## Tuesday, December 22, 2009

### Pixel Dust

I have to keep remembering the fundamental purpose of this blog. It's  Why study math? What can I do with it when I grow up?

You can count pixels. Not pixie dust, but pixels. Pixels are points of light on your screen, or dots that make up your photograph. To go on with our discussion, we need a sample picture. Here's an Oh-So-Cute-Photo of my cat Tiger with a stuffed toy.

The information contained in a picture is measured like the area of a rectangle. We use the units of pixels (i.e. so many pixels across and so many down). You may also hear pixels defined as dots per inch, or dpi.

Pixels are just one of many things you can measure in a picture. Here are information panels you get by pressing CMD-I or CNTRL-I when you are in a photo viewing program. I used 3 different programs.

This first box shows the original image data.

The left box shows the photo as it was exported from iPhoto. The right box is after I trimmed and cropped it a bit more.

The storage space required for the file has decreased from 1.4 mb to 858 kb to 444.8 kb
The pixel count has decreased from 2048x1536 to 1478x1141 to 1280x988 pixels
The dots-per-inch (dpi) stays the same in all of these tables.

How large is the original 1.4mb, 2048x1536 pixel file, IN INCHES if displayed at 72x72 dots per inch? Would it be the same size as the actual cat?

Hmmm.

2048÷72=28.444 inches
1536÷72=21.333 inches
To display that photo in its maximum original size would require a monitor 28 x 21 inches, more or less, and that's not as large as the real cat.

How large a print could we get if we used the 858 kb, 1478x1141 pixel file, IN INCHES if printed at 300x300 dots per inch?

Well, that's
1478÷300=4.92
1141÷300=3.80
The print would be approximately 5 inches by 4 inches.

How many pixels are on a typical screen?

It depends. Here are your choices. The shaded green area in the left top corner is the size of a NTSC TV screen. The purple shaded area is the pixel count on my largest monitor at Excel Math, a WUXGA. Yours is probably somewhere in the middle.

For our sample picture, my camera was set to record at QXGA resolution, or 2048x1536.

How many mega-pixels would that be?

3,145,728 or 3 megapixels.

If you don't understand math, you can forget about understanding photography and video. We haven't even started yet with scaling, zooming, interpolating, extrapolating, etc!