Add Kittler-Illingworth thresholding (#1017)

Author: ishii-norimi

README.md

@@ -136,7 +136,7 @@ for (let i = 0; i < n; i++) {
 | smoothing | (Linear weighted / Triangular / Cumulative) Moving average, Exponential average, Moving median, KZ filter, Savitzky Golay filter, Hampel filter, Kalman filter, Particle filter, Lowpass filter, Bessel filter, Butterworth filter, Chebyshev filter, Elliptic filter |
 | timeseries prediction | Holt winters, AR, ARMA, SDAR, VAR, Kalman filter, MLP, RNN |
 | change point detection | Cumulative sum, k-nearest neighbor, LOF, COF, SST, KLIEP, LSIF, uLSIF, LSDD, PELT, HMM, Markov switching |
-| segmentation | P-Tile, Automatic thresholding, Balanced histogram thresholding, Otsu's method, Sezan, Adaptive thresholding, Bernsen, Niblack, Sauvola, Phansalkar, Split and merge, Statistical Region Merging, Mean shift |
+| segmentation | P-Tile, Automatic thresholding, Balanced histogram thresholding, Otsu's method, Kittler Illingworth thresholding, Sezan, Adaptive thresholding, Bernsen, Niblack, Sauvola, Phansalkar, Split and merge, Statistical Region Merging, Mean shift |
 | denoising | NL-means, Hopfield network, RBM, GBRBM |
 | edge detection | Roberts cross, Sobel, Prewitt, Laplacian, LoG, Canny, Snakes |
 | word embedding | Word2Vec |

js/model_selector.js

@@ -548,6 +548,7 @@ const AIMethods = [
 				{ value: 'automatic_thresholding', title: 'Automatic Thresholding' },
 				{ value: 'balanced_histogram', title: 'Balanced histogram thresholding' },
 				{ value: 'otsu', title: 'Otsu' },
+				{ value: 'kittler_illingworth', title: 'Kittler-Illingworth' },
 				{ value: 'sezan', title: 'Sezan' },
 				{ value: 'adaptive_thresholding', title: 'Adaptive Thresholding' },
 				{ value: 'bernsen', title: 'Bernsen' },

js/view/kittler_illingworth.js

@@ -0,0 +1,26 @@
+import KittlerIllingworthThresholding from '../../lib/model/kittler_illingworth.js'
+import Controller from '../controller.js'
+import { specialCategory } from '../utils.js'
+
+export default function (platform) {
+	platform.setting.ml.usage = 'Click "Fit" button.'
+	platform.setting.ml.reference = {
+		author: 'J. Kittler, J. Illingworth',
+		title: 'Minimum error thresholding',
+		year: 1985,
+	}
+	platform.colorSpace = 'gray'
+	const controller = new Controller(platform)
+	const fitModel = () => {
+		const orgStep = platform._step
+		platform._step = 1
+		const model = new KittlerIllingworthThresholding()
+		const y = model.predict(platform.trainInput.flat(2))
+		threshold.value = model._t
+		platform.trainResult = y.map(v => specialCategory.density(1 - v))
+		platform._step = orgStep
+	}
+
+	controller.input.button('Fit').on('click', fitModel)
+	const threshold = controller.text({ label: ' Estimated threshold ' })
+}

lib/model/kittler_illingworth.js

@@ -0,0 +1,62 @@
+/**
+ * Minimum error thresholding / Kittler-Illingworth Thresholding
+ */
+export default class KittlerIllingworthThresholding {
+	// Minimum error thresholding
+	// https://jp.mathworks.com/matlabcentral/fileexchange/45685-kittler-illingworth-thresholding
+	// http://www.thothchildren.com/chapter/5bc4b10451d930518902af3b
+	constructor() {}
+
+	/**
+	 * Returns thresholded values.
+	 * @param {number[]} x Training data
+	 * @returns {(0 | 1)[]} Predicted values
+	 */
+	predict(x) {
+		this._cand = [...new Set(x)]
+		this._cand.sort((a, b) => a - b)
+		const n = this._cand.length
+
+		let best_j = Infinity
+		let best_t = 0
+		for (let t = 2; t < n - 1; t++) {
+			let p0 = 0
+			let p1 = 0
+			let m0 = 0
+			let m1 = 0
+			for (let i = 0; i < n; i++) {
+				if (x[i] < this._cand[t]) {
+					p0++
+					m0 += x[i]
+				} else {
+					p1++
+					m1 += x[i]
+				}
+			}
+			const r0 = p0 / n
+			const r1 = p1 / n
+			m0 /= p0
+			m1 /= p1
+
+			let s1 = 0
+			let s2 = 0
+			for (let i = 0; i < n; i++) {
+				if (x[i] < this._cand[t]) {
+					s1 += (x[i] - m0) ** 2
+				} else {
+					s2 += (x[i] - m1) ** 2
+				}
+			}
+			s1 /= p0
+			s2 /= p1
+
+			const j = r0 * Math.log(Math.sqrt(s1) / r0) + r1 * Math.log(Math.sqrt(s2) / r1)
+			if (j < best_j) {
+				best_j = j
+				best_t = t
+			}
+		}
+		this._t = this._cand[best_t]
+		return x.map(v => (v < this._t ? 0 : 1))
+	}
+}

tests/gui/view/kittler_illingworth.test.js

@@ -0,0 +1,71 @@
+import { getPage } from '../helper/browser'
+
+describe('segmentation', () => {
+	/** @type {Awaited<ReturnType<getPage>>} */
+	let page
+	beforeEach(async () => {
+		page = await getPage()
+
+		const dataURL = await page.evaluate(() => {
+			const canvas = document.createElement('canvas')
+			canvas.width = 100
+			canvas.height = 100
+			const context = canvas.getContext('2d')
+			const imdata = context.createImageData(canvas.width, canvas.height)
+			for (let i = 0, c = 0; i < canvas.height; i++) {
+				for (let j = 0; j < canvas.width; j++, c += 4) {
+					imdata.data[c] = Math.floor(Math.random() * 256)
+					imdata.data[c + 1] = Math.floor(Math.random() * 256)
+					imdata.data[c + 2] = Math.floor(Math.random() * 256)
+					imdata.data[c + 3] = Math.random()
+				}
+			}
+			context.putImageData(imdata, 0, 0)
+			return canvas.toDataURL()
+		})
+		const data = dataURL.replace(/^data:image\/\w+;base64,/, '')
+		const buf = Buffer.from(data, 'base64')
+
+		const dataSelectBox = page.locator('#ml_selector dl:first-child dd:nth-child(2) select')
+		await dataSelectBox.selectOption('upload')
+
+		const uploadFileInput = page.locator('#ml_selector #data_menu input[type=file]')
+		await uploadFileInput.setInputFiles({
+			name: 'image_kittler_illingworth.png',
+			mimeType: 'image/png',
+			buffer: buf,
+		})
+
+		const taskSelectBox = page.locator('#ml_selector dl:first-child dd:nth-child(5) select')
+		await taskSelectBox.selectOption('SG')
+		const modelSelectBox = page.locator('#ml_selector .model_selection #mlDisp')
+		await modelSelectBox.selectOption('kittler_illingworth')
+	})
+
+	afterEach(async () => {
+		await page?.close()
+	})
+
+	test('initialize', async () => {
+		const methodMenu = page.locator('#ml_selector #method_menu')
+		const buttons = methodMenu.locator('.buttons')
+
+		const threshold = buttons.locator('span:last-child')
+		await expect(threshold.textContent()).resolves.toBe('')
+	})
+
+	test('learn', async () => {
+		const methodMenu = page.locator('#ml_selector #method_menu')
+		const buttons = methodMenu.locator('.buttons')
+
+		await expect(page.locator('#image-area canvas').count()).resolves.toBe(1)
+		const threshold = buttons.locator('span:last-child')
+		await expect(threshold.textContent()).resolves.toBe('')
+
+		const fitButton = buttons.locator('input[value=Fit]')
+		await fitButton.dispatchEvent('click')
+
+		await expect(threshold.textContent()).resolves.toMatch(/^[0-9.]+$/)
+		await expect(page.locator('#image-area canvas').count()).resolves.toBe(2)
+	})
+})

tests/lib/model/kittler_illingworth.test.js

@@ -0,0 +1,20 @@
+import Matrix from '../../../lib/util/matrix.js'
+import KittlerIllingworthThresholding from '../../../lib/model/kittler_illingworth.js'
+
+import { randIndex } from '../../../lib/evaluate/clustering.js'
+
+test('clustering', () => {
+	const model = new KittlerIllingworthThresholding()
+	const n = 50
+	const x = Matrix.concat(Matrix.randn(n, 1, 0, 0.1), Matrix.randn(n, 1, 5, 0.1)).value
+
+	const y = model.predict(x)
+	expect(y).toHaveLength(x.length)
+
+	const t = []
+	for (let i = 0; i < x.length; i++) {
+		t[i] = Math.floor(i / n)
+	}
+	const ri = randIndex(y, t)
+	expect(ri).toBeGreaterThan(0.9)
+})