Midterm Exam. CS/ECE 181B Intro to Computer Vision. February 13, :30-4:45pm

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Janis Logan
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1 Nam: Midtm am CS/C 8B Into to Comput Vision Fbua, 7 :-4:45pm las spa ouslvs to th dg possibl so that studnts a vnl distibutd thoughout th oom. his is a losd-boo tst. h a also a fw pags of quations, t. inludd fo ou fn. B su to ad ah qustion afull and povid all th infomation qustd. If th qustion ass ou to plain, do so! Show ou wo. Wit ou answs in th spas povidd and, if nssa, on th ba of th pag. If ou us th ba, daw an aow o wit S BACK to ma su th gads don t miss it. If ou nd mo spa, attah ta shts of pap availabl at th font. ams must b tund in b 4:45pm shap. Good lu!

2 sptiv pojtion Othogaphi pojtion Wa psptiv pojtion m m v u M O W W W C C W C igid oodinat tansfomation M fom wold ood. fam to ama ood. fam in homognous oodinats Ow is th tanslation vto: M Anoth wa to wit this, wh is a tanslation vto: tan tan aalll pojtion tan tan m m poj poj aapsptiv pojtion t t A igid tansfomation: Affin tansfomation: ojtiv tansfomation:

3 W/m -s L adian W/s I adiant intnsit W/m Iadian J/s o W Φ adiant flu Sou pow adiatd p unit aa p unit solid angl Sou pow adiatd p unit solid angl ow falling on unit aa of tagt ng p unit tim pow J Q adiant ng ng t Q A I A I L L f d 4 4 Snso sponss: d d d Z otation about th ais: otation about th ais: otation about th Z ais: hin lns quation: f Imag iadian on th imag plan as a funtion of th objt adian L: Snll s Law fo fation: n = n

4 4 Mapping fom sou to snso sponss: Z Z Z Z CI homatiit oodinats, fom tistimulus valus,, Z: Coting fo adial distotion Convolution of H and F:

5 Sampl Midtm Qustions B su to go ov th homwo qustions too.. [5 points] Bifl dsib th lationship btwn omput vision and omput gaphis. h a basiall invs poblms, on gaphis stating with modls and poduing imags, th oth CV stating with imags and poduing infomation about thos imags suh as D modls... [ points] List th appliations of omput vision. S fist ltu. [5 points] In a psptiv pojtion, th sn point -5,, -4 pojts to what, point on a vitual imag plan that is 5 units in font of th ama? o what, point on th al imag plan if =? -5/8, 5/4 5/4, -5/ Just us th simpl psptiv quations to solv. In th vitual imag plan, th signs of and will not hang in th al imag plan, th a ngatd. 5

6 4. [5 points] Of th following pojtion modls: psptiv, othogaphi, paalll, wa-psptiv, and paapsptiv, fo whih ons do all pojtd points pass though th oigin of th ama oodinat sstm? sptiv, wa-psptiv, paapsptiv 5. [5 points] Giv th 44 homognous tansfomation mati that fist tanslats a point b [ ] and thn otats it about th ais b 45 dgs. Giv th tansfomation mati th pfoms ths in th vs od. otz, 45 * ans,, wit out atual valus ans,, * otz, 45 wit out atual valus 6. [ points] Und psptiv pojtion, what dos a il in th sn pojt to on th imag plan? An llips. 7. [5 points] A vido ama snds imags fams p sond of 64*48 tu olo pil valus. How man bts p sond a snt? *64*48* 8. [ points] o podu a lag dpth of fild, should th ama aptu b small o lag? Small 6

7 9. [ points] h pil valu odd fom a patiula point on a ama s snso aa dpnds on sval fatos, suh as th position and ointation of th objt in th wold that gts imagd at that point. Nam at last th oth fatos that dtmin th pil valu of th point. posu tim, illumination, aptu, fous,. [ points] A ditional diffus sufa fltan modl is a ombination of what two idal sufa modls? Lambtian/diffus and spula. [5 points] wo light sous, and, a mtams that is, th podu th at sam GB pil valus. Now w mi thm togth to at two nw light sous, and, as suh: = / A + / B = / A + / B A and mtams? plain wh o wh not. s, th, G, and B valus will not hang an show via th sng quations. [5 points] What D point p =,, is podud b adding th following D points, psntd in homognous oodinats: p 6 p 4 4,.5, fist onvt ah to th,,, fom,.5,, +,.75,, =,.5,, point,.5, 7

Sin mitus of two sous at olo sponss on a lin dfind b th two sous, daw a lin fom th 48 nm bounda point though th whit point to th oth sid, and ou s that appoimatl 58 nm light

8 . [5 points] wo light sous, A and B, ah podu homatiit oodinats of.5,.7. A A and B mtams? plain wh o wh not. Not nssail. h might hav diffnt bightnss, fo ampl. 4. [5 points] Ug th homatiit diagam, what wavlngth of monohomati light an b ombind with monohomati light of 48 nm to ma ga light? Appoimatl 58 nm. Ga shows up as.,., whit, on th homatiit diagam. Sin mitus of two sous at olo sponss on a lin dfind b th two sous, daw a lin fom th 48 nm bounda point though th whit point to th oth sid, and ou s that appoimatl 58 nm light would b ndd to at whit ga with 48 nm light. 5. [4 points] What would th sult b if ou onvolvd an imag with this filt: h oiginal imag blud slightl in th hoiontal dition. 8

Exercises in functional iteration: the function f(x) = ln(2-exp(-x))

Exercises in functional iteration: the function f(x) = ln(2-exp(-x)) Eiss in funtional itation: th funtion f ln2-p- A slfstudy usin fomal powsis and opato-matis Gottfid Hlms 0.2.200 updat 2.02.20. Dfinition Th funtion onsidd is an ampl tan fom a pivat onvsation with D.Gisl