From e583efc7799a2faf40b44f57cee6b550c24a6a0e Mon Sep 17 00:00:00 2001 From: Darakuu Date: Wed, 17 Jan 2024 19:59:26 +0100 Subject: [PATCH] Stima del movimento, fino a movimento camera --- content/03-Stima Movimento.md | 135 +++++++++++++++++- .../03-Stima Movimento-20240117184241159.png | Bin 0 -> 157170 bytes .../03-Stima Movimento-20240117191225297.png | Bin 0 -> 254356 bytes .../03-Stima Movimento-20240117192511672.png | Bin 0 -> 41256 bytes .../03-Stima Movimento-20240117193222700.png | Bin 0 -> 210179 bytes .../03-Stima Movimento-20240117194555031.png | Bin 0 -> 70714 bytes .../03-Stima Movimento-20240117195242072.png | Bin 0 -> 87624 bytes 7 files changed, 132 insertions(+), 3 deletions(-) create mode 100644 content/Attachments/03-Stima Movimento-20240117184241159.png create mode 100644 content/Attachments/03-Stima Movimento-20240117191225297.png create mode 100644 content/Attachments/03-Stima Movimento-20240117192511672.png create mode 100644 content/Attachments/03-Stima Movimento-20240117193222700.png create mode 100644 content/Attachments/03-Stima Movimento-20240117194555031.png create mode 100644 content/Attachments/03-Stima Movimento-20240117195242072.png diff --git a/content/03-Stima Movimento.md b/content/03-Stima Movimento.md index bf10411..62ae3f8 100644 --- a/content/03-Stima Movimento.md +++ b/content/03-Stima Movimento.md @@ -6,25 +6,149 @@ tags: # Telecamera +Siano: +- F: Lunghezza Focale; +- C: centro focale; +- Z: Profondità +## Prospettica + +Assumiamo che: +- L'origine del sistema di coordinate 3D globale sia localizzata in C; +- Il piano XY sia parallelo al piano xy (nel sistema di coordinate dell'immagine); +- Il sistema di riferimento globale e quello dell'immagine usino la stessa unità di misura. + +Sistema con Prospettiva: la dimensione di un'oggetto sull'immagine è inversamente proporzionale alla sua distanza. + +![[03-Stima Movimento-20240117184241159.png|384]] + +$x,y$ piccole rappresentano la posizione della proiezione 2D, +$X,Y,Z$ coordinate nel mondo reale 3D.  + + +Se la focale F della camera diminuisce, il piano si avvicina a C, e il punto proiettato in 2D si sposta.  + +Se aumenta C: +- Il piano si allontana; +- L'oggetto si avvicina. + +### Proiezioni Prospettiche + +Basate su proporzioni. + +- $\dfrac{x}{F}=\dfrac{X}{Z}$  +- +- $\dfrac{y}{F}=\dfrac{Y}{Z}$  +- +- $x=F\cdot \dfrac{X}{Z}$  +- +- $y=F\cdot \dfrac{Y}{Z}$  + + + ## Ortografica -## Prospettica +Assumiamo che gli oggetti da rappresentare nell'immagine siano a distanza (Z) molto grande.  + +In Ortografia, la dimensione di un oggetto sull'immagine è indipendente dalla sua distanza. + +Le proiezioni sono molto semplici: +- $x = X$ +- $y = Y$ + +Dato che non tengo conto della profondità, non mi interessa neanche la focale. ### Note sulle proiezioni +**Invertibilità:** Sia le proiezioni prospettiche che quelle ortografiche stabiliscono una relazione molti-a-uno. +- Per invertire il processo e ricostruire una scena 3D partendo da un'immagine 2D ho bisogno di informazioni aggiuntiva (z-mapping, stereoscopia...); +- Insomma, perdendo la Z, il processo non è facilmente invertibile (al più posso stimare la distanza con regressione). + +**Occlusione:** Nell'immagine compaiono solo gli oggetti che intercettano per primi le linee di visioni che partono dal centro focale C, ovviamente. + ### Modello CAHV +- $C$ : Centro focale; +- $A$ : Versore Z; +- $H_{0}$ : Versore X; +- $V_{0}$ : Versore Y + +Permette una visualizzazione più comoda del sistema di riferimento della videocamera se questa è in movimento, e inoltre, può descrivere un piano dell'immagine non allineato al sistema di riferimento della videocamera (**distorsione del sistema ottico**). + +![[03-Stima Movimento-20240117191225297.png|512]] + +Dalle formule sulle proiezioni prospettiche, ricaviamo: + +$p=\displaystyle\binom{x}{y}=\dfrac{F}{A^T\cdot (P-C)}\cdot \binom{H_{0}^T\cdot (P-C)}{V_{0}^T\cdot (P-C)}$ + +Dove: + +- $P-C$ è la traslazione dall'origine; +- I versori A,H,V sono trasposti perché normalmente troviamo i vettori in colonna, qui li rappresentiamo in riga. + +Essenzialmente questo modello applica un cambio di sistema di riferimento, dato che si ha una traslazione dell'origine. + # Movimenti ## Spostamenti in 3D e 2D +![[03-Stima Movimento-20240117192511672.png]] + +Siano: +- Posizione iniziale a $t_{1}:$ + - $X = [X,Y,Z]^T$ +   + + - $x=[x,y]^T$ +   + +- Posizione finale a $t_{2}:$ + - $X' = [X',Y',Z']^T=[X+D_{X},Y+D_{Y},Z+D_{Z}]^T$ +   + + - $x'=[x',y']^T=[x+d_{x},y+d_{y}]^T$ +   + +- Spostamento 3D: $D(X;t_{1},t_{2})=X'-X=[D_{X},D_{Y},D_{Z}]^T$ +- Spostamento 2D: $d(x;t_{1,t_{2}})=x'-x=[d_{x},d_{y}]^T$ +- D è il vettore di spostamento, il *displacement*. ### Modelli di movimento in 2D +Quando abbiamo degli istanti $t_{1}$ e $t_{2}$ ben identificati (sempre nei video) allora si può scrivere solo $d(x)$.  + +Un altro nome per $d(x)$ displacement è "Vettore di movimento 2D", oppure **Motion Vector** (MV).  + +Un'insieme di motion vector per ogni $x$ dell'immagine è detto **Motion Field**. + +![[03-Stima Movimento-20240117193222700.png|512]] +  + +Esempio di Motion Field. +#### Funzione di mapping + +$w(x)=x+d(x)$  + +Ci interessa sapere il movimento di tutti gli elementi della immagine (a seconda della separazione che utilizziamo, pixel, blocchi, etc...). + +Ogni pixel contiene un valore diverso da quello iniziale. All'inizio, $d(x)$ potrebbe non essere noto. Di solito infatti si stima un $w'(x)$, perché $w(x)$, cioè il movimento reale, è difficile da stimare correttamente.  + +Se ci sono molti elementi $w'(x)\longrightarrow 0$ significa che mi sono avvicinato molto a $w(x)$, e quindi ho stimato correttamente il movimento. + ## Movimenti della Telecamera -Booming, Tracking, Dollying, Zoom;   +| Traslazione | Asse Perno | Rotazione | +| :--: | :--: | :--: | +| Tracking | $\textcolor{red}{X}$ | Tilting | +| Booming | $\textcolor{blue}{Y}$ | Panning | +| Dollying | $\textcolor{green}{Z}$ | Rolling | + +- Con Z: asse perpendicolare all'immagine (di profondità), e Y: asse altezza. +- Potrebbe non essere immediatamente chiaro nel contesto delle rotazioni: immagina di utilizzare l'asse di rotazione appunto come 'perno' su cui la telecamera ruota. + +![[03-Stima Movimento-20240117195242072.png|512]] + +> [!warning] Dollying != Zooming + -Panning, Tilting, Rolling ### Modello a 4 parametri @@ -42,6 +166,11 @@ Panning, Tilting, Rolling ### Three-Step Search + +> [!warning] RISPOSTA DOMANDA ESAME❗ : + +$L=\log_{2}R_{0}+1$ formula fondamentale da ricordare. + ## Features from Accelerated Segment Test (FAST) ### High-Speed Test diff --git a/content/Attachments/03-Stima Movimento-20240117184241159.png b/content/Attachments/03-Stima Movimento-20240117184241159.png new file mode 100644 index 0000000000000000000000000000000000000000..9de899ed8be4112f79479c6f94f2f1ff3d71635d GIT binary patch literal 157170 zcmZU)by$?!8#N3#$j~!%$IzY9&Cs1HB}yX=(m8YqNK1DM2na}bNrOmt3Id9h#P{Gi zzw3R^_x?541rvKe`;K+5wRWVYx&k%^83qy(61I{eTpJ1L5dsMbc?$d(_)9a%n-1Uw z*;QLX2I<2X#Xb@e4U!UETG!L$unkwy==pnz8!QIBB<84m=EuQZrrac0kAv|d;V=#k zN=DVRlP51^X;iqvyalVM{ho6-2V0#e?b$^Ao60{uUqf`F#5g5KbFDbk~) zjwD;23?5;iAOdM|L%=Q0#^D|Op10I!caQQ(KX;Wi(yoV$`tm)~s?gGpIzWeV_)F6Wn;|Ja+h_OXk zNmzk%)j)G%ad42}gsjV+K3&a^h+IflRhY>b(|_zSPQq5({&RNO{0uXc98*f0vd5 zX2+MU?+%29<9sG4h~C@MWQ@k(ykpXWa|M0qk22SUA#8-t->nyif*EDGfMfg5S-Mjo zXMjZ{zwhO4goK@z1zeF(K7rHs9=9xW8l#ljecdCuu3S8NtA$GlYua39BQ|;jES?ws 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