2d:null 2e:["$","title",null,{"children":"Entropy Thresholding | Vinícius Mello | Observable"}] 33:T4cf,In general, such methods work like this: let ${tex`h(i)`} be the histogram of ${tex`I`}, that is, ${tex`h(i)`} counts the number of pixels with intensity ${tex`i`} in image ${tex`I`}. For a certain threshold ${tex`t`}, we can separate the image into two classes of pixels, class ${tex`A`} of pixels of intensity less than or equal to ${tex`t`}, and class ${tex`B`} of pixels of intensity greater than ${tex`t`}, so that we can build discrete probability distributions ${tex.block`p_A(t) : \left(\frac{h(1)}{\sum_{i=1}^t h(i)},\frac{h(2)}{\sum_{i=1}^t h(i)},\cdots,\frac{h(t)}{\sum_{i=1}^t h(i)}\right)`} and ${tex.block`p_B(t) : \left(\frac{h(t+1)}{\sum_{i=t+1}^n h(i)},\frac{h(t+2)}{\sum_{i=t+1}^n h(i)},\cdots,\frac{h(n)}{\sum_{i=t+1}^n h(i)}\right).`} Then we calculate the entropy ${tex`H_A(t)`} of the distribution ${tex`p_A(t)`} and the entropy ${tex`H_B(t)`} of the distribution ${tex`p_B(t)`} and try to find the value ${tex`t_{opt}`} for which the function ${tex.block`m(t) = op(H_A( t), H_B(t))`} gets the maximum value, where ${tex`op`} is an operator that somehow combines the entropies. The methods differ in the choice of entropy function for classes ${tex`A`} and ${tex`B`} and in the operator used to combine them. 34:T7ab,image = { let image; switch (histogramName) { case "cell": image = FileAttachment("cell1.png").image(); break; case "000280": image = FileAttachment("000280.jpg").image(); break; case "pcb": image = FileAttachment("pcb1.png").image(); break; case "135069": image = FileAttachment("135069.png").image(); break; case "67079": image = FileAttachment("67079.png").image(); break; case "00000309": image = FileAttachment("00000309.jpeg").image(); break; case "189080": image = FileAttachment("189080gray.png").image(); break; case "airplane": image = FileAttachment("airplane.png").image(); break; case "cameraman": image = FileAttachment("cameraman.png").image(); break; case "lena": image = FileAttachment("lena.png").image(); break; case "nuts": image = FileAttachment("nuts.png").image(); break; case "panzer": image = FileAttachment("panzer.png").image(); break; case "people": image = FileAttachment("people.png").image(); break; case "person": image = FileAttachment("person.png").image(); break; case "potatoes": image = FileAttachment("potatoes.png").image(); break; case "rice": image = FileAttachment("rice.png").image(); break; case "sailboat": image = FileAttachment("sailboat.png").image(); break; case "strip": image = FileAttachment("strip.png").image(); break; case "tanke": image = FileAttachment("tanke.png").image(); break; default: { let imageData = syntheticImage(); let canvas = DOM.canvas(256, 256); const context = canvas.getContext("2d"); canvas.style = "width: 100%"; context.putImageData(imageData, 0, 0); image = new Image(); image.src = canvas.toDataURL(); } } return image; }35:T444,viewof histogram = { let h = Array.from(getHistogram(imageData, 0)); let m = h.reduce((s, x) => Math.max(s, x), 0); h = h.map((x) => x / m); let pl = Plot.plot({ marginBottom: 64, width: 1024, height: 512, y: { grid: true, ticks: null }, style: { fontSize: 12 }, x: { ticks: [64, 128, 192] /* ticks: [ 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240 ]*/ }, marks: [ Plot.frame({ strokeWidth: 0.5 }), Plot.areaY(/*new Array(220).fill(0).concat(h.slice(220))*/ h, { x: (d, i) => i, y: (d) => d * m, fill: "black", opacity: 0.25 }), Plot.line(/*new Array(220).fill(0).concat(h.slice(220))*/ h, { x: (d, i) => i, y: (d) => d * m, strokeWidth: 1 }) //Plot.ruleY([0], { strokeWidth: 0.5 }), //Plot.ruleX([0], { strokeWidth: 0.5 }) ] }); pl.value = h; return pl; }36:T415,function syntheticImage() { //let mmu1 = (mu1 - 128) / 128; //let mmu2 = (mu2 - 128) / 128; //let ssigma1 = sigma1 / 128; //let ssigma2 = sigma2 / 128; const n = 256; //let arr = new Uint8ClampedArray(n * n * 4); let h = Array(n) .fill() .map((_, i) => i); // .fill() // .map((_, i) => -1 + (2 * i + 1) / n); if (histogramName == "Normal+Normal") { const f = (x) => Normal(mu1, sigma1, x) + Normal(mu2, sigma2, x); h = h.map(f); } else if (histogramName == "Normal+Cauchy") { const f = (x) => Normal(mu1, sigma1, x) + Cauchy(mu2, sigma2, x); h = h.map(f); } else if (histogramName == "Cauchy+Cauchy") { const f = (x) => Cauchy(mu1, sigma1, x) + Cauchy(mu2, sigma2, x); h = h.map(f); } h = cdf(h); h = h.map((x) => Math.ceil(n * n * x)); let l = 0; for (let i = 0; i < n; i++) { for (let j = l; j < h[i]; ++j) { arr[4 * j] = i; arr[4 * j + 1] = i; arr[4 * j + 2] = i; arr[4 * j + 3] = 255; } l = h[i]; } return new ImageData(arr, n, n); }37:T438,draw = { const texture = regl.texture({ width: imageData.width, height: imageData.height, data: imageData.data, min: "nearest", mag: "nearest", wrap: "clamp" }); const draw = regl({ frag: ` precision mediump float; uniform sampler2D texture; uniform sampler2D lut; varying vec2 uv; void main () { vec4 p = texture2D(texture, uv); p.x = texture2D(lut, vec2(p.x, 0.5)).x; p.y = texture2D(lut, vec2(p.y, 0.5)).y; p.z = texture2D(lut, vec2(p.z, 0.5)).z; gl_FragColor = p; }`, vert: ` precision mediump float; attribute vec2 position; varying vec2 uv; void main () { uv = position; gl_Position = vec4( 2.0 * position - 1.0, 0.0, 1.0); gl_Position.y = -gl_Position.y; }`, attributes: { position: [ [0, 0], [1, 0], [1, 1], [1, 1], [0, 1], [0, 0] ] }, uniforms: { texture: texture, lut: regl.prop("lut") }, primitive: "triangles", count: 6 }); return draw; }38:[{"id":"b831e23bec7bf695a3a9c233a75c15435b5e6597c3c28be9e20baa541f5c6b41fb458d98fe04ae4e30d54a9e28cb4cd2d098f5f0d219210c39b730906906655a","href":"https://static.observableusercontent.com/files/b831e23bec7bf695a3a9c233a75c15435b5e6597c3c28be9e20baa541f5c6b41fb458d98fe04ae4e30d54a9e28cb4cd2d098f5f0d219210c39b730906906655a","name":"000280.jpg","type":"image/jpeg","lastModified":1658850869207.014,"size":25462},{"id":"2c5624b33d2bb9ee61e4ae661fedb59eb044d61d69aa259091b1fe5c67d296e4b6a41029ab1b44bf7f032e746eeb35f1947f29c5dafc52b69abd32fc18a245ce","href":"https://static.observableusercontent.com/files/2c5624b33d2bb9ee61e4ae661fedb59eb044d61d69aa259091b1fe5c67d296e4b6a41029ab1b44bf7f032e746eeb35f1947f29c5dafc52b69abd32fc18a245ce","name":"135069.jpeg","type":"image/jpeg","lastModified":1658850869207.014,"size":5717},{"id":"a82e0cc736fec2202f0fccb09696b8b9b0d158aca1d34830ddd722afe8f2511b7d1e3c629f7f982c0cc09b5df94d76b791ff704f321d0a747814b7869c5b2c39","href":"https://static.observableusercontent.com/files/a82e0cc736fec2202f0fccb09696b8b9b0d158aca1d34830ddd722afe8f2511b7d1e3c629f7f982c0cc09b5df94d76b791ff704f321d0a747814b7869c5b2c39","name":"67079.jpeg","type":"image/jpeg","lastModified":1658850869207.014,"size":28300},{"id":"09654eb582d34356986a7a6dd46a33b1fe901deb405df70a90b32cf7e509dbe76b5b717b04be7da581bcb9bba656ad8c061aecff347db1b68fe74a2d74133d81","href":"https://static.observableusercontent.com/files/09654eb582d34356986a7a6dd46a33b1fe901deb405df70a90b32cf7e509dbe76b5b717b04be7da581bcb9bba656ad8c061aecff347db1b68fe74a2d74133d81","name":"cell1.png","type":"image/png","lastModified":1658850869207.014,"size":21446},{"id":"03542a1076b2680946ab7ebd0b6e9304906dabc73e43006bac21c81a8f0606ab11e1e8c55272dccd5d07ddea1485495dd438def575ed6a6ee046b0c4c32aabff","href":"https://static.observableusercontent.com/files/03542a1076b2680946ab7ebd0b6e9304906dabc73e43006bac21c81a8f0606ab11e1e8c55272dccd5d07ddea1485495dd438def575ed6a6ee046b0c4c32aabff","name":"pcb1.png","type":"image/png","lastModified":1658850869207.014,"size":36244},{"id":"5fe1dbc2e02958dcd510ec1d43d97d3153851d80a4707fce3d2bf50a3cd3e0fee23cbfd89d13fa165604726ad5ed0088eb938325e714d0e4af7db7ae36ea8b16","href":"https://static.observableusercontent.com/files/5fe1dbc2e02958dcd510ec1d43d97d3153851d80a4707fce3d2bf50a3cd3e0fee23cbfd89d13fa165604726ad5ed0088eb938325e714d0e4af7db7ae36ea8b16","name":"rice.png","type":"image/png","lastModified":1658926218512.756,"size":44542},{"id":"d04a582225ec7710f7fa3e95f0b20b2e348ff4f2a754950801215e1cfd4c1d1a66cb28721a06b131676a8e13db24b73bd8e53ca9fb8b7f0b8e90554dc171b102","href":"https://static.observableusercontent.com/files/d04a582225ec7710f7fa3e95f0b20b2e348ff4f2a754950801215e1cfd4c1d1a66cb28721a06b131676a8e13db24b73bd8e53ca9fb8b7f0b8e90554dc171b102","name":"cameraman.png","type":"image/png","lastModified":1658926218495.849,"size":38256},{"id":"999416ddc597845411fa0279c4ae543b8b8853d6eaa9b0feed6129e125141a16ef3a5002a48ff89c4a81aed007eedff1ed26c42312518c21c15e1b867af6146e","href":"https://static.observableusercontent.com/files/999416ddc597845411fa0279c4ae543b8b8853d6eaa9b0feed6129e125141a16ef3a5002a48ff89c4a81aed007eedff1ed26c42312518c21c15e1b867af6146e","name":"tanke.png","type":"image/png","lastModified":1658926218383.543,"size":25230},{"id":"8833e10bf8e395db6b9b182dca3582556f9c6bcb614bcdb692da2d7ea11b03e89119dd21c1b8d84b4a2e5349b63520d39bd0d84965b59d88c994c99070913499","href":"https://static.observableusercontent.com/files/8833e10bf8e395db6b9b182dca3582556f9c6bcb614bcdb692da2d7ea11b03e89119dd21c1b8d84b4a2e5349b63520d39bd0d84965b59d88c994c99070913499","name":"nuts.png","type":"image/png","lastModified":1658926218313.009,"size":22309},{"id":"b3126aa779ccfc5d0e66f06bc60ddfb4de2ef319eb5fab6292c7fbf4885f63dd92658f4464ec38d949a8429117418f3f937617ea94080aed5a4689b5ca50f1e5","href":"https://static.observableusercontent.com/files/b3126aa779ccfc5d0e66f06bc60ddfb4de2ef319eb5fab6292c7fbf4885f63dd92658f4464ec38d949a8429117418f3f937617ea94080aed5a4689b5ca50f1e5","name":"strip.png","type":"image/png","lastModified":1658926218304.54,"size":16356},{"id":"80c5a1029d18aa0b48ef2eeba7c8c029e9249ec15d7ad46a1c4db8058aec424836f17b931971776bf3e493618dcc1885467ad586e5d744d60c386d173ef0362f","href":"https://static.observableusercontent.com/files/80c5a1029d18aa0b48ef2eeba7c8c029e9249ec15d7ad46a1c4db8058aec424836f17b931971776bf3e493618dcc1885467ad586e5d744d60c386d173ef0362f","name":"sailboat.png","type":"image/png","lastModified":1658926218313.922,"size":25980},{"id":"6b89792f96ff368de3af571f3d9cd8a294a765538d0351f8a2c69aeb03175c3ac729aadb4e0d367aada7da21d40e7ce31df514088cba788b73bd9a09b57692e4","href":"https://static.observableusercontent.com/files/6b89792f96ff368de3af571f3d9cd8a294a765538d0351f8a2c69aeb03175c3ac729aadb4e0d367aada7da21d40e7ce31df514088cba788b73bd9a09b57692e4","name":"00000309.jpeg","type":"image/jpeg","lastModified":1658926218236.693,"size":12216},{"id":"f991499d40c6e8cfd440a81edaf9fcc7ab173b01097dc7fddd3c93c8debce6dd115c96b6f267280019be7353d7306665431d5442348eb46e40486854fccd88db","href":"https://static.observableusercontent.com/files/f991499d40c6e8cfd440a81edaf9fcc7ab173b01097dc7fddd3c93c8debce6dd115c96b6f267280019be7353d7306665431d5442348eb46e40486854fccd88db","name":"135069.png","type":"image/png","lastModified":1658926218391.073,"size":18807},{"id":"a90ccd9b339ee7a15d8d30a55011aa6b770d85114ee8b2038d0ff6ad9a6487a59d030be8ecc6c0df768e415e6263a3c6181c44f2b34a53d390329df2b90f73b9","href":"https://static.observableusercontent.com/files/a90ccd9b339ee7a15d8d30a55011aa6b770d85114ee8b2038d0ff6ad9a6487a59d030be8ecc6c0df768e415e6263a3c6181c44f2b34a53d390329df2b90f73b9","name":"189080gray.png","type":"image/png","lastModified":1658926218555.395,"size":73755},{"id":"825913fe18419db72d437b08ebc37f555ce37aafb779688625e9b158792cf8822653d4b35269e741f6a735b1f41dbf9a92d06e4a41cd9807b81674bb20797248","href":"https://static.observableusercontent.com/files/825913fe18419db72d437b08ebc37f555ce37aafb779688625e9b158792cf8822653d4b35269e741f6a735b1f41dbf9a92d06e4a41cd9807b81674bb20797248","name":"potatoes.png","type":"image/png","lastModified":1658926218444.9,"size":33367},{"id":"4a37aa3344f9399c24bc27bf29dab9173f721eb7232be2f659983239ba8770d28d5bdf6b13127eb04fd2a4df37066ac9d8ed78c910d7b0777db370bdafaeeeae","href":"https://static.observableusercontent.com/files/4a37aa3344f9399c24bc27bf29dab9173f721eb7232be2f659983239ba8770d28d5bdf6b13127eb04fd2a4df37066ac9d8ed78c910d7b0777db370bdafaeeeae","name":"person.png","type":"image/png","lastModified":1658926218402.128,"size":28578},{"id":"0abbb922a92288d004767b8c2dd8907afdf740abd71312db760cda11e0c14e0c6a88b03495fa602c52e8851866ba9b9f08e58d925b7c9de5585a593a30f36dc6","href":"https://static.observableusercontent.com/files/0abbb922a92288d004767b8c2dd8907afdf740abd71312db760cda11e0c14e0c6a88b03495fa602c52e8851866ba9b9f08e58d925b7c9de5585a593a30f36dc6","name":"lena.png","type":"image/png","lastModified":1658926218488.898,"size":38555},{"id":"315d08bf7dafc56e00aeab781fa3be60e3f10baa5de1656cc46e548923a1254cf26b83d245eb6b30ed08e568104297430b7527e0edd864f6aa4c43d409965f5f","href":"https://static.observableusercontent.com/files/315d08bf7dafc56e00aeab781fa3be60e3f10baa5de1656cc46e548923a1254cf26b83d245eb6b30ed08e568104297430b7527e0edd864f6aa4c43d409965f5f","name":"people.png","type":"image/png","lastModified":1658926218445.77,"size":38092},{"id":"f4a24d8b60bd751fd8dbe642907766ab2f939637bf115a1fc6894ec1fbc014605005dff1cbaaf4af788e1d7aefb41441f16ebd7fcdc3be4d771d5bded4f46ac1","href":"https://static.observableusercontent.com/files/f4a24d8b60bd751fd8dbe642907766ab2f939637bf115a1fc6894ec1fbc014605005dff1cbaaf4af788e1d7aefb41441f16ebd7fcdc3be4d771d5bded4f46ac1","name":"panzer.png","type":"image/png","lastModified":1658926218402.598,"size":29805},{"id":"06fd367ef8bdf4394522c30067de2130aa09c7bbcea3cea07a7c4a39966e2fdfa83ad68d7b00fe56167d88d29c63efe8cd4b74bcf6c564d14250be0efb8e5efd","href":"https://static.observableusercontent.com/files/06fd367ef8bdf4394522c30067de2130aa09c7bbcea3cea07a7c4a39966e2fdfa83ad68d7b00fe56167d88d29c63efe8cd4b74bcf6c564d14250be0efb8e5efd","name":"67079.png","type":"image/png","lastModified":1658926218640.633,"size":98452},{"id":"8d158634e160f7297018cd123681361d11bf5cbaebe2dc3ab6e615398610d933ddd30a7d2c4bce1b2c64cc788e67e2068ae5064c061bf0de6d1479a8d324ce1a","href":"https://static.observableusercontent.com/files/8d158634e160f7297018cd123681361d11bf5cbaebe2dc3ab6e615398610d933ddd30a7d2c4bce1b2c64cc788e67e2068ae5064c061bf0de6d1479a8d324ce1a","name":"airplane.png","type":"image/png","lastModified":1658926218462.039,"size":39138}] 31:{"id":"cba2b7bd42f64277","slug":"entropy-thresholding","title":"Entropy Thresholding","thumbnail":"688a954ceac6f6e4ebfa5ebe1c3c7f4adc6fa5185b7446c837ba7496d15705ea","access_level":"public","create_time":"$D2022-07-26T15:54:29.207Z","update_time":"$D2023-02-08T17:32:43.325Z","view_time":null,"first_public_time":"$D2022-08-03T19:12:49.729Z","has_unpublished_edits":null,"fork":true,"stars":2,"starred":false,"owner":{"type":"team","id":"7a4ecd430a93cd6f","login":"vinicius-mello","name":"Vinícius Mello","avatar_url":"https://avatars-next.observableusercontent.com/b5d4671aa488d8bcb984f575f985332403cde5f63942ea883a6a1a630941ec05","tier":"starter_2024"},"version":795,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"ecc4854ab7ad95b6","login":"vinicius-mello","name":"Vinícius Mello","avatar_url":"https://avatars-next.observableusercontent.com/b5d4671aa488d8bcb984f575f985332403cde5f63942ea883a6a1a630941ec05","tier":null}],"members":[{"type":"individual","id":"ecc4854ab7ad95b6","login":"vinicius-mello","name":"Vinícius Mello","avatar_url":"https://avatars-next.observableusercontent.com/b5d4671aa488d8bcb984f575f985332403cde5f63942ea883a6a1a630941ec05","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Entropy Thresholding","cells":[{"id":0,"value":"# Entropy Thresholding","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":663,"value":"One of the simplest methods of obtaining a binarized image from a grayscale image ${tex`I`} is to change the value ${tex`I_{ij}`} of each pixel to black, if ${tex`I_{ij}`} is less than or equal to a certain threshold ${tex`t`}, and by white otherwise. There is a class of methods that calculate the optimal threshold ${tex`t_{opt}`} automatically and that are based on the calculation of entropies of probability distributions associated with the histogram of ${tex`I`}. This notebook allows us to explore several of the entropy-based thresholding methods interactively.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":677,"value":"$33","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":741,"value":"The entropies that we will deal with in this notebook are described in the table below.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":714,"value":"Entropy | Formula \n----------|---------\nShannon | ${tex.block`H(p)=\\sum_{i=1}^n p_i \\ln p_i`}\nTsallis | ${tex.block`H_q(p)=\\frac{1-\\sum_{i=1}^n p_i^q}{q-1}`}\nMasi | ${tex.block`H_r(p)=\\frac{1}{1-r}\\ln\\left(1-(1-r)\\sum_{i=1}^n p_i \\ln p_i\\right)`}\nHill | ${tex.block`H_\\alpha(p)=\\left(\\sum_{i=1}^n p_i^q\\right)^{\\frac{1}{1-\\alpha}}`}\nSine | ${tex.block`H(p)=\\sum_{i=1}^n \\sin \\pi p_i`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":754,"value":"Entropies can be combined according to the following operators:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":743,"value":"Operator | Definition\n----------- | -------------------------------\nsum | ${tex`\\text{sum}(A,B)=A+B`}\npseudo_sum | ${tex`\\text{pseudo\\_sum}_q(A,B)=A+B+(1-q)AB`}\nmin | ${tex.block`\\text{min}(A,B)= \\left\\{\\begin{array}{rl} A, & \\text{if }A\\leq B \\\\\\ B,&\\text{if }Bq | q \nNie et al. | Masi | Masi | sum | r\nLin & Ou | Shannon | Tsallis | min | q\nLin & Ou (Sym.) | Tsallis | Shannon | min | q\nFerreira Jr. et al. | Masi | Tsallis | min | r, q \nFerreira Jr. et al. (Sym) | Tsallis | Masi | min | r, q\nElaraby & Moratal | Hill | Hill | pseudo_sum_α | α\nManda & Hyu | Sine | Sine | sum | -\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":57,"value":"Plot.plot({\n width: 1024,\n y: {\n grid: true\n },\n x: { ticks: [0, 128, 255] },\n marks: [\n Plot.lineY(output.o, { stroke: \"black\", strokeWidth: 4 }),\n Plot.lineY(output.a, { stroke: \"red\", strokeWidth: 2 }),\n Plot.lineY(output.b, { stroke: \"blue\", strokeWidth: 2 }),\n Plot.barY(histogram.slice(topt), {\n x: (d, i) => i + topt,\n y: (d) => maxOutput * d,\n fill: \"blue\",\n opacity: 0.5\n }),\n Plot.barY(histogram.slice(0, topt), {\n x: (d, i) => i,\n y: (d) => maxOutput * d,\n fill: \"red\",\n opacity: 0.5\n }),\n Plot.text([[topt, 0]], {\n text: (d) => `t_opt=${d[0]}`,\n dy: 10,\n fontSize: 14\n })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":416,"value":"viewof entropyA = Inputs.select(\n [\"Shannon\", \"Tsallis\", \"Masi\", \"Hill\", \"Sine\"],\n {\n value: \"Shannon\",\n label: \"Entropy A\"\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":418,"value":"viewof entropyB = Inputs.select(\n [\"Shannon\", \"Tsallis\", \"Masi\", \"Hill\", \"Sine\"],\n {\n value: \"Shannon\",\n label: \"Entropy B\"\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":422,"value":"viewof operator = Inputs.select([\"sum\", \"pseudo_sum\", \"min\"], {\n value: \"sum\",\n label: \"Operator\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":126,"value":"viewof histogramName = Inputs.select(\n [\n \"Normal+Normal\",\n \"Normal+Cauchy\",\n \"Cauchy+Cauchy\",\n \"cell\",\n \"pcb\",\n \"000280\",\n \"135069\",\n \"67079\",\n \"00000309\",\n \"189080\",\n \"airplane\",\n \"cameraman\",\n \"lena\",\n \"nuts\",\n \"panzer\",\n \"people\",\n \"person\",\n \"potatoes\",\n \"rice\",\n \"sailboat\",\n \"strip\",\n \"tanke\"\n ],\n {\n value: \"Two Gaussians\",\n label: \"Image\"\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":468,"value":"#### Entropy Parameters","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":75,"value":"viewof q = Inputs.range([-2, 2], { label: \"q (or α)\", value: 0.5 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":78,"value":"viewof r = Inputs.range([0, 2], { label: \"r\", value: 0.5 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":277,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":228,"value":"topt = {\n const o = output.o;\n const n = o.length;\n let topt = 0;\n for (let t = 0; t < n; ++t) if (o[t] > o[topt]) topt = t;\n return topt;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":363,"value":"viewof regl = {\n const div = html`

`;\n const output = DOM.canvas(imageData.width, imageData.height);\n /*output.style = \"width: 50%\";\n const input = DOM.canvas(imageData.width, imageData.height);\n const context = input.getContext(\"2d\");\n context.drawImage(image, 0, 0, imageData.width, imageData.height);\n input.style = \"width: 50%\";\n div.appendChild(input);*/\n div.appendChild(output);\n div.value = reglWrap(output);\n return div;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":472,"value":"### Synthetic Image Parameters","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":28,"value":"viewof mu1 = Inputs.range([0, 255], { label: \"μ1\", value: 64, step: 1 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":31,"value":"viewof mu2 = Inputs.range([0, 255], { label: \"μ2\", value: 192, step: 1 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"viewof sigma1 = Inputs.range([0, 64], { label: \"σ1\", value: 10, step: 1 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"viewof sigma2 = Inputs.range([0, 64], { label: \"σ2\", value: 10, step: 1 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":49,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":85,"value":"output = {\n const n = histogram.length;\n const a = Array(n).fill(0);\n const b = Array(n).fill(0);\n const o = Array(n).fill(0);\n const operators = {\n min: (x, y) => Math.min(x, y),\n sum: (x, y) => x + y,\n pseudo_sum: (x, y) => x + y + (1 - q) * x * y\n };\n const op = operators[operator];\n const entropies = {\n Shannon: (A) => Shannon(A),\n Tsallis: (A) => Tsallis(A, q),\n Masi: (A) => Masi(A, r),\n Hill: (A) => Hill(A, q),\n Sine: (A) => Sine(A)\n };\n const eA = entropies[entropyA];\n const eB = entropies[entropyB];\n for (let t = 1; t < n - 1; ++t) {\n const A = histogram.slice(0, t);\n const B = histogram.slice(t);\n a[t] = eA(A);\n b[t] = eB(B);\n o[t] = op(a[t], b[t]);\n }\n return { a, b, o };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":190,"value":"maxOutput = {\n const om = output.o.reduce((s, x) => Math.max(s, x), 0);\n const am = output.a.reduce((s, x) => Math.max(s, x), 0);\n const bm = output.b.reduce((s, x) => Math.max(s, x), 0);\n return Math.max(om, am, bm);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":284,"value":"imageData = {\n const canvas = DOM.canvas(image.naturalWidth, image.naturalHeight);\n const context = canvas.getContext(\"2d\");\n canvas.style = \"width: 100%\";\n context.drawImage(image, 0, 0, image.naturalWidth, image.naturalHeight);\n const imageData = context.getImageData(\n 0,\n 0,\n image.naturalWidth,\n image.naturalHeight\n );\n return imageData;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":312,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":288,"value":"function getPixel(im, i, j, c) {\n if (i < 0 || i >= im.width || j < 0 || j >= im.height) return 0;\n return im.data[4 * im.width * j + 4 * i + c];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":308,"value":"function setPixel(im, i, j, c, v) {\n if (i < 0 || i >= im.width || j < 0 || j >= im.height)\n im.data[4 * im.width * j + 4 * i + c] = v;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":286,"value":"function getHistogram(im, c) {\n let hist = new Uint32Array(256);\n for (let i = 0; i < im.width; ++i) {\n for (let j = 0; j < im.height; ++j) {\n let v = getPixel(im, i, j, c);\n hist[v]++;\n }\n }\n return hist;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"function pdf(counts) {\n let sum = counts.reduce((s, a) => s + a, 0);\n sum = sum == 0 ? 1 : sum;\n return counts.map((a) => a / sum);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":338,"value":"function cdf(counts) {\n let sum = 0;\n let a = counts.map((x) => (sum += x));\n sum = sum == 0 ? 1 : sum;\n return a.map((x) => x / sum);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"function Shannon(counts) {\n let p = pdf(counts);\n return -p.reduce((s, x) => s + (x == 0 ? 0 : x * Math.log(x)), 0);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"function Tsallis(counts, q) {\n let p = pdf(counts);\n let s = p.reduce((s, x) => s + x ** q, 0);\n return s == 0 ? 0 : (1 - s) / (q - 1);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"function Masi(counts, r) {\n let h = Shannon(counts);\n return 1 + (1 - r) * h > 0 ? Math.log(1 + (1 - r) * h) / (1 - r) : 0;\n // : Math.log(-1 - (1 - r) * h) / (1 - r);\n //return Log(1 + (1 - r) * h) / (1 - r);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":550,"value":"function Hill(counts, q) {\n let p = pdf(counts);\n let s = p.reduce((s, x) => s + x ** q, 0);\n return s ** (1 / (1 - q));\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":559,"value":"function Sine(counts, q) {\n const sin = Math.sin;\n const PI = Math.PI;\n let p = pdf(counts);\n let s = p.reduce((s, x) => s + sin(PI * x), 0);\n return s;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"function Normal(mu, sigma, x) {\n return (\n (1 / (sigma * Math.sqrt(2 * Math.PI))) *\n Math.exp(-0.5 * ((x - mu) / sigma) ** 2)\n );\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":157,"value":"function Cauchy(x0, gamma, x) {\n return gamma / Math.PI / ((x - x0) ** 2 + gamma ** 2);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":348,"value":"arr = {\n const n = 256;\n return new Uint8ClampedArray(n * n * 4);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":365,"value":"reglWrap = require(\"regl\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":367,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":371,"value":"{\n const at = (i, c, v) => {\n lut[4 * i + c] = v;\n };\n for (let i = 0; i < 256; ++i) {\n for (let c = 0; c < 3; ++c) {\n if (i > topt) at(i, c, 255);\n else at(i, c, 0);\n }\n }\n const lutTex = regl.texture({\n width: 256,\n height: 1,\n data: lut,\n min: \"nearest\",\n mag: \"nearest\",\n wrap: \"clamp\"\n });\n draw({ lut: lutTex });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":369,"value":"lut = new Uint8ClampedArray(4 * 256)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W38","stdlib":"1","titling":"auto"}} 32:"$31:body"