diff --git a/web/src/lib/core/background.test.ts b/web/src/lib/core/background.test.ts
new file mode 100644
index 0000000..2657a1e
--- /dev/null
+++ b/web/src/lib/core/background.test.ts
@@ -0,0 +1,108 @@
+import { describe, expect, it } from 'vitest';
+import {
+	backgroundMaskPreview,
+	backgroundRemovalMask,
+	removeBackground
+} from './background';
+import { makeImage } from './test-helpers';
+
+const GREEN = [0, 255, 0, 255];
+const RED = [255, 0, 0, 255];
+
+describe('backgroundRemovalMask', () => {
+	it('глобальный режим удаляет все совпадающие пиксели', () => {
+		const mask = backgroundRemovalMask(
+			makeImage(2, 1, [GREEN, RED]),
+			{ color: '#00ff00', tolerancePercent: 0, outerOnly: false, smoothPasses: 0 }
+		);
+		expect([...mask]).toEqual([1, 0]);
+	});
+
+describe('режим внешних областей', () => {
+	const ringRedCenterGreen = [
+		RED, RED, RED,
+		RED, GREEN, RED,
+		RED, RED, RED
+	];
+
+	it('заливка от краёв не достаёт до изолированного совпадающего острова', () => {
+		const mask = backgroundRemovalMask(
+			makeImage(3, 3, ringRedCenterGreen),
+			{ color: '#00ff00', tolerancePercent: 0, outerOnly: true, smoothPasses: 0 }
+		);
+		expect(mask[4]).toBe(0);
+	});
+
+	it('глобальный режим удаляет и изолированный остров', () => {
+		const mask = backgroundRemovalMask(
+			makeImage(3, 3, ringRedCenterGreen),
+			{ color: '#00ff00', tolerancePercent: 0, outerOnly: false, smoothPasses: 0 }
+		);
+		expect(mask[4]).toBe(1);
+		expect(mask[0]).toBe(0);
+	});
+});
+
+	it('допуск расширяет захват по цветовому расстоянию', () => {
+		const img = makeImage(2, 1, [
+			[10, 10, 10, 255],
+			[128, 128, 128, 255]
+		]);
+		const tight = backgroundRemovalMask(img, {
+			color: '#000000', tolerancePercent: 40, outerOnly: false, smoothPasses: 0
+		});
+		const wide = backgroundRemovalMask(img, {
+			color: '#000000', tolerancePercent: 60, outerOnly: false, smoothPasses: 0
+		});
+		expect(tight[1]).toBe(0);
+		expect(wide[1]).toBe(1);
+	});
+});
+
+describe('smoothMask-поведение через backgroundRemovalMask', () => {
+	const ringRedCenterGreen = [
+		RED, RED, RED,
+		RED, GREEN, RED,
+		RED, RED, RED
+	];
+	const opts = { color: '#00ff00', tolerancePercent: 0, outerOnly: false };
+
+	const alphaAtCenter = (img: { data: Uint8ClampedArray }) => img.data[19];
+
+	it('без сглаживания центр удалён', () => {
+		const img = removeBackground(makeImage(3, 3, ringRedCenterGreen), { ...opts, smoothPasses: 0 });
+		expect(alphaAtCenter(img)).toBe(0);
+	});
+
+	it('два прохода мажоритарного фильтра возвращают изолированный пиксель', () => {
+		const img = removeBackground(makeImage(3, 3, ringRedCenterGreen), { ...opts, smoothPasses: 2 });
+		expect(alphaAtCenter(img)).toBe(255);
+	});
+});
+
+describe('removeBackground', () => {
+	it('обнуляет альфу удалённых, сохраняет RGB остальных', () => {
+		const out = removeBackground(
+			makeImage(2, 1, [GREEN, [5, 6, 7, 200]]),
+			{ color: '#00ff00', tolerancePercent: 0, outerOnly: false, smoothPasses: 0 }
+		);
+		expect(out.data[3]).toBe(0);
+		expect([...out.data.slice(4, 8)]).toEqual([5, 6, 7, 200]);
+	});
+});
+
+describe('backgroundMaskPreview', () => {
+	it('белое там, где удаление, чёрное — где остаёмся, всё непрозрачно', () => {
+		const preview = backgroundMaskPreview(
+			makeImage(2, 1, [
+				GREEN,
+				[9, 9, 9, 60]
+			]),
+			{ color: '#00ff00', tolerancePercent: 0, outerOnly: false, smoothPasses: 0 }
+		);
+		expect([...preview.data]).toEqual([
+			255, 255, 255, 255,
+			0, 0, 0, 255
+		]);
+	});
+});
diff --git a/web/src/lib/core/background.ts b/web/src/lib/core/background.ts
new file mode 100644
index 0000000..464da35
--- /dev/null
+++ b/web/src/lib/core/background.ts
@@ -0,0 +1,131 @@
+import { parseHex } from './alpha';
+import { createPixelImage, type PixelImage } from './types';
+
+export type BackgroundOptions = {
+	color: string;
+	tolerancePercent: number;
+	outerOnly: boolean;
+	smoothPasses: number;
+};
+
+function buildRawMask(
+	img: PixelImage,
+	targetR: number,
+	targetG: number,
+	targetB: number,
+	tolerancePercent: number
+): Uint8Array {
+	const tolerance = (clamp(tolerancePercent, 0, 100) / 100) * Math.sqrt(3 * 255 * 255);
+	const thresholdSq = tolerance * tolerance;
+	const mask = new Uint8Array(img.width * img.height);
+	for (let i = 0; i < mask.length; i++) {
+		const dr = img.data[i * 4] - targetR;
+		const dg = img.data[i * 4 + 1] - targetG;
+		const db = img.data[i * 4 + 2] - targetB;
+		mask[i] = dr * dr + dg * dg + db * db <= thresholdSq ? 1 : 0;
+	}
+	return mask;
+}
+
+function floodFromBorders(mask: Uint8Array, w: number, h: number): void {
+	const queue: number[] = [];
+	const push = (index: number) => {
+		if (mask[index] === 1) {
+			mask[index] = 2;
+			queue.push(index);
+		}
+	};
+	for (let x = 0; x < w; x++) {
+		push(x);
+		push((h - 1) * w + x);
+	}
+	for (let y = 0; y < h; y++) {
+		push(y * w);
+		push(y * w + w - 1);
+	}
+	let head = 0;
+	while (head < queue.length) {
+		const index = queue[head++];
+		const x = index % w;
+		if (x > 0) push(index - 1);
+		if (x < w - 1) push(index + 1);
+		if (index >= w) push(index - w);
+		if (index < (h - 1) * w) push(index + w);
+	}
+	for (let i = 0; i < mask.length; i++) {
+		mask[i] = mask[i] === 2 ? 1 : 0;
+	}
+}
+
+export function smoothMask(
+	mask: Uint8Array,
+	w: number,
+	h: number,
+	passes: number
+): Uint8Array {
+	let current = mask;
+	const count = clamp(Math.trunc(passes), 0, 8);
+	for (let pass = 0; pass < count; pass++) {
+		const next = new Uint8Array(current.length);
+		for (let y = 0; y < h; y++) {
+			for (let x = 0; x < w; x++) {
+				let removed = 0;
+				let total = 0;
+				for (let dy = -1; dy <= 1; dy++) {
+					const sy = clamp(y + dy, 0, h - 1);
+					for (let dx = -1; dx <= 1; dx++) {
+						const sx = clamp(x + dx, 0, w - 1);
+						removed += current[sy * w + sx];
+						total++;
+					}
+				}
+				next[y * w + x] = removed * 2 >= total ? 1 : 0;
+			}
+		}
+		current = next;
+	}
+	return current;
+}
+
+export function backgroundRemovalMask(
+	img: PixelImage,
+	options: BackgroundOptions
+): Uint8Array {
+	const [tr, tg, tb] = parseHex(options.color);
+	const mask = buildRawMask(img, tr, tg, tb, options.tolerancePercent);
+	if (options.outerOnly) {
+		floodFromBorders(mask, img.width, img.height);
+	}
+	return smoothMask(mask, img.width, img.height, options.smoothPasses);
+}
+
+export function removeBackground(img: PixelImage, options: BackgroundOptions): PixelImage {
+	const mask = backgroundRemovalMask(img, options);
+	const out = createPixelImage(img.width, img.height);
+	for (let i = 0; i < mask.length; i++) {
+		const di = i * 4;
+		out.data[di] = img.data[di];
+		out.data[di + 1] = img.data[di + 1];
+		out.data[di + 2] = img.data[di + 2];
+		out.data[di + 3] = mask[i] === 1 ? 0 : img.data[di + 3];
+	}
+	return out;
+}
+
+export function backgroundMaskPreview(img: PixelImage, options: BackgroundOptions): PixelImage {
+	const mask = backgroundRemovalMask(img, options);
+	const out = createPixelImage(img.width, img.height);
+	for (let i = 0; i < mask.length; i++) {
+		const v = mask[i] === 1 ? 255 : 0;
+		const di = i * 4;
+		out.data[di] = v;
+		out.data[di + 1] = v;
+		out.data[di + 2] = v;
+		out.data[di + 3] = 255;
+	}
+	return out;
+}
+
+function clamp(value: number, min: number, max: number): number {
+	return Math.min(max, Math.max(min, value));
+}
diff --git a/web/src/lib/core/convolution.test.ts b/web/src/lib/core/convolution.test.ts
new file mode 100644
index 0000000..bf33d77
--- /dev/null
+++ b/web/src/lib/core/convolution.test.ts
@@ -0,0 +1,154 @@
+import { describe, expect, it } from 'vitest';
+import { convolve, gaussianBlur, sharpen } from './convolution';
+import { makeImage } from './test-helpers';
+
+const SHARPEN_KERNEL = [0, -1, 0, -1, 5, -1, 0, -1, 0];
+
+describe('convolve', () => {
+	it('крестовое ядро резкости на полоске из трёх пикселей', () => {
+		const out = convolve(
+			makeImage(3, 1, [
+				[0, 0, 0, 255],
+				[100, 100, 100, 255],
+				[0, 0, 0, 255]
+			]),
+			SHARPEN_KERNEL,
+			3
+		);
+		expect([...out.data.slice(4, 8)]).toEqual([255, 255, 255, 255]);
+		expect([...out.data.slice(0, 4)]).toEqual([0, 0, 0, 255]);
+		expect([...out.data.slice(8, 12)]).toEqual([0, 0, 0, 255]);
+	});
+
+	it.each([
+		[2, 3],
+		[3.5, 3],
+		[0, 3]
+	])('бросает ошибку на некорректном размере ядра %i', (size) => {
+		expect(() => convolve(makeImage(1, 1, [[0, 0, 0, 255]]), [1], size as number)).toThrow();
+	});
+});
+
+describe('sharpen', () => {
+	it('сила 0 возвращает копию', () => {
+		const img = makeImage(2, 2, [
+			[10, 20, 30, 255],
+			[40, 50, 60, 128],
+			[70, 80, 90, 255],
+			[100, 110, 120, 200]
+		]);
+		expect([...sharpen(img, 0).data]).toEqual([...img.data]);
+	});
+
+	it('сила 100 применяет чистое ядро резкости', () => {
+		const out = sharpen(
+			makeImage(3, 1, [
+				[0, 0, 0, 255],
+				[100, 100, 100, 255],
+				[0, 0, 0, 255]
+			]),
+			100
+		);
+		expect(out.data[4]).toBe(255);
+		expect(out.data[0]).toBe(0);
+	});
+});
+
+describe('gaussianBlur', () => {
+	it('постоянное изображение не меняется ни в RGB, ни в альфе', () => {
+		const img = makeImage(3, 3, new Array(9).fill([40, 80, 120, 128]));
+		const out = gaussianBlur(img, 16);
+		for (let i = 0; i < out.data.length; i++) {
+			expect(out.data[i]).toBe(img.data[i]);
+		}
+	});
+
+	it('далёкие углы остаются прозрачными, цвет центра не искажается', () => {
+		const size = 61;
+		const pixels: number[][] = [];
+		for (let y = 0; y < size; y++) {
+			for (let x = 0; x < size; x++) {
+				pixels.push(
+					x >= 26 && x <= 34 && y >= 26 && y <= 34 ? [200, 50, 25, 255] : [0, 0, 0, 0]
+				);
+			}
+		}
+		const out = gaussianBlur(makeImage(size, size, pixels), 8);
+		const corner = 0;
+		expect(out.data[corner]).toBe(0);
+		expect(out.data[corner + 1]).toBe(0);
+		expect(out.data[corner + 2]).toBe(0);
+		expect(out.data[corner + 3]).toBe(0);
+		const center = (30 * size + 30) * 4;
+		expect(out.data[center]).toBe(200);
+		expect(out.data[center + 1]).toBe(50);
+		expect(out.data[center + 2]).toBe(25);
+	});
+
+	it('симметричный вход даёт симметричный результат', () => {
+		const leftByRow = [
+			[
+				[255, 0, 0, 255],
+				[10, 20, 30, 255],
+				[64, 64, 64, 64],
+				[5, 5, 5, 200]
+			],
+			[
+				[10, 20, 30, 255],
+				[200, 100, 50, 255],
+				[1, 2, 3, 4],
+				[90, 90, 90, 250]
+			],
+			[
+				[64, 64, 64, 64],
+				[1, 2, 3, 4],
+				[128, 128, 128, 128],
+				[40, 40, 40, 240]
+			],
+			[
+				[200, 100, 50, 255],
+				[90, 90, 90, 250],
+				[40, 40, 40, 240],
+				[7, 7, 7, 255]
+			],
+			[
+				[10, 20, 30, 255],
+				[1, 2, 3, 4],
+				[64, 64, 64, 64],
+				[90, 90, 90, 250]
+			],
+			[
+				[64, 64, 64, 64],
+				[200, 100, 50, 255],
+				[5, 5, 5, 200],
+				[1, 2, 3, 4]
+			],
+			[
+				[5, 5, 5, 200],
+				[40, 40, 40, 240],
+				[90, 90, 90, 250],
+				[128, 128, 128, 128]
+			]
+		];
+		const pixels: number[][] = [];
+		for (let y = 0; y < 7; y++) {
+			for (let x = 0; x < 7; x++) {
+				pixels.push(leftByRow[y][Math.min(x, 6 - x)]);
+			}
+		}
+		const img = makeImage(7, 7, pixels);
+		const blurred = gaussianBlur(img, 3);
+		for (let y = 0; y < 7; y++) {
+			for (let x = 0; x < 3; x++) {
+				const li = (y * 7 + x) * 4;
+				const ri = (y * 7 + (6 - x)) * 4;
+				expect([...blurred.data.slice(li, li + 4)]).toEqual([
+					blurred.data[ri],
+					blurred.data[ri + 1],
+					blurred.data[ri + 2],
+					blurred.data[ri + 3]
+				]);
+			}
+		}
+	});
+});
diff --git a/web/src/lib/core/convolution.ts b/web/src/lib/core/convolution.ts
new file mode 100644
index 0000000..9fcc6ec
--- /dev/null
+++ b/web/src/lib/core/convolution.ts
@@ -0,0 +1,177 @@
+import { clonePixelImage, createPixelImage, type PixelImage } from './types';
+
+type Plane = Float64Array;
+
+export function convolve(
+	img: PixelImage,
+	kernel: readonly number[],
+	size: number
+): PixelImage {
+	if (!Number.isInteger(size) || size < 1 || size % 2 === 0) {
+		throw new Error('Размер ядра должен быть нечётным положительным числом');
+	}
+	if (kernel.length !== size * size) {
+		throw new Error('Длина ядра не совпадает с его размером');
+	}
+	const half = Math.floor(size / 2);
+	const out = createPixelImage(img.width, img.height);
+	for (let y = 0; y < out.height; y++) {
+		for (let x = 0; x < out.width; x++) {
+			for (let ch = 0; ch < 3; ch++) {
+				let acc = 0;
+				for (let ky = 0; ky < size; ky++) {
+					const sy = clampInt(y + ky - half, 0, img.height - 1);
+					for (let kx = 0; kx < size; kx++) {
+						const sx = clampInt(x + kx - half, 0, img.width - 1);
+						acc += img.data[(sy * img.width + sx) * 4 + ch] * kernel[ky * size + kx];
+					}
+				}
+				out.data[(y * out.width + x) * 4 + ch] = acc;
+			}
+			out.data[(y * out.width + x) * 4 + 3] = img.data[(y * img.width + x) * 4 + 3];
+		}
+	}
+	return out;
+}
+
+const SHARPEN_KERNEL = [0, -1, 0, -1, 5, -1, 0, -1, 0];
+
+export function sharpen(img: PixelImage, strengthPercent: number): PixelImage {
+	const strength = clamp(strengthPercent, 0, 100) / 100;
+	if (strength === 0) return clonePixelImage(img);
+	const sharp = convolve(img, SHARPEN_KERNEL, 3);
+	const out = createPixelImage(img.width, img.height);
+	for (let i = 0; i < out.data.length; i += 4) {
+		for (let ch = 0; ch < 3; ch++) {
+			out.data[i + ch] =
+				img.data[i + ch] * (1 - strength) + sharp.data[i + ch] * strength;
+		}
+		out.data[i + 3] = img.data[i + 3];
+	}
+	return out;
+}
+
+export function gaussianBlur(img: PixelImage, radiusPx: number): PixelImage {
+	const radius = clamp(radiusPx, 0, 512);
+	if (radius < 1) return clonePixelImage(img);
+	const sigma = Math.max(0.25, radius / 2);
+	const boxes = boxesForGauss(sigma, 3);
+
+	const w = img.width;
+	const h = img.height;
+	const pixels = w * h;
+
+	const red = new Float64Array(pixels);
+	const green = new Float64Array(pixels);
+	const blue = new Float64Array(pixels);
+	const alpha = new Float64Array(pixels);
+	for (let i = 0; i < pixels; i++) {
+		const a = img.data[i * 4 + 3] / 255;
+		red[i] = (img.data[i * 4] / 255) * a;
+		green[i] = (img.data[i * 4 + 1] / 255) * a;
+		blue[i] = (img.data[i * 4 + 2] / 255) * a;
+		alpha[i] = a;
+	}
+
+	const tmp = new Float64Array(pixels);
+	for (const box of boxes) {
+		const r = Math.max(0, (box - 1) / 2);
+		if (r < 1) continue;
+		blurPlanePass(red, tmp, w, h, r);
+		blurPlanePass(green, tmp, w, h, r);
+		blurPlanePass(blue, tmp, w, h, r);
+		blurPlanePass(alpha, tmp, w, h, r);
+	}
+
+	const out = createPixelImage(w, h);
+	for (let i = 0; i < pixels; i++) {
+		const a = alpha[i];
+		const di = i * 4;
+		if (a < 1 / 255) {
+			out.data[di] = 0;
+			out.data[di + 1] = 0;
+			out.data[di + 2] = 0;
+			out.data[di + 3] = 0;
+			continue;
+		}
+		out.data[di] = (red[i] / a) * 255;
+		out.data[di + 1] = (green[i] / a) * 255;
+		out.data[di + 2] = (blue[i] / a) * 255;
+		out.data[di + 3] = a * 255;
+	}
+	return out;
+}
+
+function blurPlanePass(plane: Plane, tmp: Plane, w: number, h: number, r: number): void {
+	blurPlaneHorizontal(plane, tmp, w, h, r);
+	blurPlaneVertical(tmp, plane, w, h, r);
+}
+
+function blurPlaneHorizontal(
+	src: Plane,
+	dst: Plane,
+	w: number,
+	h: number,
+	r: number
+): void {
+	const div = 2 * r + 1;
+	const inv = 1 / div;
+	for (let y = 0; y < h; y++) {
+		const row = y * w;
+		let sum = src[row] * (r + 1);
+		for (let k = 1; k <= r; k++) {
+			sum += src[row + clampInt(k, 0, w - 1)];
+		}
+		for (let x = 0; x < w; x++) {
+			dst[row + x] = sum * inv;
+			const addIndex = clampInt(x + r + 1, 0, w - 1);
+			const removeIndex = clampInt(x - r, 0, w - 1);
+			sum += src[row + addIndex] - src[row + removeIndex];
+		}
+	}
+}
+
+function blurPlaneVertical(
+	src: Plane,
+	dst: Plane,
+	w: number,
+	h: number,
+	r: number
+): void {
+	const div = 2 * r + 1;
+	const inv = 1 / div;
+	for (let x = 0; x < w; x++) {
+		let sum = src[x] * (r + 1);
+		for (let k = 1; k <= r; k++) {
+			sum += src[clampInt(k, 0, h - 1) * w + x];
+		}
+		for (let y = 0; y < h; y++) {
+			dst[y * w + x] = sum * inv;
+			const addIndex = clampInt(y + r + 1, 0, h - 1);
+			const removeIndex = clampInt(y - r, 0, h - 1);
+			sum += src[addIndex * w + x] - src[removeIndex * w + x];
+		}
+	}
+}
+
+function boxesForGauss(sigma: number, boxes: number): number[] {
+	const wIdeal = Math.sqrt((12 * sigma * sigma) / boxes + 1);
+	let wl = Math.floor(wIdeal);
+	if (wl % 2 === 0) wl--;
+	const wu = wl + 2;
+	const mIdeal = (12 * sigma * sigma - boxes * wl * wl - boxes * wl - boxes) / (4 * wl + 4);
+	const m = Math.round(mIdeal);
+	const sizes: number[] = [];
+	for (let i = 0; i < boxes; i++) {
+		sizes.push(i < m ? wl : wu);
+	}
+	return sizes;
+}
+
+function clamp(v: number, min: number, max: number): number {
+	return Math.min(max, Math.max(min, v));
+}
+
+function clampInt(value: number, min: number, max: number): number {
+	return Math.min(max, Math.max(min, Math.trunc(value)));
+}