2d:null 2e:["$","title",null,{"children":"The CAHVORE camera model | Andreas Plesch | Observable"}] 33:T408,CAHVOREtable = { const descriptions = { C : 'Center of camera in local coordinate system', A : 'camera Axis, normal to image plane', H : 'Horizontal information vector', V : 'Vertical information vector', O : 'Optical axis, similar to A', R : 'lens distortion coefficients (ρ)', E : 'fisheye correction coefficients', T : 'CAHVORE model type: 1, 2 or 3', P : 'L, CAHVORE parameter: linearity, 0 for CAHVORE-2' }; const comps = s.map( p => p.split(",").map( n => +n )); const map = new Map([ [ 'C', comps[0]], [ 'A', comps[1]], [ 'H', comps[2]], [ 'V', comps[3]], [ 'O', comps[4]], [ 'R', comps[5]], [ 'E', comps[6]], [ 'T', [comps[7], null, null]], [ 'P', [comps[8], null, null]] ]); const table = []; map.forEach ( (v, k) => { table.push( { parameter: k, description: descriptions[k], p1:v[0], p2:v[1], p3:v[2] } ) } ); return table } 34:[] 31:{"id":"9e06fe276621dd88","slug":"the-cahvore-camera-model","title":"The CAHVORE camera model","thumbnail":"d08f84088defbc4c6213eea8ec5b1ec94b0ca461091eb9a35f27310aed35d780","access_level":"public","create_time":"$D2021-05-31T21:43:41.663Z","update_time":"$D2021-06-02T05:21:18.313Z","view_time":null,"first_public_time":"$D2021-06-01T02:52:15.378Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"3a7167e5e638bcd0","login":"andreasplesch","name":"Andreas Plesch","avatar_url":"https://avatars-next.observableusercontent.com/4da1ba746a4b25e755d1c9b71ca1c72165a9c40e02aee1f3fcae880584d70c9c","tier":"starter_2024"},"version":392,"publish_version":392,"role":null,"authored":false,"authors":[{"type":"individual","id":"171053d51d09c7fc","login":"andreasplesch","name":"Andreas Plesch","avatar_url":"https://avatars-next.observableusercontent.com/4da1ba746a4b25e755d1c9b71ca1c72165a9c40e02aee1f3fcae880584d70c9c","tier":null}],"members":[{"type":"individual","id":"171053d51d09c7fc","login":"andreasplesch","name":"Andreas Plesch","avatar_url":"https://avatars-next.observableusercontent.com/4da1ba746a4b25e755d1c9b71ca1c72165a9c40e02aee1f3fcae880584d70c9c","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"The CAHVORE camera model","cells":[{"id":0,"value":"md`# The CAHVORE camera model\nNASA Mars2020 and other exploration projects use the CAHVORE camera model (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2003JE002199). Each letter stands for a 3-tuple parameters, most geometric vectors, which are derived from an experimental calibration process. This notebook analyses such sets of parameters. For example, the camera_model_component_list key in json metadata of NASA raw images can contain such a set.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":154,"value":"viewof component_list = Inputs.textarea({label:\"model component list\", rows: 6, value:\"(-0.000385336,0.0896009,0.117889);(0.0119194,0.72545,0.688172);(-1755.77,1629.89,1400.25);(-87.3827,-116.053,2334.34);(-0.000662614,0.723521,0.690302);(0.000144295,0.468504,-0.0528464);(-0.00068363,-0.00098111,-0.00156945);2.0;0.0\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":163,"value":"viewof pixel_size_string = Inputs.text({label:\"pixel size [mm]\", datalist: [0.00112, 0.003], value:\"0.00112\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":168,"value":"viewof image_width = Inputs.text({label:\"image width [pixels]\", type: \"number\", datalist:[640,4208], value:4208})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":180,"value":"viewof image_height = Inputs.text({label:\"image height [pixels]\", type: \"number\", datalist:[480,3120], value:3120})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"md`## Parsing the metadata\nHere is the entered json entry: \n\n\\`\\`${component_list}\\`\\`\n\nAnd here the tabulated CAHVORE parameters:\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":257,"value":"viewof tab = Inputs.table(CAHVOREtable, {\n rows: 20,\n format: { \n description: d => html`${d}`,\n p1: v => html`${v}`,\n p2: v => html`${v}`,\n p3: v => html`${v}`\n },\n width: {\n description: '25em'\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":387,"value":"md`\nCAHVORE model types (T):\n 1. Perspective-projection\n 2. Fish-eye\n 3. General (1 or 2, uses P)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":75,"value":"md`# Deriving associated parameters\nDi & Li (2004) provide simple formulas to derive associated parameters from the CAHVORE model. Here is a table:\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":294,"value":"viewof hvtable = Inputs.table(\n hvTable,\n { \n format:\n {\n parameter: p => html`${p}`\n },\n align:\n {\n value: 'right'\n }\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":307,"value":"md`# Conversion to photogrammetric parameters\n\nFollowing Di & Li (2004) we can compute the corresponding photogrammetric camera model.\nThe photogrammetric camera model requires knowledge of the pixel size in mm. For example, the OV7251 (https://www.ovt.com/sensors/OV7251) sensor has a 3 micrometer pixel size, and the IMX\n214 (https://www.mouser.com/datasheet/2/897/ProductBrief_IMX214_20150428-1289331.pdf) a 1.12 micrometer pixel size.\n\nWe also need to know the image width and height in pixels. For example, the OV7251 has a 640 x 480 image size, and the IMX 214 a 4208 x 3120 active image size.\n\nThe photogrammetric camera model groups parameters into exterior and interior orientation parameters.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":311,"value":"md`## Exterior orientation (EO) parameters`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":315,"value":"viewof EO = Inputs.table(EOtable, {\n format: {\n parameter: p => html`${p}`,\n value: v => html`

${v}

`\n },\n align: {\n value: 'right'\n },\n width: {\n value: '40em',\n description: '15em'\n }\n}\n )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":96,"value":"md`## Interior orientation (IO) parameters`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":337,"value":"viewof IO = Inputs.table(IOtable, {\n format: {\n parameter: p => html`${p}`,\n //value: v => html`

${v}

`\n },\n align: {\n value: 'right'\n }\n}\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":328,"value":"md`## Radial lens distortion parameters`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":349,"value":"viewof RD = Inputs.table(RDtable, {\n format: {\n parameter: p => html`${p}`,\n //value: v => html`

${v}

`\n },\n align: {\n value: 'right'\n }\n}\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":228,"value":"md`# Related materials\nhttps://github.com/bvnayak/CAHVOR_camera_model\nhttp://www.unmannedspaceflight.com/index.php?showtopic=3911&pid=85926&st=0&#entry85926\nhttps://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2003JE002199\nhttps://trs.jpl.nasa.gov/bitstream/handle/2014/20686/98-1739.pdf?sequence=1\nhttps://www-mipl.jpl.nasa.gov/vicar/dev/html/vichelp/marscahv.html\nhttps://pds-imaging.jpl.nasa.gov/data/mer/spirit/mer2no_0xxx/document/geometric_cm.txt\nhttps://trs.jpl.nasa.gov/bitstream/handle/2014/37251/03-0869.pdf?sequence=1&isAllowed=y\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":203,"value":"md`### Internals`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":208,"value":"pixel_size = +pixel_size_string / 1000;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":212,"value":"image_size = {\n return {\n width: +image_width,\n height: +image_height\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"component_list_example = \"(-0.000385336,0.0896009,0.117889);(0.0119194,0.72545,0.688172);(-1755.77,1629.89,1400.25);(-87.3827,-116.053,2334.34);(-0.000662614,0.723521,0.690302);(0.000144295,0.468504,-0.0528464);(-0.00068363,-0.00098111,-0.00156945);2.0;0.0\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":111,"value":"pixel_size_imx = 1.12e-6;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":123,"value":"image_size_imx = {\n return {\n width: 4208,\n height: 3120\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"s = component_list.replaceAll(\"(\",\"\").replaceAll(\")\",\"\").split(\";\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"CAHVORE = {\n const comps = s.map( p => p.split(\",\").map( n => +n ));\n return {\n C: comps[0],\n A: comps[1],\n H: comps[2],\n V: comps[3],\n O: comps[4],\n R: comps[5],\n E: comps[6],\n extra: [comps[7], comps[8]]\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":246,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":64,"value":"hv = {\n const m = CAHVORE;\n const hv = {\n h_c: math.dot(m.A, m.H),\n v_c: math.dot(m.A, m.V),\n h_s: math.norm(math.cross(m.A, m.H)),\n v_s: math.norm(math.cross(m.A, m.V)),\n theta: math.evaluate(\"atan( dot(cross(V, H), A) / (dot(cross(A, V), cross(A, H))))\", {\n V: CAHVORE.V,\n A: CAHVORE.A,\n H: CAHVORE.H\n })\n };\n hv.Hp = math.divide(math.subtract(m.H, math.multiply(hv.h_c,m.A)), hv.h_s);\n hv.Vp = math.divide(math.subtract(m.V, math.multiply(hv.v_c,m.A)), hv.v_s);\n return hv;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":288,"value":"hvTable = {\n const table =\n [\n ['h_c', 'hor. optical center in pixels', math.format(hv.h_c, {precision:6})],\n ['v_c', 'vert. optical center in pixels', math.format(hv.v_c, {precision:6})],\n ['h_s', 'hor. focal length/hor.scale in pixels', math.format(hv.h_s, {precision:6})],\n ['v_s', 'vert. focal length/vert. scale in pixels', math.format(hv.v_s, {precision:4})],\n [\"H^'\", 'horizontal unit vector', math.format(hv.Hp, {precision:4})],\n [\"|H^'|\", 'horizontal unit vector length', math.format(math.norm(hv.Hp), {precision:4})],\n [\"V^'\", 'vertical unit vector', math.format(hv.Vp, {precision:4})],\n [\"|V^'|\", 'vertical unit vector length', math.format(math.norm(hv.Vp), {precision:4})],\n [\"θ\", \"angle between H' and V'\", math.format(hv.theta * 180/Math.PI)]\n ];\n return table.map( r => { return {parameter: r[0], description:r[1], value:r[2]} });\n\n \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":103,"value":"PHOTO = {\n const M = [hv.Hp, math.multiply(hv.Vp, -1), math.multiply(CAHVORE.A, -1)];\n const XYZc = CAHVORE.C;\n const phi = math.asin(M[2][0]);\n const w = - math.asin(M[2][1] / math.cos(phi));\n const k = math.acos(M[0][0] / math.cos(phi));\n const photo = {\n XYZ_c : XYZc,\n M: M,\n f_x: hv.h_s * pixel_size,\n f_y: hv.v_s * pixel_size,\n x0: ( hv.h_c - image_size.width/2 ) * pixel_size,\n y0: ( - hv.v_c + image_size.height/2 ) * pixel_size,\n phi: phi,\n omega: w,\n kappa: k\n };\n photo.k = [ CAHVORE.R[0], CAHVORE.R[1]/math.pow(photo.f_x,2), CAHVORE.R[2]/math.pow(photo.f_x, 4) ];\n return photo\n \n}\n ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":285,"value":"EOtable = {\n const table = [\n ['X_c, Y_c, Z_c', 'exposure/perspective center', math.format(PHOTO.XYZ_c, 4)],\n ['M', 'rotation matrix', math.format(PHOTO.M, 4)],\n ['ω', 'Euler angle around x in degrees', math.format(PHOTO.XYZ_c, 4)],\n ['φ', 'Euler angle around y in degrees', math.format(PHOTO.phi, 4)],\n ['κ', 'Euler angle around z in degrees', math.format(PHOTO.kappa, 4)]\n ];\n return table.map( r => { return {parameter: r[0], description:r[1], value:r[2]} });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":334,"value":"IOtable = {\n const table = [\n ['f_x', 'focal length in x [mm]', math.format(PHOTO.f_x * 1000,6)],\n ['f_y', 'focal length in y [mm]', math.format(PHOTO.f_y * 1000,6)],\n ['f', 'average focal length [mm]', math.format((PHOTO.f_x + PHOTO.f_y)/2 * 1000,6)],\n ['x₀', 'principal point in x [mm]', math.format(PHOTO.x0 * 1000,6)],\n ['y₀', 'principal point in y [mm]', math.format(PHOTO.y0 * 1000,6)]\n ];\n return table.map( r => { return {parameter: r[0], description:r[1], value:r[2]} });\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":342,"value":"RDtable = {\n const table = [\n ['k₀', 'first order lens correction coefficient', math.format(PHOTO.k[0],6)],\n ['k₁', 'third order lens correction coefficient', math.format(PHOTO.k[1],6)],\n ['k₂', 'fifth order lens correction coefficient', math.format(PHOTO.k[2],6)]\n ];\n return table.map( r => { return {parameter: r[0], description:r[1], value:r[2]} });\n}\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":66,"value":"math = require ( \"mathjs\");","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"1","titling":"auto"}} 32:"$31:body"