From 24731542a5829cdfaedea1a6d5b2a0c7fdddd8b6 Mon Sep 17 00:00:00 2001 From: lenkamilojcevic Date: Sun, 9 Oct 2022 17:22:40 +0200 Subject: [PATCH 01/10] Ovo je verzija[0] koja ne sadrzi slike, aspekt i zakljucak --- content/2022/videookulografija.md | 52 +++++++++++++++++++++++++++++++ 1 file changed, 52 insertions(+) diff --git a/content/2022/videookulografija.md b/content/2022/videookulografija.md index 4fab0aa..a89166d 100644 --- a/content/2022/videookulografija.md +++ b/content/2022/videookulografija.md @@ -2,3 +2,55 @@ title: Videookulografija summary: Projekat iz videookulografije rađen na letnjem kampu za stare polaznike 2022. godine od Anje Kovačev i Lenke Milojčević. --- +## **Aparatura i metode** + + +#### **Aparatura** +Koristili smo web kameru za praćenje zenice sa koje je skinut IR filter (filter za vidljivi spektar). Kamera ja zakačena na naočare gde je postavljena i led dioda kako bi svetlost bila konstantna. U ispod prikazanoj slici može se videti kako naočare izgledaju. + +slike + + +#### **Sivi spektar** +Kako bi lakše detektovali ivice naše zenice prvo je potrebno RGB(crvena-zelena-plava) sliku prebaciti u sivi spektar metodom greyscale. Kako bi konvertovali sliku potrebno je RGB vrednosti piksela koje zauzimaju 24 bita konvertovati u vrednosti sivog spektra(eng. *greyscale*) koji zauzima 8 bita memorije. Korišćenjem sledećeg algoritma[^1] dobijamo željeni rezultat. + + +1. $Y = (0.299 x R) + (0.587 x G) + (0.114 x B)$ +2. $U = (B - Y) x 0.565$ +3. $V = (R - Y) x 0.713$ +4. $UV = U + V$ +5. $R1=R*0.299$ $R2=R*0.587$ $R3=R*0.114$ +6. $G1=G*0.299$ $G2=G*0.587$ $G3=G*0.114$ +7. $B1=B*0.299$ $B2=B*0.587$ $B3=B*0.114$ +8. $R4=(R1+R2+R3)/3$ +9. $G4=(G1+G2+G3)/3$ +10. $B4=(B1+B2+B3)/3$ +11. $I1=(R4+G4+B4+UV)/4$ + +U koracima od 1 do 3 izračunavamo osvetljenost i vrednosti hrominacije naše primarne slike u boji. RGB vrednosti su aproksimirane u koracima od 5 do 10 korišćenjem RGB komponenti. U 11. koraku izračunavanjem proseka vrednosti R4, G4, B4 i UV dobijamo vrednost I1 koja predstavlja našu sliku u sivom spektru. + +#### **Zamućivanje** +Kako bi naša detekcija ivice funkcionisala, neophodno je da sliku zamutimo Gausovim filterom i na taj način smanjimo količinu detalja na datoj slici. Gausov filter je zapravo niskopropusni filter jer ima efekat smanjenja visokofrekventnih komponenti slike. Korišćenjem Gausove funkije za dve dimenzije dobijamo vrednosti iz kojih se gradi konvoluciona matrica koja se primenjuje na sliku sivog spektra. Nove vrednosti svakog piksela postavljaju se na srednje vrednosti susednih piksela. Vrenosti originalnog piksela dobija najveću Gausovu vrednost, susedni pikseli dobijaju manje vrednosti kako bi se njihova udaljenost od origanalnih piksela poveća. Na ovaj način se rezultira zamućenost kojom se čuvaju granice i ivce bolje nego drugim metodama. + + +#### **Detekcija ivica** +Kako bi detektovale ivice koristili smo funkciju Keni(eng. *Canny*). Detektor ivica Keni će piksel detektovati kao ivivcu ako je veličina gradijenta piksela veća nego veličina piksela sa obe njegove strane u pravcu promene maksimalnog inteziteta. Proces detekcije[^2] je sledeći: +1. Prvo je potrebno sliku zamutiti Gausovim filtrom kako bi se smanjili detalji na datoj slici. +2. Sledeći korak je da izračunamo veličinu i pravac(pravac maksimalne promene inteziteta piksela) gradijenta. +3. Kada je veličina gradijenta piksela veća od njemu dva susedna, piksel označavamo kao ivicu. U suprotnom, piksel označavamo kao pozadinu. +4. Uklanjanje slabih ivica pomoću praga histerza. + + +#### **Linearna regresija** +Kako bi mogli da uz spomoć naše detekcije zenice kontrolišemo neki objekat na računaru potrebno je da znamo na osnovu koordinata našeg oka u koju tačku na ekranu gledamo. Za to smo koristili linearnu, tj. polinomialnu regresiju jer naš sistem nije linearan. + +Linearna regresija predstavlja modelovanje relacija između jedne ili više zavisnih promenljivih i jedne ili više nezavisnih promenljivih. Model linearne regresije ima oblik $Y = X x b $, gde je Y vektor izmerenih vrednosti(u našem slučaju koordinate našeg pogkleda na ekranu), X vektor inputne promenljive(u našem slučaju koordinate zenice oka) i b vektor koificijenta modela. + + + + + + +### Reference +[^1]: Saravanan, Chandran. "Color image to grayscale image conversion." 2010 Second International Conference on Computer Engineering and Applications. Vol. 2. IEEE, 2010. +[^2]: Ding, Lijun, and Ardeshir Goshtasby. "On the Canny edge detector." Pattern recognition 34.3 (2001): 721-725. \ No newline at end of file From 1d7bcd41beaf6fdbb93346b0d72e27eca3e07e3f Mon Sep 17 00:00:00 2001 From: lenkamilojcevic Date: Sat, 15 Oct 2022 15:53:55 +0200 Subject: [PATCH 02/10] Ima par izmena koje sam stigla da dodam, Keni je u procesu prepravljanja --- content/2022/videookulografija.md | 66 ++++++++++++++++++++++++++++++- 1 file changed, 65 insertions(+), 1 deletion(-) diff --git a/content/2022/videookulografija.md b/content/2022/videookulografija.md index a89166d..1721996 100644 --- a/content/2022/videookulografija.md +++ b/content/2022/videookulografija.md @@ -2,6 +2,19 @@ title: Videookulografija summary: Projekat iz videookulografije rađen na letnjem kampu za stare polaznike 2022. godine od Anje Kovačev i Lenke Milojčević. --- + +## **Uvod** +Život u današnjem društvu ima mnogo prednosti u svakom pogledu. Tehnologija napreduje iz dana u dan. Taj brz razvoj zahteva velike potrebe koje ne mogu svi ljudi da ispune. Na ideju za ovaj projekat smo došle uvidevši potrebe osoba sa invaliditetom da komuniciraju, igraju video igre, da koriste kompijuter ili da se kreću. +Napretkom tehnologije, VOG (videookulografiju) je zamenila EOG (elektrookulografiju) metodu. Videookulografija je metoda u kojoj se pomoću kamere prate pokreti oka, tj. zenice. U ovom radu proučavan je 2D VOG sistem, što znači da se posmatraju dve ose – horizontalna osa na kojoj se detektuju pokreti na levo i desno, i vertikalna osa na kojoj je prate pogled na gore i dole. + + +2D VOG smatra se jednom od najpouzdanijih metoda, a ima široku primenu. Primenjuje se u oftalmologiji za proučavanje patoloških stanja kao što je nistagmus1 (nistagmus predstavlja ritmičke, nevoljne trzaje očnih jabučica). VOG koriste kvadriplegičari i osobe sa oštećenjima motornih neurona kao sredstvo za komunikaciju ili kretanje (upravljanje tastaturom i invalidskim kolicima pokretima očiju). Takođe, u industriji se koristi za praćenje reakcija klijenata. Još se koristi za posmatranje reakcije vozača prilikom vožnje, u vojnie svrhe i slično. + + +Postoje različiti radovi koji koriste različite metode. U većini slučajeva se nakon obrade slike detektuje centar zenice i dalje se radi test praćenja kretanja oka po utvrđenim putanjama. Metode detekcije centra zenice i ugla oka se ispostavljaju brzim. U nekim radovima se koristi mašinsko učenje gde istreniran model može da isprati i prepozna pokret oka. + + + ## **Aparatura i metode** @@ -27,12 +40,16 @@ Kako bi lakše detektovali ivice naše zenice prvo je potrebno RGB(crvena-zelena 10. $B4=(B1+B2+B3)/3$ 11. $I1=(R4+G4+B4+UV)/4$ + U koracima od 1 do 3 izračunavamo osvetljenost i vrednosti hrominacije naše primarne slike u boji. RGB vrednosti su aproksimirane u koracima od 5 do 10 korišćenjem RGB komponenti. U 11. koraku izračunavanjem proseka vrednosti R4, G4, B4 i UV dobijamo vrednost I1 koja predstavlja našu sliku u sivom spektru. #### **Zamućivanje** Kako bi naša detekcija ivice funkcionisala, neophodno je da sliku zamutimo Gausovim filterom i na taj način smanjimo količinu detalja na datoj slici. Gausov filter je zapravo niskopropusni filter jer ima efekat smanjenja visokofrekventnih komponenti slike. Korišćenjem Gausove funkije za dve dimenzije dobijamo vrednosti iz kojih se gradi konvoluciona matrica koja se primenjuje na sliku sivog spektra. Nove vrednosti svakog piksela postavljaju se na srednje vrednosti susednih piksela. Vrenosti originalnog piksela dobija najveću Gausovu vrednost, susedni pikseli dobijaju manje vrednosti kako bi se njihova udaljenost od origanalnih piksela poveća. Na ovaj način se rezultira zamućenost kojom se čuvaju granice i ivce bolje nego drugim metodama. +#### **Binarizacija** +Binarizacija za cilj ima da izdvoji objekat iz slike, u ovom slučaju zenicu. Postiže se tako što sliku koju smo prebacili u sivu spektar sada konvertujemo u crno-belo. Prvo je potrebno naći trešhold vrednosti, odnosno vrednost praga, što radimo pomoću histograma. Kao trešhold uzimamo najveću vrednost kumulativne sume histograma. Sada dodeljujemo vrednosti pikselima na sledeći način – oni pikseli čija je vrednost manja ili jednaka od vrednosti trešholda, dobijaju vrednost 0 (postaju crni), a oni čija je vrednost veća od trešholda dobijaju vrednost 255 (postaju beli). Sada možemo da vidimo jasno izdvojenu zenicu (slika znice). + #### **Detekcija ivica** Kako bi detektovale ivice koristili smo funkciju Keni(eng. *Canny*). Detektor ivica Keni će piksel detektovati kao ivivcu ako je veličina gradijenta piksela veća nego veličina piksela sa obe njegove strane u pravcu promene maksimalnog inteziteta. Proces detekcije[^2] je sledeći: 1. Prvo je potrebno sliku zamutiti Gausovim filtrom kako bi se smanjili detalji na datoj slici. @@ -40,6 +57,23 @@ Kako bi detektovale ivice koristili smo funkciju Keni(eng. *Canny*). Detektor iv 3. Kada je veličina gradijenta piksela veća od njemu dva susedna, piksel označavamo kao ivicu. U suprotnom, piksel označavamo kao pozadinu. 4. Uklanjanje slabih ivica pomoću praga histerza. +#### **Hafova transformacija za krug** +Hafova transformacija se može koristiti za određivanje parametara kruga kada je poznat broj tačaka koje padaju na perimetar. Krug čiji je radijus R i centar sa koordinatama (a, b) može se opisati sledećim jednačinama: +$x = a + R cos(θ), y = b + R sin(θ)$ +Kada ugao θ prođe pun krug, tačke x i y, prate opseg kruga. Kada slika ima više krugova koji spadaju u opseg, traže se trojke parametara (R, a, b) koje će definisati krugove. + + +##### *Detekcija krugova* +Ako poznajemo radijus, tada pretragu sužavamo na dve dimenzije i cilj nam je da nađemo koordinate centra. Mesto tačaka (a, b) u opsegu pada na krug radijusa R i centra (x, y). Pravi krug ima zajednički centar za sve krugove u datom opsegu i nalazi se pomoću Hafovog akumulacionog niza. Kada je više krugova na slici, preklapanje prouzrokuje pronalaženje lažnih centara (slika 2.2). Ovaj problem se uklanja poređenjem sa originalnom slikom (slika 2.1). + + +#### **Mean filter** +Kada smo detektovali našu zenicu potrebno je uraditi test gde nam se na ekranu pojavljuje devet tačaka u koje gledamo određen broj sekundi. U toku eksperimenta dobijamo koordinate zenice i tačke u koju trenutno gledamo i tako pravimo bazu podataka koje će nam biti potrebna za dalji rad. + + +Dobijeni podaci imaju šum, kao što je treptaj, koje otklanjamo mean filterom (filter srednje aritmetičke vrednosti). Prolazići kroz bazu izračunavamo aritmetičku vrednost prethodnih n koordinata i tu novu vrednost stavljamo kao novu koordinatu. Na taj način dobijamo bazu bez šuma. + + #### **Linearna regresija** Kako bi mogli da uz spomoć naše detekcije zenice kontrolišemo neki objekat na računaru potrebno je da znamo na osnovu koordinata našeg oka u koju tačku na ekranu gledamo. Za to smo koristili linearnu, tj. polinomialnu regresiju jer naš sistem nije linearan. @@ -47,10 +81,40 @@ Kako bi mogli da uz spomoć naše detekcije zenice kontrolišemo neki objekat na Linearna regresija predstavlja modelovanje relacija između jedne ili više zavisnih promenljivih i jedne ili više nezavisnih promenljivih. Model linearne regresije ima oblik $Y = X x b $, gde je Y vektor izmerenih vrednosti(u našem slučaju koordinate našeg pogkleda na ekranu), X vektor inputne promenljive(u našem slučaju koordinate zenice oka) i b vektor koificijenta modela. +#### **Polinomialna regresija** +Poliomilna regresija je specijalan slučaj višestruke linearne regresije gde se modeluje veza između zavisne i nezavisne promenljive, u ovom slučaju, između stvarnog položaja zenice i položaja tačke na ekranu, kao polinom n-tog stepena. U našem slučaju, nema linearne korelacije između promenljivih (slika 1.1), pa se radi veće preciznosti promenjuje poliomilna regresija (slika 1.2). + +slika 1 slika 2 + +Formula glasi: $y= b0+b1x1+ b2x12+ b2x13+...... bnx1n$, gde su: +c - koificijenti regresije +n - stepen regresije (u ovo slučaju $n = 3$) + + +### **Rezultati i istraživanja** +Model dobijen poliomilnom regresijom smo proverile tako što smo test snimile još jednom, ali ovog puta smo dobile predviđanja položaja zenice. +Na kraju, kao rezultat smo dobile tabelu u kojoj, u odnosu na tačku na ekranu (x, y), vidimo koificijent sličnosti koordinata na ekranu i predviđenih koordinata (σx, σy). Takođe, izračunat je pomeraj između ovih dveju tačaka. (Napomena – ovo je tabela rezultata sa jednim snimanjem, dodatno prikupljanje podataka je u toku.) + + +| X | Y | pomeraj | σx | σy | +|---|---|---------|----|----| +| 100 | 100 | 133,06 | 39,53 | 57,59 | +| 700 | 100 | 162,63 | 63,66 | 13,31 | +| 1300 | 100 | 143,28 | 1,07 | 2,18 | +| 100 | 400 | 171,49 | 41,3 | 98,29 | +| 700 | 100 | 110,9 | 51,82 | 26,37 | +| 1300 | 400 | 140,46 | 32,69 | 50,97 | +| 700 | 100 | 105,11 | 59,04 | 78,9 | +| 700 | 700 | 20,02 | 67,81 | 8,08 | +| 1300 | 700 | 107,48 | 34,37 | 52,48 | +U budućnosti planiramo da kroz ovaj projekat omogućimo kontrolisanje kursora, tj. tastature, ili igranje video igara. ### Reference [^1]: Saravanan, Chandran. "Color image to grayscale image conversion." 2010 Second International Conference on Computer Engineering and Applications. Vol. 2. IEEE, 2010. -[^2]: Ding, Lijun, and Ardeshir Goshtasby. "On the Canny edge detector." Pattern recognition 34.3 (2001): 721-725. \ No newline at end of file +[^2]: Ding, Lijun, and Ardeshir Goshtasby. "On the Canny edge detector." Pattern recognition 34.3 (2001): 721-725. +https://www.cis.rit.edu/class/simg782/lectures/lecture_10/lec782_05_10.pdf +https://www.javatpoint.com/machine-learning-polynomial-regression +https://www.sciencedirect.com/science/article/pii/S1877705812046085 From bec73c89ebab80c65b8cb7cebdf94052e61980a4 Mon Sep 17 00:00:00 2001 From: lenkamilojcevic Date: Sun, 16 Oct 2022 15:58:19 +0200 Subject: [PATCH 03/10] Ovo je sve sve stoo smo stigle da promenimo za ovo vreme. --- content/2022/videookulografija.md | 245 +++++++++++++----- static/images/2022/videookulografija/BIN.jpg | Bin 0 -> 24290 bytes .../images/2022/videookulografija/CANNY.jpg | Bin 0 -> 16889 bytes .../2022/videookulografija/DETEKTOVANA.jpg | Bin 0 -> 25115 bytes .../2022/videookulografija/GRAYTOBIN.jpg | Bin 0 -> 6474 bytes .../2022/videookulografija/GRAYTOBLUR.png | Bin 0 -> 349743 bytes .../images/2022/videookulografija/OPREMA1.jpg | Bin 0 -> 183211 bytes .../images/2022/videookulografija/OPREMA2.jpg | Bin 0 -> 211712 bytes .../2022/videookulografija/RGBtoGRAY.jpg | Bin 0 -> 10993 bytes .../2022/videookulografija/eksperiment.jpg | Bin 0 -> 50310 bytes .../2022/videookulografija/filtriranx.jpg | Bin 0 -> 23444 bytes .../2022/videookulografija/filtrirany.jpg | Bin 0 -> 14864 bytes 12 files changed, 178 insertions(+), 67 deletions(-) create mode 100644 static/images/2022/videookulografija/BIN.jpg create mode 100644 static/images/2022/videookulografija/CANNY.jpg create mode 100644 static/images/2022/videookulografija/DETEKTOVANA.jpg create mode 100644 static/images/2022/videookulografija/GRAYTOBIN.jpg create mode 100644 static/images/2022/videookulografija/GRAYTOBLUR.png create mode 100644 static/images/2022/videookulografija/OPREMA1.jpg create mode 100644 static/images/2022/videookulografija/OPREMA2.jpg create mode 100644 static/images/2022/videookulografija/RGBtoGRAY.jpg create mode 100644 static/images/2022/videookulografija/eksperiment.jpg create mode 100644 static/images/2022/videookulografija/filtriranx.jpg create mode 100644 static/images/2022/videookulografija/filtrirany.jpg diff --git a/content/2022/videookulografija.md b/content/2022/videookulografija.md index 1721996..6a45a51 100644 --- a/content/2022/videookulografija.md +++ b/content/2022/videookulografija.md @@ -2,119 +2,230 @@ title: Videookulografija summary: Projekat iz videookulografije rađen na letnjem kampu za stare polaznike 2022. godine od Anje Kovačev i Lenke Milojčević. --- +**Autori** - Anja Kovačev i Lenka Milojčević -## **Uvod** -Život u današnjem društvu ima mnogo prednosti u svakom pogledu. Tehnologija napreduje iz dana u dan. Taj brz razvoj zahteva velike potrebe koje ne mogu svi ljudi da ispune. Na ideju za ovaj projekat smo došle uvidevši potrebe osoba sa invaliditetom da komuniciraju, igraju video igre, da koriste kompijuter ili da se kreću. -Napretkom tehnologije, VOG (videookulografiju) je zamenila EOG (elektrookulografiju) metodu. Videookulografija je metoda u kojoj se pomoću kamere prate pokreti oka, tj. zenice. U ovom radu proučavan je 2D VOG sistem, što znači da se posmatraju dve ose – horizontalna osa na kojoj se detektuju pokreti na levo i desno, i vertikalna osa na kojoj je prate pogled na gore i dole. +**Mentori** - Milomir Stefanović i Pavle Pađin -2D VOG smatra se jednom od najpouzdanijih metoda, a ima široku primenu. Primenjuje se u oftalmologiji za proučavanje patoloških stanja kao što je nistagmus1 (nistagmus predstavlja ritmičke, nevoljne trzaje očnih jabučica). VOG koriste kvadriplegičari i osobe sa oštećenjima motornih neurona kao sredstvo za komunikaciju ili kretanje (upravljanje tastaturom i invalidskim kolicima pokretima očiju). Takođe, u industriji se koristi za praćenje reakcija klijenata. Još se koristi za posmatranje reakcije vozača prilikom vožnje, u vojnie svrhe i slično. +## **1. Apstrakt** -Postoje različiti radovi koji koriste različite metode. U većini slučajeva se nakon obrade slike detektuje centar zenice i dalje se radi test praćenja kretanja oka po utvrđenim putanjama. Metode detekcije centra zenice i ugla oka se ispostavljaju brzim. U nekim radovima se koristi mašinsko učenje gde istreniran model može da isprati i prepozna pokret oka. +.... -## **Aparatura i metode** +## **2. Uvod** +Život u današnjem društvu ima mnogo prednosti u svakom pogledu. +Tehnologija napreduje iz dana u dan. +Taj brz razvoj zahteva velike potrebe koje ne mogu svi ljudi da ispune. +Na ideju za ovaj projekat smo došle uvidevši potrebe osoba sa invaliditetom da komuniciraju, igraju video igre, da koriste kompijuter ili da se kreću. +Napretkom tehnologije, VOG (videookulografiju) je zamenila EOG (elektrookulografiju). Videookulografija je metoda u kojoj se pomoću kamere prate pokreti oka, tj. zenice. U ovom radu proučavan je 2D VOG sistem, što znači da se posmatraju dve ose – horizontalna osa na kojoj se detektuju pokreti na levo i desno, i vertikalna osa na kojoj je prate pogled na gore i dole. -#### **Aparatura** -Koristili smo web kameru za praćenje zenice sa koje je skinut IR filter (filter za vidljivi spektar). Kamera ja zakačena na naočare gde je postavljena i led dioda kako bi svetlost bila konstantna. U ispod prikazanoj slici može se videti kako naočare izgledaju. +2D VOG smatra se jednom od najpouzdanijih metoda, a ima široku primenu. +Primenjuje se u oftalmologiji za proučavanje patoloških stanja kao što je nistagmus1 (nistagmus predstavlja ritmičke, nevoljne trzaje očnih jabučica). +VOG koriste kvadriplegičari i osobe sa oštećenjima motornih neurona kao sredstvo za komunikaciju ili kretanje (upravljanje tastaturom i invalidskim kolicima pokretima očiju). Takođe, u industriji se koristi za praćenje reakcija klijenata. +Još se koristi za posmatranje reakcije vozača prilikom vožnje, u vojne svrhe i slično. -slike +Postoje različiti radovi koji koriste različite metode. +U većini slučajeva se nakon obrade slike detektuje centar zenice i dalje se radi test praćenja kretanja oka po utvrđenim putanjama. +Metode detekcije centra zenice i ugla oka se ispostavljaju brzim. +U nekim radovima se koristi mašinsko učenje gde istreniran model može da isprati i prepozna pokret oka. -#### **Sivi spektar** -Kako bi lakše detektovali ivice naše zenice prvo je potrebno RGB(crvena-zelena-plava) sliku prebaciti u sivi spektar metodom greyscale. Kako bi konvertovali sliku potrebno je RGB vrednosti piksela koje zauzimaju 24 bita konvertovati u vrednosti sivog spektra(eng. *greyscale*) koji zauzima 8 bita memorije. Korišćenjem sledećeg algoritma[^1] dobijamo željeni rezultat. -1. $Y = (0.299 x R) + (0.587 x G) + (0.114 x B)$ -2. $U = (B - Y) x 0.565$ -3. $V = (R - Y) x 0.713$ -4. $UV = U + V$ -5. $R1=R*0.299$ $R2=R*0.587$ $R3=R*0.114$ -6. $G1=G*0.299$ $G2=G*0.587$ $G3=G*0.114$ -7. $B1=B*0.299$ $B2=B*0.587$ $B3=B*0.114$ -8. $R4=(R1+R2+R3)/3$ -9. $G4=(G1+G2+G3)/3$ -10. $B4=(B1+B2+B3)/3$ -11. $I1=(R4+G4+B4+UV)/4$ +## **3. Aparatura i metode** -U koracima od 1 do 3 izračunavamo osvetljenost i vrednosti hrominacije naše primarne slike u boji. RGB vrednosti su aproksimirane u koracima od 5 do 10 korišćenjem RGB komponenti. U 11. koraku izračunavanjem proseka vrednosti R4, G4, B4 i UV dobijamo vrednost I1 koja predstavlja našu sliku u sivom spektru. +#### **3.1 Aparatura** -#### **Zamućivanje** -Kako bi naša detekcija ivice funkcionisala, neophodno je da sliku zamutimo Gausovim filterom i na taj način smanjimo količinu detalja na datoj slici. Gausov filter je zapravo niskopropusni filter jer ima efekat smanjenja visokofrekventnih komponenti slike. Korišćenjem Gausove funkije za dve dimenzije dobijamo vrednosti iz kojih se gradi konvoluciona matrica koja se primenjuje na sliku sivog spektra. Nove vrednosti svakog piksela postavljaju se na srednje vrednosti susednih piksela. Vrenosti originalnog piksela dobija najveću Gausovu vrednost, susedni pikseli dobijaju manje vrednosti kako bi se njihova udaljenost od origanalnih piksela poveća. Na ovaj način se rezultira zamućenost kojom se čuvaju granice i ivce bolje nego drugim metodama. +Web kameru je koriščen za praćenje zenice sa koje je skinut IR filter (filter za ultraljubičasti spektar). +Korišćen je 3D model držača koji .... +Kamera ja zakačena na naočare gde je postavljena i led dioda kako bi osvetljenje slike bilo konstantno. -#### **Binarizacija** -Binarizacija za cilj ima da izdvoji objekat iz slike, u ovom slučaju zenicu. Postiže se tako što sliku koju smo prebacili u sivu spektar sada konvertujemo u crno-belo. Prvo je potrebno naći trešhold vrednosti, odnosno vrednost praga, što radimo pomoću histograma. Kao trešhold uzimamo najveću vrednost kumulativne sume histograma. Sada dodeljujemo vrednosti pikselima na sledeći način – oni pikseli čija je vrednost manja ili jednaka od vrednosti trešholda, dobijaju vrednost 0 (postaju crni), a oni čija je vrednost veća od trešholda dobijaju vrednost 255 (postaju beli). Sada možemo da vidimo jasno izdvojenu zenicu (slika znice). +![Slika hardvera](/images/2022/videookulografija/OPREMA1.jpg)(slika 1) -#### **Detekcija ivica** -Kako bi detektovale ivice koristili smo funkciju Keni(eng. *Canny*). Detektor ivica Keni će piksel detektovati kao ivivcu ako je veličina gradijenta piksela veća nego veličina piksela sa obe njegove strane u pravcu promene maksimalnog inteziteta. Proces detekcije[^2] je sledeći: -1. Prvo je potrebno sliku zamutiti Gausovim filtrom kako bi se smanjili detalji na datoj slici. -2. Sledeći korak je da izračunamo veličinu i pravac(pravac maksimalne promene inteziteta piksela) gradijenta. -3. Kada je veličina gradijenta piksela veća od njemu dva susedna, piksel označavamo kao ivicu. U suprotnom, piksel označavamo kao pozadinu. -4. Uklanjanje slabih ivica pomoću praga histerza. -#### **Hafova transformacija za krug** -Hafova transformacija se može koristiti za određivanje parametara kruga kada je poznat broj tačaka koje padaju na perimetar. Krug čiji je radijus R i centar sa koordinatama (a, b) može se opisati sledećim jednačinama: -$x = a + R cos(θ), y = b + R sin(θ)$ -Kada ugao θ prođe pun krug, tačke x i y, prate opseg kruga. Kada slika ima više krugova koji spadaju u opseg, traže se trojke parametara (R, a, b) koje će definisati krugove. +![Slika hardvera](/images/2022/videookulografija/OPREMA2.jpg)(slika 1) (slika 2) -##### *Detekcija krugova* -Ako poznajemo radijus, tada pretragu sužavamo na dve dimenzije i cilj nam je da nađemo koordinate centra. Mesto tačaka (a, b) u opsegu pada na krug radijusa R i centra (x, y). Pravi krug ima zajednički centar za sve krugove u datom opsegu i nalazi se pomoću Hafovog akumulacionog niza. Kada je više krugova na slici, preklapanje prouzrokuje pronalaženje lažnih centara (slika 2.2). Ovaj problem se uklanja poređenjem sa originalnom slikom (slika 2.1). +#### **3.2. Metode** -#### **Mean filter** -Kada smo detektovali našu zenicu potrebno je uraditi test gde nam se na ekranu pojavljuje devet tačaka u koje gledamo određen broj sekundi. U toku eksperimenta dobijamo koordinate zenice i tačke u koju trenutno gledamo i tako pravimo bazu podataka koje će nam biti potrebna za dalji rad. +##### **3.2.1. Obrada slike** -Dobijeni podaci imaju šum, kao što je treptaj, koje otklanjamo mean filterom (filter srednje aritmetičke vrednosti). Prolazići kroz bazu izračunavamo aritmetičku vrednost prethodnih n koordinata i tu novu vrednost stavljamo kao novu koordinatu. Na taj način dobijamo bazu bez šuma. +... +#### 3.2.1.1. Prebacivanje slike iz RGB u grayscale prostor boja -#### **Linearna regresija** -Kako bi mogli da uz spomoć naše detekcije zenice kontrolišemo neki objekat na računaru potrebno je da znamo na osnovu koordinata našeg oka u koju tačku na ekranu gledamo. Za to smo koristili linearnu, tj. polinomialnu regresiju jer naš sistem nije linearan. -Linearna regresija predstavlja modelovanje relacija između jedne ili više zavisnih promenljivih i jedne ili više nezavisnih promenljivih. Model linearne regresije ima oblik $Y = X x b $, gde je Y vektor izmerenih vrednosti(u našem slučaju koordinate našeg pogkleda na ekranu), X vektor inputne promenljive(u našem slučaju koordinate zenice oka) i b vektor koificijenta modela. +Kako bi zanemarili sve nepotrebne informacije i kako bi sve dužice blie u sivim nijansama potrebno je sliku iz RGB(crvena-zelena-plava) prostora prebaciti u grayscale prostor boja. +Potrebno je konvertovati RGB vrednosti piksela slike koje zauzimaju 24 bita konvertovati u grayscale prostor boja koji zauzima 8 bita memorije korišćenjem funkcije grayscale. +Na slici 3 može se videti kako slika izgleda na početku i njen sivi ekvivalent. + + ![RGB u GRAYSCALE](/images/2022/videookulografija/RGBtoGRAY.jpg)(slika 3) -#### **Polinomialna regresija** -Poliomilna regresija je specijalan slučaj višestruke linearne regresije gde se modeluje veza između zavisne i nezavisne promenljive, u ovom slučaju, između stvarnog položaja zenice i položaja tačke na ekranu, kao polinom n-tog stepena. U našem slučaju, nema linearne korelacije između promenljivih (slika 1.1), pa se radi veće preciznosti promenjuje poliomilna regresija (slika 1.2). + +#### 3.2.1.2 Zamućivanje + +// promeni !!! +Kako bi naša detekcija ivice funkcionisala, neophodno je da sliku zamutimo Gausovim filterom i na taj način smanjimo količinu detalja na datoj slici. Gausov filter je niskopropusni filter. +Korišćenjem Gausove funkije za dve dimenzije dobijamo vrednosti iz kojih se gradi konvoluciona matrica koja se primenjuje na sliku . +Nove vrednosti svakog piksela postavljaju se na srednje vrednosti susednih piksela. Vrenosti originalnog piksela dobija najveću Gausovu vrednost, susedni pikseli dobijaju manje vrednosti kako bi se njihova udaljenost od origanalnih piksela poveća. +Na ovaj način se rezultira zamućenost kojom se čuvaju granice i ivce bolje nego drugim metodama. + +![Slika pre i nakon korišćenja Gausovog filtera](/images/2022/videookulografija/GRAYTOBLUR.png) + +#### 3.2.1.3. Binarizacija + + +Binarizacije kao priprema za segmentaciju ima zadatak da svaki piksel označi labelama 0 (crno) ili 1 (belo). +Postiže se tako što se slika koja je prebačena u sivi spektar sada konvertuje u crno-belo. Ovo se radi procesom koji se naziva poređenje sa pragom. +Pomoću ovoga svaki piksel pretvaramo u 0 ili 255 u zavisnosti od toga da li je njegova vrednost manja ili veća u odnosu na vrednost praga. +Za vrednost praga uzimamo onu vrednost od koje je manje 17.5% piksela sa slike. +Zatim, vrednosti piksela se dodeljuju na sledeći način – oni pikseli čija je vrednost manja ili jednaka od vrednosti prga, dobijaju vrednost 0, a oni čija je vrednost veća od praga dobijaju vrednost 255. +Proizvod primene ovih metoda je crno-bela slika nad kojom se vrši segmentacija - izdvajanje jasnih objekata (u ovom slučaju zenice). + + +![Slika pre i nakon nakon binarizacije](/images/2022/videookulografija/GRAYTOBIN.jpg) + + + +#### 3.2.1.4. Detekcija ivica + + +Za detekciju ivica zenice korišćen je Keni(eng. *Canny*) algoritam. +Keni algoritam je jedan od najboljih metoda sa preciznu i pouzdanu detekciju ivica. +Proces detekcije je sledeći[^2]: + + +1. Zamućivanje - Svaka slika na sebi ima neke šumove koje je potrebno odbaciti kako ne bi pogrešno bili detektovani kao ivice. U te svrhe se koristi prethodno opisan Gausov filter. + + +2. Pronalaženje gradijenta intenziteta - Cilj Keni algoritma je da nađe ivice gde je razlika između piksela u sivom prostoru boja najveća, a to se može postići pronalaženjem gradijenta slike. Korišćenjem Sobelovog operatora određuje se gradijent svakog piksela. + + +3. Potiskivanje lokalnih ne-maksimuma - U ovoj fazi se ,,zamućene'' ivice pretvaraju u ,,oštre'' tako što se zadržavaju svi pikseli čiji je gradijent maksimalan u odnosu na gradijente osam piksela sa kojim se graniči, u suprotnom, vrednost piksela će biti eliminisana. Pikseli koji su maksimalni u svom ,,susedstvu'' se označavaju belim ivicama. + + +4. Histerzno poređenje sa pragom - Kako bi se postigao mali procenta lažnih i veći procenat pravih detekcija definišu se dva praga $T_H$ i $T_L$. Viši prag $T_H$ se postavlja tako da najveći deo piksela koji ne spadaju u ivice imaju manju magnitudu gradijrnta u odnosu na vrednost parag. Niži prag $T_L$ se postavlja tako da najveći deo piksela koji pripadaju ivice koje želimo da detektujemo imaju magnitudu gradijenta veću od vrednosti praga. Na ovaj način dobijamo mapu jakih i slabih (potencijalnih) ivica. + + +5. Detektovanja ivica - Prolaženjem kroz mapu slabih ivica, svi pikseli koji u svom susedstvu imaju barem jednu jaku ivicu proglašavaju se ivičnim pikselima. Ova iteracija se ponavlja sve dok broj ivica ne postane konstantan tokom cele iteracije. + + + +![Slika pre Canny-ja](/images/2022/videookulografija/BIN.jpg) +![Slika posle Canny-ja](/images/2022/videookulografija/CANNY.jpg) + + +#### 3.2.1.5. Hafova transformacija za krug + +Hafova transformacija kruga (HF)[3] [4] je algoritam koji se koristi za detekciju objekata u zavisnosti od zadatih parametara. +U ovom radu HF se primenjuje kako bi se istakla tačna lokacija zenice, njenog prečnika i koordinata centra, tj. potreban je 3D Hafov prostor za detekciju kruga. +Jedan nedostatak predstavlja to što je kompijutersko računanje ovim metodom zahtevno jer traži najveću vrednost koja definiše krug u prostoru. +Zato, u slučaju da se pojavi više krugova na slici, radi se sledeće: + + +1. parametrom minimalnog rastojanja se zadaje rastojanje između centra krugova i tako se sužava broj onih koji se posmatraju + + +2. metod Hafov Gradijent koji koristi informacije o gradijentu ivica i ima veći prag nego oni u Keni metodi + + +3. zadavanje praga akumulatora za centre krugova u fazi detekcije - više lažnih krugova se otkrije ako je prag manji + + +4. zadavanje minimalnog i maksimalnog prečnika kruga koji dolazi u obzir. +Na ovaj način je sigurno detekovan jedan, najveći krug u zadatom opsegu, tj. detektovana je zenica oka. + +![Slika sa detektovanom zenicom](/images/2022/videookulografija/DETEKTOVANA.jpg) +#### **3.2.2. Obrada podataka** + +#### 3.2.2.1. Mean average filter + + +Kada je zenicu detektovana potrebno je uraditi test gde se na ekranu pojavljuje devet tačaka u koje se gleda određen broj sekundi. +U toku eksperimenta dobijaju se koordinate zenice i tačke u koju trenutno gledamo, tako pravimo bazu podataka koje će nam biti potrebna za dalji rad. + + +Dobijeni podaci imaju šum (kao što je treptaj, nenamerno pomeranje oka ili kamere i slično) koji se otklanjaju mean avarage filterom (filter srednje aritmetičke vrednosti). +Prolazići kroz bazu izračunava se aritmetička vrednost prethodnih n merenja koordinata zenice i te nove vrednosti se postavlja kao nove koordinate zenice. Na taj način se dobija filtrirano merenje. + +Na slikama ispod se mogu videti grafovi filtriranih merenja, x i z ose u odnosu na vreme. + + +![Koordinate x-ose u odnosu na t](/images/2022/videookulografija/filtriranx.jpg) + + +![Koordinate y-ose u odnosu na t](/images/2022/videookulografija/filtrirany.jpg) + + + +#### 3.2.2.2. Linearna regresija + + +Kako bi mogli da uz spomoć naše detekcije zenice kontrolišemo neki objekat na računaru potrebno je da znamo na osnovu koordinata našeg oka u koju tačku na ekranu gledamo. +Za to smo koristili linearnu, tj. polinomialnu regresiju jer naš sistem nije linearan. + +Linearna regresija predstavlja modelovanje relacija između jedne ili više zavisnih promenljivih i jedne ili više nezavisnih promenljivih. +Model linearne regresije ima oblik $Y = X * b $, gde je Y vektor izmerenih vrednosti(u našem slučaju koordinate našeg pogkleda na ekranu), X vektor inputne promenljive(u našem slučaju koordinate zenice oka) i b vektor koificijenta modela. + + +#### 3.2.2.3. Polinomialna regresija +Poliomilna regresija je specijalan slučaj višestruke linearne regresije gde se modeluje veza između zavisne i nezavisne promenljive, u ovom slučaju, između stvarnog položaja zenice i položaja tačke na ekranu, kao polinom n-tog stepena. +U našem slučaju, nema linearne korelacije između promenljivih (slika 1.1), pa se radi veće preciznosti promenjuje poliomilna regresija (slika 1.2). slika 1 slika 2 -Formula glasi: $y= b0+b1x1+ b2x12+ b2x13+...... bnx1n$, gde su: -c - koificijenti regresije -n - stepen regresije (u ovo slučaju $n = 3$) +Formula glasi: $y= b_0+b_1 \cdot x_1+ b_2 \cdot x_2+ b_2 \cdot x_2+...... b_n \cdot x_n$, gde su: +b - koificijenti regresije +n - stepen regresije (u našem slučaju $n = 3$) -### **Rezultati i istraživanja** -Model dobijen poliomilnom regresijom smo proverile tako što smo test snimile još jednom, ali ovog puta smo dobile predviđanja položaja zenice. -Na kraju, kao rezultat smo dobile tabelu u kojoj, u odnosu na tačku na ekranu (x, y), vidimo koificijent sličnosti koordinata na ekranu i predviđenih koordinata (σx, σy). Takođe, izračunat je pomeraj između ovih dveju tačaka. (Napomena – ovo je tabela rezultata sa jednim snimanjem, dodatno prikupljanje podataka je u toku.) +## **4. Rezultati i istraživanja** +Model dobijen poliomilnom regresijom je proveren tako što je eksperiment snimiljen još jednom, ali ovog puta je dobijen predviđen položaja zenice. +Na kraju, kao rezultat je dobijena tabela u kojoj, u odnosu na tačku na ekranu (x, y), se može videti pomerenost estimacije i standard devijacije rasipanja (σx, σy). +Prosečan pomeraj 121.6, a prosečan +(Napomena – ovo je tabela rezultata sa jednim snimanjem, dodatno prikupljanje podataka je u toku.) | X | Y | pomeraj | σx | σy | |---|---|---------|----|----| -| 100 | 100 | 133,06 | 39,53 | 57,59 | -| 700 | 100 | 162,63 | 63,66 | 13,31 | -| 1300 | 100 | 143,28 | 1,07 | 2,18 | -| 100 | 400 | 171,49 | 41,3 | 98,29 | -| 700 | 100 | 110,9 | 51,82 | 26,37 | -| 1300 | 400 | 140,46 | 32,69 | 50,97 | -| 700 | 100 | 105,11 | 59,04 | 78,9 | -| 700 | 700 | 20,02 | 67,81 | 8,08 | -| 1300 | 700 | 107,48 | 34,37 | 52,48 | +| 100 | 100 | 133.06 | 39.53 | 57.59 | +| 700 | 100 | 162.63 | 63.66 | 13.31 | +| 1300 | 100 | 143.28 | 1.07 | 2.18 | +| 100 | 400 | 171.49 | 41.3 | 98.29 | +| 700 | 100 | 110.9 | 51.82 | 26.37 | +| 1300 | 400 | 140.46 | 32.69 | 50.97 | +| 700 | 100 | 105.11 | 59.04 | 78.9 | +| 700 | 700 | 20.02 | 67.81 | 8.08 | +| 1300 | 700 | 107.48 | 34.37 | 52.48 | + + + + + +## **5. Zaključak** U budućnosti planiramo da kroz ovaj projekat omogućimo kontrolisanje kursora, tj. tastature, ili igranje video igara. +... -### Reference +### 6. Reference [^1]: Saravanan, Chandran. "Color image to grayscale image conversion." 2010 Second International Conference on Computer Engineering and Applications. Vol. 2. IEEE, 2010. -[^2]: Ding, Lijun, and Ardeshir Goshtasby. "On the Canny edge detector." Pattern recognition 34.3 (2001): 721-725. -https://www.cis.rit.edu/class/simg782/lectures/lecture_10/lec782_05_10.pdf -https://www.javatpoint.com/machine-learning-polynomial-regression -https://www.sciencedirect.com/science/article/pii/S1877705812046085 + + +[^2]: Ahmed, Ahmed Shihab. "Comparative study among Sobel, Prewitt and Canny edge detection operators used in image processing." J. Theor. Appl. Inf. Technol 96.19 (2018): 6517-6525. + + +[3]Valentina, Christie, et al. "Iris localization using circular hough transform and horizontal projection folding." Proceedings of International Conference on Information Technology and Applied Mathematics. 2012. + + +[4]Ye, Huashan & Shang, Guocan & Wang, Lina & Zheng, Min. (2015). 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