How do I know when I need to interpolate an image to get a good print? When we need to make our pictures larger, we have a number of options.

• If an image is to be increased by a small amount, it is frequently possible to do this in a single call to "image size" by entering the required value directly.
• We could reduce the resolution, although lowering image quality, when viewed from appropriate distances, results are acceptable - an example of this is a billboard where close inspection reveals the individual pixels. A common publishing standard is to use 300 dpi or greater for printing. Large prints that are viewed at a distance are sometimes printed at 200 dpi with satisfactory results.

The output from a 6 megapixel camera is a 3000 x 2000 pixel resolution. Sizing for printing at 300 dpi yields a 6.7 x 10 inch print. To obtain a larger print, we can down-rate the dpi to 200, which yields a 10x15 print. The quality can be good, but if you wanted a 12x18 print and lowered the resolution to 150 dpi, you need extra work to maintain the sharpness. A 12x18 at 150 dpi may be passable from a distance, but is not of good quality. To produce good quality enlarged images generally requires an up-sampling of the image.

• We can use software based interpolation methods to up-sample. Photo interpolation is the process by which a small image is made larger. Software tools stretch the size of an image and generate pixels to fill in the blanks. Interpolated images produce smoother lines and a better large print than if the original small image was just printed large.  Image interpolation tools enable low megapixel count images to print large images with excellent results.
• Many people believe that to increase an image size, it is better to use what is commonly referred to as stair interpolation. Some experts discovered you can get better results when up-sampling by increasing the image size in several small increments rather than one extreme step. This technique is referred to as stair interpolation. One advantage to stair interpolation is that it will work on 16-bit mode images and requires no additional software other than a standard photo editor, such as Photoshop.

The concept of stair interpolation is simple. Rather than using the image size command to go directly from 100% to 400%, you would use the image size command and only increase by about 10% to say, 110%. Then you would repeat the command as many times as it takes to get to the size you need. This can be tedious if your software does not have some automation capability. When you are done, remember that images that have been interpolated always need a bit of sharpening to give them "snap." Otherwise they will look soft.

The stair interpolation method can be used with Photoshop, Photoshop Elements and Paint Shop Pro. There are usually three formulas you can choose when interpolating your image. Bicubic, Bilinear, and Nearest Neighbor. Bicubic is usually the one that will give you the best results, but try the others. Depending on how your picture was taken, one of them may occasionally give you a better image. You can preview the results on your monitor and it's interesting to see the differences. You'll probably end up using Bicubic most of the time.

If you use Photoshop 5.0 or higher and want an automated method for stair interpolation, you could purchase Fred Miranda's stair interpolation action for about $15.

Another software interpolation method is Genuine Fractals by LizardTech's. Genuine Fractals is a Photoshop filter that can take a large file and reduce to it a much smaller file size without apparent loss of quality and yet be able to resample it upwards with no degradation of the image. With it, you can encode low to medium resolution files to a scalable, resolution-free format called STiNG (*.stn). These STN files can then be opened at any resolution you choose. For extreme up-sampling, Genuine Fractals is pretty amazing. It offers other benefits such as smaller encoded files for archival and storage.

Another popular Photoshop software filter plug-in is Extensis pxl SmartScale. This Photoshop filter offers an easy intuitive way to resample images up to 1600% with no discernable loss in printed quality.

A brief description of interpolation theory is outlined below as Interpolation Theory. This is provided for those who seek additional information.

When evaluating methods for increasing resolution, try to avoid getting caught up with how the images look on-screen. Your printer capabilities are going to play a big factor in the final results. Some comparisons may appear distinctly different on screen, but barely discernible when printed. Always make your final judgment based on printed results.

Interpolation Theory

(Extracted from: Cambridge Color)

Up-sampling requires interpolation. Image interpolation occurs in all digital photos at some stage. It occurs anytime you resize or distort your image from one pixel grid to another. Image resizing is necessary when you need to increase or decrease the total number of pixels. Remapping can occur under a wide variety of scenarios: correcting for lens distortion, changing perspective, and rotating an image.

Even if the same image resize or remap is performed, results can vary significantly depending on interpolation algorithms. It is an approximation; an image always loses some quality when interpolation is performed.

Interpolation works in two directions, and tries to achieve a best approximation of a pixel's color and intensity based on the values of surrounding pixels. The following illustrates how resizing / enlargement works:

	2D Interpolation
Original		Before	After	No Interpolation

Pixel values vary far more abruptly from one location to the next. The more that is known about the surrounding pixels, the better the interpolation becomes. Results quickly deteriorate the more you stretch an image, and it will never add detail to your image that is not already present.

There are several algorithms available to up-sample an image file and the most obvious method found within Photoshop itself, known as Bicubic Interpolation. For Photoshop users, you do not need to purchase additional software. There are other techniques offered by third parties, some for cost and some - free.

There are two types of interpolation algorithms: adaptive and non-adaptive. Adaptive methods change depending on what they are interpolating (sharp edges vs. smooth texture), whereas non-adaptive methods treat all pixels equally.

Non-adaptive algorithms include: nearest neighbor, bilinear, bicubic, spline, sinc, lanczos. Depending on their complexity, they use from 0 to 256 (or more) adjacent pixels to interpolate. The more adjacent pixels included, the more accurate they become. With more pixels being interpolated, the processing time increases. These algorithms can be used to both distort and resize.

Adaptive algorithms include many proprietary algorithms in software such as: Qimage, PhotoZoom Pro, Genuine Fractals and others. Many apply a different version of their algorithm (on a pixel-by-pixel basis) when an edge is detected - aiming to minimize unsightly interpolation artifacts in regions where they are most visible. These algorithms are designed to maximize artifact-free detail, so some cannot be used to distort or rotate.

Nearest Neighbor Interpolation

Nearest neighbor is the most basic and requires the least processing time of all interpolation algorithms. It only considers one pixel - the one closest to the interpolated point, which has the effect of simply making each pixel bigger.

Bilinear Interpolation

Bilinear interpolation considers the closest 2x2 neighborhood of known pixel values surrounding the unknown pixel. It takes a weighted average of these 4 pixels to arrive at its interpolated value. This results in a smoother looking image than nearest neighbor.

Bicubic Interpolation

Bicubic goes a step beyond bilinear by considering the closest 4x4 neighborhood of known pixels-- for a total of 16 pixels. Since these are at various distances from the unknown pixel, closer pixels are given a higher weighting in calculations. Bicubic produces noticeably sharper images than the previous methods, and may be the ideal combination of processing time and image output quality. This is the standard found in many image editing programs (e.g.; Photoshop), print drivers and in cameras.

Higher Order Interpolation: SPLINE & SINC

There are many other interpolators which take more surrounding pixels into consideration, and are thus also much more computationally intensive. These include spline and sinc, and retain the most image information after interpolation. They are useful when images require multiple rotations / distortions in separate steps. For single-step enlargements or rotations, these higher-order algorithms provide diminishing visual improvements while processing time is increased.

Interpolation Artifacts to Watch Out For

All non-adaptive interpolators attempt to find a balance between three undesirable artifacts: edge halos, blurring and aliasing.

Original
		Aliasing	Blurring	Edge Halo

Even the most advanced non-adaptive interpolators must increase or decrease one of the artifacts at the expense of the others-- therefore at least one will be visible. Note how the edge halo is similar to theartifact produced by over sharpening with the unsharp mask, and while it improves the appearance of sharpness by increasing acutance.

Adaptive interpolators may/may not produce artifacts. They can also induce non-image textures or strange pixels at small-scales. Some of the "artifacts" from adaptive interpolators may be benefits. The eye expects to see detail down to the smallest scales in fine-textured areas such as foliage, these patterns may trick the eye from a distance (for some subjects).

Anti-Aliasing

Anti-aliasing minimizes the appearance of aliased or jagged diagonal edges, or "jaggies." These give images a rough digital appearance:

Anti-aliasing removes jaggies and gives the appearance of smoother edges and higher resolution. It works by taking into account how much an ideal edge overlaps adjacent pixels. The aliased edge rounds up or down with no intermediate value, while the anti-aliased edge gives a value proportional to the amount of the edge is within each pixel:

A major obstacle when enlarging images is preventing interpolator from inducing or making aliasing worse. Many adaptive interpolators detect the presence of edges and adjust to minimize aliasing while retainingedge sharpness. Because an anti-aliased edge contains information about the edge's location at higher resolutions, it is conceivable that a powerful adaptive (edge-detecting) interpolator could to some degree reconstruct this edge when enlarging.