# How Can an Object Move by Less Than a Pixel Between Two Consecutive Frames?

I think video is a series of picture frames. Consider a black & white scenario (no RGB). A picture frame is a 2D array of pixel. Each pixel has a single color. A pixel can't be half black or half white. It will be filled completely with one shade of color.

Consider 2 consecutive frames of video - let's say frame 1 and frame 2 .
Suppose frame 1 has a square-shaped object with coordinates $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ and $(x_4,y_4)$ (top-left, top-right, bottom-right and bottom-left, respectively).

Now, if the object moves to the right then in frame 2 its coordinates can be $(x_1+1,y_1)$, $(x_2+1,y_2)$, $(x_3+1,y_3)$ and $(x_4+1,y_4)$ (top-left, top-right, bottom-right and bottom-left, respectively).

How is less than that possible?

• Can you clarify what your question is? – MBaz Mar 22 '17 at 16:00
• I am more inclined to vote for the question to remain open at this point, provided that it is rephrased to more accurately reflect its subject. In the meantime, please see this link. Can you please provide a practical example of what the ideal output of determining sub pixel movement be in your application? – A_A Mar 22 '17 at 16:14
• I am not able to comprehend that an object can move by less than a pixel in consecutive frames. – user1371666 Mar 23 '17 at 14:58
• Also read the wiki link - it says anti aliasing is done so that we don't get jagged edges . Seems they fill corner pixel by lighter black so that sharp stair case isn't apparent. – user1371666 Mar 23 '17 at 15:02

## 1 Answer

The frame is 2D Grid which samples the continuous world in Discrete way.

Leave alone video for a second.
Let's talk about taking a photo of a white paper laid on a black surface.
The photo is taken from above and let's assume there is no lens issues.
Do you expect the end of the paper to end at edge of a pixel of the camera perfectly?

It won't.
The end of the paper will fall in the middle of a pixel.
Let's say that now this pixel (I leave out the blurring due to limited Frequency Sampling) has 70% White and 30% Black.
Now the camera moves the smallest movement and now the pixel is 30% White and 70% Black.

This is a less than 1 pixel movement.