One astute reader of
a previous post observed that
although I seemed to imply that only
bitmaps
can be digital images, there also exists such a thing as
vector graphics
which are also considered
digital images. At the time, it was not clear in context what was meant in
describing an image as *digital*. While I conflated digital images with bitmaps,
which is inaccurate, I was only discussing bitmaps in that post, and the
conclusions therein are still valid.

Nevertheless, that reader raised a few interesting and related points.

What does it mean for an image to

*be*digital?What does it mean for a digital image to

*contain digital data*? What does it mean for a digital image to contain non-digital (continuous) data?Why do we not care about applying our techniques to non-digital images?

I would like to address the second point, which may be a point of confusion. In answering it, I hope the answer to the first and third points will become more readily apparent.

### Bitmaps and Digital Data

As discussed in the previous post, bitmaps (also known
as raster images) are a kind of digital image. Actually when people discuss
digital images they are * almost always* referring to bitmaps. This is in no
small part due to the ready availability of bitmaps in the form of digital
photographs, Adobe Photoshop, and even Microsoft Paint, all of which contain and
operate on bitmaps. The vast majority of digital images are bitmaps.

However, there is more to calling bitmaps digital images than just the
commonality of bitmaps. The bitmap actually *contains* digital data in the form
of pixels, which are element-wise approximations of a greater whole. In the
majority case of a digital photograph, the digital photograph is approximating
the real, continuous image seen by a digital camera when the picture was taken.

To elaborate on that point, consider the case of film photography vs. digital photography — how much information is stored in each image? Ken Rockwell explains on his excellent website that the “resolution” of film is anywhere between about 87 megapixels to almost 2000! As most digital cameras these days take images with around 15 megapixels, that means film is still technically between 6 to several hundred times more data- dense than digital. Does that mean that digital images actually convey less information? Yes and no. Yes, they technically don’t have as much data, but at the same time, both formats present a perfectly acceptable presentation of the original scene. The takeaway is — a set of digital data are approximating a nearly infinitely large set of data using a small, finite sampling of the original set; and that the digital data represents the camera’s “own subjective reality” of the image it saw.

### Vector Graphics

When explaining bitmaps, I referenced pointillism, the art of creating a picture from many small points, and how these points approximate a larger, whole picture. For painters (and likewise for drawers), the points are only painted to facilitate the greater painting. However, if they so chose, they could simply paint shapes. In fact, painting shapes is the classical art form when it comes to painting, and pointillism is an alternate form.

Although obtaining digital images in the form of bitmaps is easy due to digital photography, there is another way to obtain a digital image (digital here meaning able to be stored on a computer). Much like painters can paint shapes of color and texture, digital graphic artists can also generate shapes of color and texture.

The technique for doing this is a little bit involved, but it revolves around
the idea of Bézier curves.
Put simply,
Bézier curves are special, mathematically defined lines which can be coaxed into
any shape, have any length, and be placed in any position in space. (The name
*vector* comes from the mathematical notion of vector being a line in space with
specific endpoints.) This makes them very powerful for forming shapes —
essentially a circle is just a singe curve, a square four curves, etc. Even
letters can be so represented!

The advantage to approaching digital images as a series of mathematically- defined geometric shapes is related to resizing the image. Because the shapes are described mathematically, their “size” is arbitrary. A circle can be small or large, a line can be any width, etc. This is ideal for distributing graphics on the Internet, because viewers' screens can be any size. The scalability of the size of vector images means that the image can be perfectly clear and the right size in all situations. This is not so with bitmaps, where either multiple copies of the same graphic are used at various sizes, or one extremely large image is used everywhere. (This is in addition to the storage advantages from storing a constant set of mathematical equations which work at all sizes.)

### Why Do We Only Process Bitmaps?

If you’ve followed everything so far, the answers to the questions raised previously should be falling into place. A digital image is, generally speaking, an image stored digitally on a computer; however, it more often refers to bitmaps, which is a digital image containing digital data.

Furthermore, we only speak about processing bitmaps because bitmaps
*represent something greater than the sum of their pixels*,
while vectors are
*nothing more than the sum of their equations*. A digital photograph is trying to capture an
entire scene of infinite details with only a finite set of information!
Processing that digital photograph can reveal hidden details, enhance
aesthetics, and more. Simply put, there is more to the photograph than just the
pixels.

On the other hand, vectors are generated by artists in a vacuum. There are no
hidden details or sub-optimal aesthetics which can be improved by analyzing the
properties of the image. The generated image *is exactly the sum of its parts*.
There is nothing more or less than what was put their by its artist.

That’s not to say that techniques which work on bitmaps won’t work on vectors — in fact, they would most likely be easier to apply. There just isn’t any point. Unlike bitmaps, where the image is a finite, lossy approximation of what once was, a “secondary source”, a vector is an infinite representation of the present, a “primary source”. Advanced algorithms are needed to coax more details out of a bitmap, or to try and modify it without damaging the original image, because it is difficult to modify the secondary source without losing the information it has from its primary source. On the other hand, anyone can simply open up a vector image and begin modifying it, because they have the primary source.

### Conclusion

In one sense, bitmaps are much more crude than vectors, because they’re a limited copy. Yet there’s also many more possibilities — a vector image needs to be generated in order to convey information, while a bitmap intrinsically has information. In fact, detailed digital images such as digital photographs can have many fine details which can be incredibly hard to recreate using vector images. Although bitmaps may only have so many pixels, each pixel is its own sandbox.