g += basis * sRGBToLinear(buffer[bytesPerPixel * x + pixelOffset + 1 + y * bytesPerRow])
-                b += basis * sRGBToLinear(buffer[bytesPerPixel * x + pixelOffset + 2 + y * bytesPerRow])
+                r += basis * (sRGBToLinear(buffer[bytesPerPixel * x + pixelOffset + 0 + y * bytesPerRow]))
+                g += basis * (sRGBToLinear(buffer[bytesPerPixel * x + pixelOffset + 1 + y * bytesPerRow]))
+                b += basis * (sRGBToLinear(buffer[bytesPerPixel * x + pixelOffset + 2 + y * bytesPerRow]))
+                scale += basis * basis
             }
         }
 
-        let scale = Float(width * height)
-
         return (r / scale, g / scale, b / scale)
     }
 }
@@ -84,9 +116,9 @@ func encodeDC(_ value: (Float, Float, Float)) -> Int {
 }
 
 func encodeAC(_ value: (Float, Float, Float), maximumValue: Float) -> Int {
-    let quantR = Int(max(0, min(15, floor(signPow(value.0 / maximumValue, 0.333) * 8 + 8.5))))
-    let quantG = Int(max(0, min(15, floor(signPow(value.1 / maximumValue, 0.333) * 8 + 8.5))))
-    let quantB = Int(max(0, min(15, floor(signPow(value.2 / maximumValue, 0.333) * 8 + 8.5))))
+    let quantR = Int(max(0, min(15, floor(signPow(value.0 / maximumValue, 0.333) * 7 + 8.5))))
+    let quantG = Int(max(0, min(15, floor(signPow(value.1 / maximumValue, 0.333) * 7 + 8.5))))
+    let quantB = Int(max(0, min(15, floor(signPow(value.2 / maximumValue, 0.333) * 7 + 8.5))))
 
     return (quantR << 8) + (quantG << 4) + quantB
 }