Bitmap Image Rotation: Staircasing & Interpolation

London Wall in Rain, 1981
London Wall in Rain, 1981

When you perform a rotation operation on a bitmap image, such as a digital photograph that you’re trying to straighten, you may sometimes create an undesirable effect called staircasing, where what were apparently straight and smooth edges in the original image become noticeably “stepped” in the rotated result. I noticed this problem recently when I tried to correct a shooting error in the image above (the version above shows the corrected image).

This article explains:

Staircasing: the Problem

Generally, whenever someone takes a photograph of a natural scene, they attempt to align the camera so that the ground line will appear exactly horizontal, and so that vertical edges in the scene will be truly vertical in the image.

However, the photographer doesn’t always achieve this, and that is becoming a more frequent problem in these days of smaller cameras. When you’re holding up your phone camera, it can be very difficult to ensure that it is exactly perpendicular to the horizon.

There are apps that you can install on your phone that display a “torpedo level” widget, so that you can determine when your device is exactly horizontal, but most people don’t use such apps. In any case, once a photo has been taken, you usually can’t go back and take it again.

Below is an example of an image where what should be vertical edges are not quite vertical, due to the angle at which the camera was held when the photograph was taken. I took this photo in London in 1981, and since then many of the buildings in the picture have been demolished, so there’s zero chance of being able to retake the photo!

Uncorrected Image
Uncorrected Image

If you look closely at the image above, you can see that what should be a vertical edge nearest to the centerline of the picture is not quite vertical. It’s tilted about 1° counter-clockwise. In theory, it’s easy to fix this by rotating the entire image 1° clockwise. However, if this is not done carefully, staircasing effects can result.

Below is an example of visible staircasing in a portion of the rotated image, resulting from an attempt to straighten the verticals in the original. (This is an enlargement to show the effect.) Notice the jagged transitions where the bright lamps contrast with the dark background.

Staircasing Effect in Bitmap Image
Staircasing Effect in Bitmap Image

How can you avoid this undesirable effect? Below, I offer a couple of solutions, but it’s important to bear in mind these overriding principles:

  • Except for rotations in multiples of 90°, you should avoid rotating images unless absolutely necessary, because most rotations result in loss of detail.
  • If you must rotate an image, perform only one rotation to achieve the final result, because each individual rotation introduces errors. For example, if you want to rotate your image by 3°, do that as one 3° operation rather than three consecutive 1° operations.

Staircasing: the Cause

As I explained in an earlier post, when you take a digital photograph, your camera creates a rectangular bitmap matrix of colored “dots” or pixels. The color value of each pixel is determined by the color of light shining on that particular detector in the sensor.

If you subsequently want to change the mapping of the color values to the bitmap matrix, as happens if you want to resize or rotate the image, then there has to be a way to determine the new color value of each pixel in the modified image.

The simplest way to determine the new color value of each pixel is simply to pick the value of the nearest corresponding pixel in the original image. (This is called Nearest-Neighbor Interpolation.) However, in areas of the image where there are sharp transitions of color, this method can lead to jagged edges and the effect called Staircasing.

(If you rotate a bitmap through some exact multiple of 90°, then this effect does not appear, because the original rectangular matrix maps exactly to a new rectangular matrix. The discussion here relates to rotations that are not a multiple of 90°.)

The following example shows a simple case of this problem. In these images, I’ve deliberately enlarged everything to the point that you can see the individual pixel boundaries; you would rarely see these at normal viewing magnifications. I’ve also tilted an edge that was originally vertical into a non-vertical position, rather than vice versa, because this shows the effect more plainly.

In the first image, on the left is the original unrotated image, which consists only of a dark rectangle abutting a light-colored rectangle. The transition between the two colors is a vertical edge, which maps neatly to the vertical alignment of the pixels.

Rotation of Bitmap without Interpolation
Rotation of Bitmap without Interpolation

On the right above is the result of rotating this image by 1 degree counter-clockwise, without any interpolation. Each new pixel takes the color value of the nearest pixel in the original image. Since the transition between the colors no longer maps neatly into vertically-aligned pixels, a jagged edge transition has now been created.

To reduce the quantization effects, a more sophisticated way of determining the new pixel values is by interpolation. Interpolation is basically a sophisticated form of averaging, whereby the color value of each interpolated pixel is determined by averaging the values of the nearest few pixels in the original image.

Here’s the same rotation operation, but with interpolation applied:

Rotated Bitmap with Interpolation
Rotated Bitmap with Interpolation

As you can see, the jaggedness is reduced, although there are still visible discontinuities, due to the small number of pixels involved.

Staircasing: the Solution

As demonstrated above, the staircasing effect is caused by inadequate interpolation of color values between adjacent pixels in a bitmap. If the interpolation could somehow be made perfect, the problem would not occur.

Typically, when we rotate an image, we’re using third-party software, and we’re stuck with whatever interpolation algorithm has been provided by the software manufacturer (which may consist of no interpolation at all). Thus, we can’t improve the interpolation, so all we can do is to take steps to disguise the problem.

  1. Use Interpolation
  2. Increase Resolution

Solution #1: Make Sure to Use Interpolation

Whenever you notice staircasing in a rotated image, the first thing to check is whether interpolation was applied during the rotation operation. Depending on the software you used to perform the rotation, interpolation may not have been applied by default, or, in the case of some low-end software, it may not even be available.

Look for an “interpolation” setting in your software. In some cases, this is referred to as “anti-aliasing”, even though there isn’t really any “aliasing” in this case. Make sure that “interpolation” or “anti-aliasing” are switched on.

Solution #2: Increase Image Resolution

If using interpolation doesn’t work, then the second approach is to try to reduce the quantization artefacts by temporarily increasing the Image Resolution. Most modern bitmap processing (“Paint”) software allows you to do this quite easily.

The procedure is as follows:

  1. Use your paint software to increase the image DPI. To minimize the amount of unnecessary interpolation required, it’s usually best to set the new DPI value to be an exact multiple of the current value. For example, if the image currently has 72 DPI, try increasing to four times that (288 DPI), or another higher multiple. (In general, the higher the DPI, the better, but of course increasing the resolution increases the total image size, so processing takes longer and requires more memory.)
  2. Perform the rotation operation.
  3. Reduce the image DPI back to the original value.
  4. Evaluate the results. If staircasing is still visible, repeat from Step 1, but this time increase the image DPI to an even higher multiple of the original.

Use Your Own Judgment

Ultimately, fixing this problem is a matter of aesthetic judgment; you have to view the results and decide when they’re good enough. What’s good enough in one situation may not be good enough in another.

I hope that my explanation has been helpful, but, if you need more detail, here is a very good post describing these concepts.

Definition: Image Size, Dimensions and Resolution

It may be helpful to remind ourselves of the differences between bitmap image size, dimensions and resolution. In my experience, these important distinctions can cause immense confusion to people working with bitmap images. That is not helped by the fact that some of these terms are used loosely and interchangeably in existing documentation, which merely adds to the confusion.

Each pixel in a bitmap image has a constant color value. The illusion that the colors in the image vary continuously occurs because the image typically consists of a very large number of pixels.

It’s intuitively obvious that each bitmap has a particular “size”, but what exactly does that term mean in this context? There’s more to it than just the number of pixels in the matrix, because that does not specify the size at which the bitmap is supposed to be viewed.

Note that these are my definitions of the terms, and you may find varying definitions in other documentation. The important point is to understand what is meant by each term, rather than which term is used for which concept.

Definitions
Definitions

Image Size: The width and height of the image (W x H) in pixels

Image Dimensions: The width and height of the image (W x H) in measurement units

Image Resolution: Dots Per Inch. It is possible for an image to have different horizontal and vertical DPI values, but this is rarely done in practice. The horizontal and vertical resolutions are usually the same.

Definition: Interpolation

Interpolation is a mathematical concept, which involves creating new data points between the data points of an existing set.

When applied to images, interpolation usually involves creating a new pixel color value by averaging the values of nearby pixels, according to some algorithm.

Digital Color Palettes: the Essential Concepts

 

Fantasy Illustration of Computer Artist using Palette for Digital Color Palettes
An Unlikely Computer Artist

The word “palette” (or “pallet”) has several meanings: it can refer to a tray used to transport items, or to a board used by artists to mix colors (as shown in the fantasy illustration above, which I produced many years ago for a talk on Computer Artwork). In this article, I’ll discuss the principles of Digital Color Palettes. If you’re working with digital graphics files, you’re likely to encounter “palettes” sooner or later. Even though the use of palettes is less necessary and less prevalent in graphics now than it was years ago, it’s still helpful to understand them, and the pros and cons of using them.

Even within the scope of digital graphics, there are several types of palette, including Aesthetic Palettes and Technical Palettes.

I discussed the distinction between bitmap and vector representations in a previous post [The Two Types of Computer Graphics]. Although digital color palettes are more commonly associated with bitmap images, vector images can also use them.

The Basic Concept

A digital color palette is essentially just an indexed table of color values. Using a palette in conjunction with a bitmap image permits a type of compression that reduces the size of the stored bitmap image.

In A Trick of the Light, I explained how the colors you see on the screen of a digital device display, such as a computer or phone, are made up of separate red, green and blue components. The pixels comprising the image that you see on-screen are stored in a bitmap matrix somewhere in the device’s memory.

In most modern bitmap graphic systems, each of the red, green and blue components of each pixel (which I’ll also refer to here as an “RGB Triple” for obvious reasons) is represented using 8 bits. This permits each pixel to represent one of 224 = 16,777,216 possible color values. Experience has shown that this range of values is, in most cases, adequate to allow images to display an apparently continuous spectrum of color, which is important in scenes that require smooth shading (for example, sky scenes). Computers are generally organized to handle data in multiples of bytes (8 bits), so again this definition of an RGB triple is convenient. (About twenty years ago, when memory capacities were much smaller, various smaller types of RGB triple were used, such as the “5-6-5” format, where the red and blue components used 5 bits and the green component 6 bits. This allowed each RGB triple to be stored in a 16-bit word instead of 24 bits. Now, however, such compromises are no longer worthwhile.)

There are, however, many bitmap images that don’t require the full gamut of 16,777,216 available colors. For example, a monochrome (grayscale) image requires only shades of gray, and in general 256 shades of gray are adequate to create the illusion of continuous gradation of color. Thus, to store a grayscale image, each pixel only needs 8 bits (since 28 = 256), instead of 24. Storing the image with 8 bits per pixel (instead of 24 bits) reduces the file size by two-thirds, which is a worthwhile size reduction.

Even full-color images may not need the full gamut of 16,777,216 colors, because they have strong predominant colors. In these cases, it’s useful to make a list of only the colors that are actually used in the image, treat the list as an index, and then store the image using the index values instead of the actual RGB triples.

The indexed list of colors is then called a “palette”. Obviously, if the matrix of index values is to be meaningful, you also have to store the palette itself somewhere. The palette can be stored as part of the file itself, or somewhere else.

To restate, whether implemented in hardware or software, an image that uses a palette does not store the color value of each pixel as an actual RGB triple. Instead, each color value is stored as an index to a single entry in the palette. The palette itself stores the RGB triples. You specify the pixels of a palettized* image by creating a matrix of index values, rather than a matrix of the actual RGB triples. Because each index value is significantly smaller than a single triple, the size the resulting bitmap is much smaller than it would be if each RGB triple were stored.

The table below shows the index values and colors for a real-world (albeit obsolete) color palette; the standard palette for the IBM CGA (Color Graphics Adapter), which was the first color graphics card for the IBM PC. This palette specified only 16 colors, so it’s practical to list the entire palette here.

CGA Color Palette Values
CGA Color Palette Table

(* For the action associated with digital images, this is the correct spelling. If you’re talking about placing items on a transport pallet, then the correct spelling is “palletize”.)

Aesthetic Palettes*

In this context, a palette is a range of specific colors that can be used by an artist creating a digital image. The usual reason for selecting colors from a palette, instead of just choosing any one of the millions of available colors, is to achieve a specific “look”, or to conform to a branding color scheme. Thus, the palette has aesthetic significance, but there is no technical requirement for its existence. The use of aesthetic palettes is always optional.

(* As I explained in Ligatures in English, this section heading could have been spelled “Esthetic Palettes”, but I personally prefer the spelling used here, and it is acceptable in American English.)

Technical Palettes

This type of palette is used to achieve some technological advantage in image display, such as a reduction of the amount of hardware required, or of the image file size. Some older graphical display systems require the use of a color palette, so their use is not optional.

Displaying a Palettized Image

The image below shows how a palettized bitmap image is displayed on a screen. The screen could be any digital bitmap display, such as a computer, tablet or smartphone.

Diagram of Palettized Image Display for Digital Color Palettes
Palette-based Display System

The system works as follows (the step numbers below correspond to the callout numbers in the image):

  1. As the bitmap image in memory is scanned sequentially, each index value in the bitmap is used to “look up” a corresponding entry in the palette.
  2. Each index value acts as a lookup to an RGB triple value in the palette. The correct RGB triple value for each pixel is presented to the Display Drivers.
  3. The Display Drivers (which may be Digital-to-Analog Converters, or some other circuity, depending on the screen technology) create red, green and blue signals to illuminate the pixels of the device screen.
  4. The device screen displays the full-color image reconstituted from the index bitmap and the palette.

Hardware Palette

In the early days of computer graphics, memory was expensive and capacities were small. It made economic sense to maximize the use of digital color palettes where possible, to minimize the amount and size of memory required. This was particularly important in the design of graphics display cards, which required sufficient memory to store at least one full frame of the display. By adding a small special area of memory on the card for use as a palette, it was possible to reduce the size of the main frame memory substantially. This was achieved at the expense of complexity, because now every image that was displayed had to have a palette. To avoid having to create a special palette for every image, Standard color palettes and then Adaptive color palettes were developed; for more details, see Standard vs. Adaptive Palettes below.

One of the most famous graphics card types that (usually) relied on hardware color palettes was the IBM VGA (Virtual or Video Graphics Array) for PCs (see https://en.wikipedia.org/wiki/Video_Graphics_Array).

As the cost of memory has fallen, and as memory device capacities have increased, the use of hardware palettes has become unnecessary. Few, if any, modern graphics cards implement hardware palettes. However, there are still some good reasons to use software palettes.

Software Palette

Generally, the software palette associated with an image is included in the image file itself. The palette and the image matrix form separate sections within one file. Some image formats, such as GIF, require the use of a software palette, whereas others, such as BMP, don’t support palettes at all.

Modern bitmap image formats, such as PNG, usually offer the option to use a palette, but do not require it.

Standard & Adaptive Palettes

Back when most graphics cards implemented hardware palettes, rendering a photograph realistically on screen was a significant problem. For example, a photograph showing a cloud-filled sky would include a large number of pixels whose values are various shades of blue, and the color transitions across the image would be smooth. If you were to try to use a limited color palette to encode the pixel values in the image, it’s unlikely that the palette would include every blue shade that you’d need. In that case, you were faced with the choice of using a Standard Palette plus a technique called Dithering, or else using an Adaptive Palette, as described below.

Standard Palette

Given that early graphics cards could display only palettized images, it simplified matters to use a Standard palette, consisting of only the most commonly-used colors. If you were designing a digital image, you could arrange to use only colors in the standard palette, so that it would be rendered correctly on-screen. However, the standard palette could not, in general, render a photograph realistically—the only way to approximate that was to apply Dithering.

The most commonly-used Standard palette for the VGA graphics card was that provided by BIOS Mode 13H.

Dithering

One technique that was often applied in connection with palettized bitmap images is dithering. The origin of the term “dithering” seems to go back to World War II. When applied to palettized bitmap images, the dithering process essentially introduces “noise” in the vicinity of color transitions, in order to disguise abrupt color changes. Dithering creates patterns of interpolated color values, using only colors available in the palette, that, to the human eye, appear to merge and create continuous color shades. For a detailed description of this technique, see https://en.wikipedia.org/wiki/Dither.

While dithering can improve the appearance of a palettized image (provided that you don’t look too closely), it achieves its results at the expense of reduced image resolution, because of the fact that the dithering of pixel values introduces “noise” into the image. Therefore, you should never dither an image that you want to keep as a “master”.

Adaptive Palette

Instead of specifying a Standard Palette that includes entries for any image, you can instead specify a palette that is restricted only to colors that are most appropriate for the image that you want to palettize. Such palettes are called Adaptive Palettes. Most modern graphics software can create an Adaptive Palette for any image automatically, so this is no longer a difficult proposition.

A significant problem with Adaptive Palettes is that a display device that relies on a hardware palette can typically use only one palette at a time. This makes it difficult or impossible to display more than one full-color image on the screen. You can set the device’s palette to be correct for the first photograph and the image will look great. However, as soon as you change the palette to that for the second photograph, the colors in the first image are likely to become completely garbled.

Fortunately, the days when graphical display devices used hardware palettes are over, so you can use Adaptive Palettes where appropriate, without having to worry about rendering conflicts.

Should you Use Digital Color Palettes?

Palettization of an image is usually a lossy process. As I explained in a previous post [How to Avoid Mosquitoes], you should never apply lossy processes to “master” files. Thus, if your master image is full-color (e.g., a photograph), you should always store it in a “raw” state, without a palette.

However, if you want to transmit an image as efficiently as possible, it may reduce the file size if you palettize the image. This also avoids the necessity to share the high-quality unpalettized master image, which could be useful if you’re posting the image to a public web page.

If it’s obvious that your image uses only a limited color range, such as a monochrome photograph, then you can palettize it without any loss of color resolution. In the case of monochrome images, you don’t usually have to create a custom palette, because most graphics programs allow you to store the image “as 8-bit Grayscale”, which achieves the same result.

In summary, then, in general it’s best not to use palettes for full-color images. However, if you know that your image is intended to contain only a limited color range, then you may be able to save file space by using a palette. Experimentation is sometimes necessary in such cases. You may also want to palettize an image so that you don’t have to make the high-quality original available publicly. If you’re an artist who has created an image that deliberately uses a limited palette of colors, and you want to store or communicate those choices, then that would also be a good reason to use a palettized image.

How to Avoid Mosquitoes (in Compressed Bitmap Images)

In this post, I’m going to explain how you can avoid mosquitoes. However, if you happen to live in a humid area, I’m afraid my advice won’t help you, because the particular “mosquitoes” I’m talking about are undesirable artifacts that occur in bitmap images.

For many years now, my work has included the writing of user assistance documents for various hardware and software systems. To illustrate such documents, I frequently need to capture portions of the display on a computer or device screen. As I explained in a previous post, the display on any device screen is a bitmap image. You can make a copy of the screen image at any time for subsequent processing. Typically, I capture portions of the screen display to illustrate the function of controls or regions of the software I’m describing. This capture operation seems like it should be simple, and, if you understand bitmap image formats and compression schemes, it is. Nonetheless, I’ve encountered many very experienced engineers and writers who were “stumped” by the problem described here, hence the motivation for my post.

Below is the sample screen capture that I’ll be using as an example in this post. (The sample shown is deliberately enlarged.) As you can see, the image consists of a plain blue rectangle, plus some black text and lining, all on a plain white background.

Screen Capture Example
Screen Capture Example

Sometimes, however, someone approaches me complaining that a screen capture that they’ve performed doesn’t look good. Instead of the nice, clean bitmap of the screen, as shown above, their image has an uneven and fuzzy appearance, as shown below. (In the example below, I’ve deliberately made the effect exceptionally bad and magnified the image – normally it’s not this obvious!)

Poor Quality Screen Capture, with Mosquitoes
Poor Quality Screen Capture, with Mosquitoes

In the example above, you can see dark blemishes in what should be the plain white background around the letters, and further color blemishes near the colored frame at the top. Notice that the blemishes appear only in areas close to sharp changes of color in the bitmap. Because such blemishes appear to be “buzzing around” details in the image, they are colloquially referred to as “mosquitoes”.

Typically, colleagues present me with their captured bitmap, complete with mosquitoes, and ask me how they can fix the problems in the image. I have to tell them that it actually isn’t worth the effort to try to fix these blemishes in the final bitmap, and that, instead, they need to go back and redo the original capture operation in a different way.

What Causes Mosquitoes?

Mosquitoes appear when you apply the wrong type of image compression to a bitmap. How do you know which is the right type of compression and which is wrong?

There are many available digital file compression schemes, but most of them fall into one of two categories:

  • Block Transform Compression
  • Lossless Huffman & Dictionary-Based Compression

Block Transform Compression Schemes

Most people who have taken or exchanged digital photographs are familiar with the JPEG (Joint Photographic Experts Group) image format. As the name suggests, this format was specifically designed for the compression of photographs; that is, images taken with some type of camera. Most digitized photographic images display certain characteristics that affect the best choice for compressing them. The major characteristics are:

  • Few sharp transitions of color or luminance from one pixel to the next. Even a transition that looks sharp to the human eye actually occurs over several pixels.
  • A certain level of electrical noise in the image. This occurs due to a variety of causes, but it has the effect that pixels in regions of “solid” color don’t all have exactly the same value. The presence of this noise adds high-frequency information to the image that’s actually unnecessary and undesirable. In most cases, removing the noise would actually improve the image quality.

As a result, it’s usually possible to remove some of the image’s high-frequency information without any noticeable reduction in its quality. Schemes such as JPEG achieve impressive levels of compression, partially by removing unnecessary high-frequency information in this way.

JPEG analyzes the frequency information in an image by dividing up the bitmap into blocks of 16×16 pixels. Within each block, high-frequency information is removed or reduced. The frequency analysis is performed by using a mathematical operation called a transform. The problem is that, if a particular block happens to contain a sharp transition, removing the high-frequency components tends to cause “ringing” in all the pixels in the block. (Technically, this effect is caused by something called the Gibbs Phenomenon, the details of which I won’t go into here.) That’s why the “mosquitoes” cluster around areas of the image where there are sharp transitions. Blocks that don’t contain sharp transitions, such as plain-colored areas away from edges in the example, don’t contain so much high-frequency information, so they compress well and don’t exhibit mosquitoes.

In the poor-quality example above, you can actually see some of the 16×16 blocks in the corner of the blue area, because I enlarged the image to make each pixel more visible.

Note that the removal of high-frequency information from the image results in lossy compression. That is, some information is permanently removed from the image, and the original information can never be retrieved exactly.

Huffman Coding & Dictionary-Based Compression Schemes

Computer screens typically display bitmaps that have many sharp transitions from one color to another, as shown in the sample screen capture. These images are generated directly by software; they aren’t captured via a camera or some other form of transducer.

If you’re reading this article on a computer screen, it’s likely that the characters you’re viewing are rendered with very sharp black-to-white transitions. In fact, modern fonts for computer displays are specifically designed to be rendered in this way, so that the characters will appear sharp and easy to read even when the font size is small. The result is that the image has a lot of important high-frequency information. Similarly, such synthesized images have no noise, because they were not created using a transducer that could introduce noise.

Applying block-transform compression to such synthesized bitmaps results in an image that, at best, looks “fuzzy” and at worst contains mosquitoes. Text in such bitmaps can quickly become unreadable.

If you consider the pixel values in the “mosquito-free” sample screen capture above, it’s obvious that the resulting bitmap will contain many pixels specifying “white”, many specifying “black”, and many specifying the blue shade. There’ll also be some pixels with intermediate gray or blue shades, in areas where there’s a transition from one color to another, but far fewer of those than of the “pure” colors. For synthesized images such as this, an efficient form of compression is that called Huffman Coding. Essentially, this coding scheme compresses an image by assigning shorter codewords to the pixel values that appear more frequently, and longer codewords to values that are less frequent. When an image contains a large number of similar pixels, the overall compression can be substantial.

Another lossless approach is to create an on-the-fly “dictionary” of pixel sequences that appear repeatedly in the image. Again, in bitmaps that contain regions with repeated patterns, this approach can yield excellent compression. The details of how dictionary compression works can be found in descriptions of, for example, the LZW algorithm.

Unlike many block transform schemes, such compression schemes are lossless. Even though all the pixel values are mapped from one coding to another, there is no loss of information, and, by reversing the mapping, it’s possible to restore the original image, pixel-for-pixel, in its exact form.

One good choice for a bitmap format that offers lossless compression is PNG (Portable Network Graphics). This format uses a two-step compression method, by applying firstly dictionary-based compression, then following that by Huffman coding of the results.

A Mosquito-Free Result

Here is the same screen capture sample, but this time I saved the bitmap as a PNG file instead of as a JPEG file. Although PNG does compress the image, the compression is lossless and there’s no block transform. Hence, there’s no danger that mosquitoes will appear.

High Quality Screen Capture without Artifacts
High Quality Screen Capture without Artifacts

Avoiding Mosquitoes: Summary

As I’ve shown, the trick to avoiding mosquitoes in screen capture bitmaps or other computer-generated imagery is simply to avoid using file formats or compression schemes that are not suitable for this kind of image. The reality is that bitmap formats were designed for differing purposes, and are not all equivalent to each other.

  • Unsuitable formats include those that use block-transform and/or lossy compression, such as JPEG.
  • Suitable formats are those that use lossless Huffman coding and/or dictionary-based compression, or no compression at all, such as PNG.

The Two Types of Computer Graphics: Bitmaps and Vector Drawings

I received some feedback from my previous posts on computer graphics asking for a basic explanation of the differences between the two main ways of representing images in digital computer files, which are:

  • Bitmap “paintings”
  • Vector “drawings”

Most people probably view images on their computers (or phones, tablets or any other digital device with a pictorial interface) without giving any thought to how the image is stored and displayed in the computer. That’s fine if you’re just a user of images, but for those of us who want to create or manipulate computer graphic images, it’s important to understand the internal format of the files.

Bitmap Images

If you’ve ever taken or downloaded a digital photo, you’re already familiar with bitmap images, even if you weren’t aware that that’s what digital photos are.

A bitmap represents an image by treating the image area as a rectangle, and dividing up the rectangle into a two-dimensional array of tiny pixels. For example, an image produced by a high-resolution phone camera may have dimensions of 4128 pixels horizontally and 3096 pixels vertically, requiring 4128×3096 = 12,780,288 pixels for the entire image. (Bitmap images usually involve large numbers of pixels, but computers are really good at handling large numbers of items!) Each pixel specifies a single color value for the image at that point. The resulting image is displayed simply by copying (“blitting”) the array of pixels to the screen, with each pixel showing its defined color.

Some of the smallest bitmap images you’ll see are the icons used for programs and other items in computer user interfaces. The size of these bitmaps can be as small as 16×16 pixels, which provides very little detail, but is sufficient for images that will always be viewed in tiny sizes. Here’s one that I created for a user interface some time ago:

icon16x16_versions2

Enlarging this image enables you to see each individual pixel:

icon16x16_versions_enlarged

You can see the pixel boundaries here, and count them to confirm that (including the white pixels at the edges) the image is indeed 16×16 pixels.

Obviously, the enlarged image looks unacceptably crude, but, since the image would normally never be viewed at this level of magnification, it’s good enough for use as an icon. In most cases, such as digital photographs, there are so many pixels in the bitmap that your eye can’t distinguish them at normal viewing sizes, so you see the image as a continuous set of tones.

Bitmap images have a “resolution”, which limits the size to which you can magnify the image without visible degradation. Images with higher numbers of pixels have higher resolution.

Given that bitmap image files are usually large, it’s helpful to be able to be able to compress the pixel map in some way, and there are many well-known methods for doing this. The tradeoff is that, the more compression you apply, the worse the image tends to look. One of the best-known is JPEG (a standard created by the Joint Photographic Experts’ Group), which is intended to allow you to apply variable amounts of compression to digital photographs. However, it’s important to realize that bitmap image files are not necessarily compressed.

Programs that are designed to process bitmap images are referred to as “paint” programs. Well-known examples are: Adobe Photoshop and Corel PhotoPaint.

Vector Images

The alternative way of producing a computer image is to create a list of instructions describing how to draw the image, then store that list as the image file. When the file is opened, the computer interprets each instruction and redraws the complete image, usually as a bitmap for display purposes. This process is called rasterization.

This may seem to be an unnecessarily complex way to create a computer image. Wouldn’t it just be simpler to stick to bitmap images for everything? Well, it probably wouldn’t be a good idea to try to store a photo of your dog as a vector image, but it turns out that there are some cases where vector images are preferable to bitmap images. Part of the skill set of a digital artist is knowing which cases are best suited to vector images, and which to bitmaps.

There are many vector drawing standards, and many of those are proprietary (e.g., AI, CDR). One open vector drawing standard that’s becoming increasingly popular is SVG (Scalable Vector Graphics). You can view the contents of an SVG file by opening it with a text editor program (such as Notepad).

Here’s a very simple example of an SVG image file, consisting of a white cross on a red circle:

icon_err_gen

(Not all browsers can interpret SVG files, so I rendered the image above as a bitmap to ensure that you can see it!)

If you open the SVG file with a text editor, you can see the instructions that create the image shown above. In this case, the important instructions look like this:

<g id=”Layer_x0020_1″>

<circle class=”fil0″ cx=”2448″ cy=”6098″ r=”83″/>

<path class=”fil1″ d=”M2398 6053l5 -5c4,-4 13,-1 20,5l26 26 26 -26c7,-7 16,-9 20,-5l5 5c4,4 1,13 -5,20l-26 26 26 26c7,7 9,16 5,20l-5 5c-4,4 -13,1 -20,-5l-26 -26 -26 26c-7,7 -16,9 -20,5l-5 -5c-4,-4 -1,-13 5,-20l26 -26 -26 -26c-7,-7 -9,-16 -5,-20z”/>

</g>

As you’d expect, the instructions tell the computer to draw a “circle”, and then create the cross item by following the coordinates specified for the “path” item.

Of course, if you were to try to represent a photograph of your dog as a vector image, the resulting file would contain a huge number of instructions. That’s why bitmap images are usually preferable for digital photographs and other very complex scenes.

A major advantage of vector image formats is that the picture can be rendered at any size without degradation. Bitmap images have inherent resolutions, which vector images do not have.

Programs that are designed to process vector images are referred to as “drawing” programs. Well-known examples are: Adobe Illustrator and Corel Draw.

Converting Between Bitmap and Vector Images

It’s often necessary to convert a vector image into a bitmap image, and, less frequently, to convert a bitmap image into a vector image.

Conversion of vector images to bitmaps occurs all the time, every time you want to view the content of a vector image. When you open a vector image, the computer reads the instructions in the file, and draws the shapes into a temporary bitmap that it displays for you.

Converting bitmaps to vector images requires special software. The process is usually called “Tracing”. Years ago, you had to buy tracing software separately, but now most vector drawing software includes built-in tracing capabilities. As the name suggests, tracing software works by “drawing around” the edges of the bitmap, so that it creates shapes and lines representing the image. The result of the operation is that the software generates a set of mathematical curves that define the vector image.

Summary of the Pros and Cons

There are situations where bitmap images are preferable to vector images, and vice versa. Here’s a summary of the pros and cons of each type.

Bitmap

Advantages:

  • Complex scenes can be depicted as easily as simple scenes.
  • Significant compression is usually possible, at the expense of loss of quality.
  • Rendering is computationally easy; requires minimal computing power.

Disadvantages:

  • Size: Files tend to be large.
  • Not scalable: attempting to magnify an image causes degradation.

Vector

Advantages:

  • Compact: Files tend to be small.
  • Scalable: images can be displayed at any resolution without degradation.

Disadvantages:

  • Complex scenes are difficult to encode, which tends to create very large files.
  • Rendering is computationally intensive; requires significant computing power.