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![Page 1: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/1.jpg)
Fundamentals of Image Formation
Lecture 2Jitendra Malik
![Page 2: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/2.jpg)
A camera creates an image …
The image I(x,y) measures how much light is captured at pixel (x,y)
We want to know•Where does a point (X,Y,Z) in the world get imaged?•What is the brightness at the resulting point (x,y)?
![Page 3: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/3.jpg)
The Pinhole Camera
xy
![Page 4: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/4.jpg)
Let us prove this …(This diagram is for the special case of a point P in the Y-Z plane)
![Page 5: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/5.jpg)
Let us prove this …(This diagram is for the special case of a point P in the Y-Z plane)
![Page 6: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/6.jpg)
The Pinhole Camera
xy
![Page 7: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/7.jpg)
The image is invertedThis was pointed out by Kepler in 1604
But this is no big deal. The brain can interpret it the right way. And for a camera, software can simply flip the image top-down and right-left. After this trick, we get
From Descartes(1637), La Dioptrique
![Page 8: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/8.jpg)
Some perspective phenomena…
![Page 9: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/9.jpg)
Parallel lines converge to a vanishing point
![Page 10: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/10.jpg)
Nearer objects are lower in the image
![Page 11: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/11.jpg)
Nearer objects look bigger
![Page 12: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/12.jpg)
Parallel lines converge to a vanishing point
![Page 13: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/13.jpg)
ProofLet there be a point A and a direction vector D in three dimensional space.
![Page 14: prueba](https://reader036.fdocuments.in/reader036/viewer/2022070501/568bf1351a28ab893392577d/html5/thumbnails/14.jpg)