Digital versus Analog -- The Kell Factor

Our best definition of the Kell Factor: The ratio of the perceived number of lines of resolution to the number of scan lines or pixels covering the same distance.

"The smallest detail that can be reproduced in the image is known as a picture element (pixel). Ideally, each [of the smallest] detail [s] of the [original] scene should be represented by one picture element [in the image], that is, each scanning line would be available for one picture element along any vertical line in the image. In practice, however, some of the details in the scene fall between scanning lines, so two [scanning] lines are required for such ... [details that are one scan line high]. Thus some vertical resolution is lost. Measurements of this effect show that only about 70% of the vertical detail [s one scan line high] is represented by the scanning lines. This ratio is known as the Kell factor; it applies irrespective of the manner of scanning, whether the lines follow each other sequentially (progressive scan) or alternately (interlaced scan)."  From K. Blair Benson and Donald G. Fink, "HDTV: Advanced Television for the 1990's", 1991, McGraw Hill, NY, bracketed words added by me.

We are continuing to research this topic, some sources say that the Kell factor only pertains to the degradation caused by interlacing. One source states that the Kell factor is the ratio of the scan line thickness to the scan line spacing, which coincidentally approximates the ratio of lines of resolution to scan lines when it is close to but less than unity. We will use the term "Extended Kell Factor" to relate the vertical resolution (lines of resolution) as perceived to the number of scan lines taking into account all reasons for the degradation.

There is also recognized the "Interlace Factor" which is the ratio of lines of resolution as perceived in a video picture produced using interlaced scan, divided by the lines of resolution as perceived in the same video picture except produced using progressive scan.

The number of lines of resolution must be less than the number of scan lines or pixels (spanning the same distance) because the scan lines or pixels can straddle picture details and can sometimes yield a total blur. Since the early days of television, the effective resolution has been expressed as a Kell factor. There are probably some more modern formulas for use with digital video today but none have been widely published.

What the Kell Factor is
The Interlace Factor
Computer scanners
Judge for yourself
DVD versus analog laser disks
Redigitizing, resampling

Video resolution in general
Nyquist Theorem details
Other video topics
Other subjects

Extended Kell factor  (Revised Feb. '00)

The Extended Kell Factor is the name we give to ratio between the number of lines of resolution perceived and the number of pixels or TV scan lines being used (across the same distance) taking into account degradation that might occur in any or all steps of the image reproduction process related to the use of pixels and/or scan lines.

1.  Fine details of the original picture land between scan lines or pixels (pixel straddling) and are either lost or are widened by being represented by two adjacent scan lines (or pixels),

2.  The cathode ray tube electron beam may be finer than the scan line spacing resulting in gaps between scan lines, or may be wider resulting in overlap,

3.  The even and odd lines might not be uniformly spaced, their landing on top of one another (line pairing) being the worst case),

4.  In interlaced video on a CRT, the odd lines start to fade (darken) as the even lines are being drawn and vice versa,

5.  In an effort to reduce flicker, particularly in interlaced video, content of adjacent scan lines is blended (commingled; vertical filtering) during preparation of the source material.

In digital video, scan lines are divided into pixels horizontally and a Kell factor, not necessarily the same value perceived for vertical resolution, is applied in the horizontal direction as well. No Kell factor is applied in the horizontal direction for analog video.

Computer scanners are affected by both #1 and #2 since their sensors may pick up content from parallel stripes that could be slightly wider or narrower than the sensor sub-element spacing.

The Kell factor was based on psychological rather than scientific studies and stood for an approximation of how the human eye and brain interpreted the resolution of the video picture. In the early days (1950's), viewers of very good program material on a very good (black and white) TV set tended to see that a vertical resolution test pattern blurred out at the point where ten scan lines corresponded to seven picture details, giving a Kell factor of 0.7.

Current research suggests that the (original) Kell factor takes into account only #1 and perhaps #2 and #3 above. We do conjecture that when tests were originally done, using cathode ray tube imaging, a progressively scanned picture was not available most of the time and a photograph of the original subject was used as a comparison. This would cause #4 and perhaps #5 to affect the test results as well. Therefore researchers  back in the 1950's attempting to determine the Kell factor for a given video system may well have ended up with what I refer to here as an Extended Kell factor.

The larger the Extended Kell factor, the better. The maximum possible Extended Kell factor is 1.0. You can never reproduce more details than you have pixels. Today an Extended Kell factor of 0.85 seems about right for horizontally  moving subject matter as in digital TV while 0.7 still seems right for still pictures as in computer scanning and newspaper halftones, and for subject matter moving vertically.

The Kell factor varies depending on what expert you are talking to and also on the quality of the image reproduction system. The only Kell factor widely published so far is the value 0.7 mentioned above.

In a standard definition picture made up of 480 scan lines (the rest of the 525 lines for NTSC analog video are "black" and contain format information), applying the Kell factor of 0.7 gives about 335 lines of vertical resolution. This closely matches the broadcast horizontal resolution of 330 lines over the same distance. This was not an accident; the TV picture was originally designed to have about the same resolution both horizontally and vertically. Adding other contraints such as 4.2 MHz video bandwidth to fit the broadcast channel and a frame rate without too much flicker, the NTSC 525 line standard was arrived at. The PAL system also has horizontal and vertical resolution about the same. There are 560 visible scan lines (out of 625 total) giving vertical resolution of about 390, and a five megahertz video bandwidth giving horizontal resolution of about 400

Interlace Factor

As we stated earlier, some experts claim that the Kell factor is what is described as the Interlace Factor here.

"When interlaced scanning [drawing all the odd lines then all the even lines] is used, as in all the conventional [video] systems, the 70 percent figure applies only when the image is fully stationary and the line of sight from the viewer does not move vertically by even a small amount. In practice, these conditions are seldom met, so an additional loss of reslution, called the interlace factor, occurs under typical viewing conditions. This additional loss depends on may aspects of the subject matter and viewer attention, so there is a wide range of opinion on its extent. Under favorable conditions, the additional loss reduces the effective value of vertical resolution to not more than 50 %, that is, no more than half the scanning lines display the vertical detail of an interlaced image. Under unfavorable conditions, a larger loss can occur. The effective loss also increases with image brightness, as the scanning beam becomes ... [fatter]."  From K. Blair Benson and Donald G. Fink, "HDTV: Advanced Television for the 1990's", 1991, McGraw Hill, NY, bracketed words added by me.

You Be the Judge

First I will lay down some ground rules. Stand back a few feet when viewing these diagrams.

Analog resolution limits

If you do not understand the term "high frequency transition" you will have to take my word that as we push the limit of resolution for an analog video system (a system that does not utilize sampling into pixels), smaller and smaller details being reproduced gradually blur to a neutral gray as suggested by the diagrams above.

In other words, suppose we were viewing not so finely detailed material fully reproduced as comparable to the left diagram. Then imagine viewing similar material except smaller with correspondingly finer horizontal detail and using more and more powerful magnifying glasses to view the images. Sooner or later original source material with an appearance comparable to the left diagram, when reproduced, will start to resemble the center diagram and then the right diagram.

Let us regard the center diagram above as being "very good" video reproduction of fine detail.

The right diagram above is the approximate appearance of analog video systems near their limit of resolution. Some experts will argue that the black to white to black details must appear crisper in order to be considered "resolved". One source sets 25% and 75% for the black and white, respectively, although it requires considerable time spent working with test equipment in order to eyeball a reproduced image and state that the 25%/75% threshhold has been reached.

Now on to the judging.

The diagrams below show the blurring effects of pixel straddling when resolving fine details digitally. Stand back a few feet from the screen and judge how well you can distinguish as many dark and light bars in the lower half as there are in the upper half.. For example if you feel that the 8 details per ten pixels diagram is the last (lowest) diagram that resolved all the bars, then your opinion of the Extended Kell factor for this (still life) display is 0.8

For reference, the pixel positions are marked in red and white at the top of each diagram.

7 details per 10 pixels across

8 details per 10 pixels

8-1/2 details per 10 pixels

9 details per 10 pixels

9-1/2 details per 10 pixels

DVD versus Laser Disk

As we explained earlier, when picture details are close to one pixel in size, the pixels can straddle the details and blur them out. But when the pixels line up with the details, the details are crisp without fading if the TV set has the capability.

Because video is a motion picture, details that are straddled out in one frame will likely be resolved clearly in another frame.The viewer will therefore see fine details come and go. This writer can conjecture that today's thinking is that if the details are resolved some of the time, then the system has succeeded in resolving them. This allows the DVD player manufacturers to contend that DVD has an Extended Kell factor of 1.0 meaning the resolution equals the number of pixels. The Kell factor is also 1.0 for computer generated video where all the details line up with pixels and scan lines. Traditionally a distance equal to the screen height is used for horizontal resolution measurements so for a 4:3 aspect ratio screen, 540 pixels of the 720 pixel video frame fit within this distance. Thus DVD is often advertised as having 540 lines of resolution. Like many other consumer products, there are some DVD players that are dumbed down; for example 480 lines of resolution is quite common.

Meanwhile analog laser disks with resolution rated at 425 lines will never resolve details requiring 540 lines of resolution to resolve but will also never lose details to pixel straddling.

Computer Scanners

For digitized still pictures, such as from scanners or digital cameras, there is just one image recorded as opposed to video with its 30 or so frames per second. Thus if picture details were straddled out, they are completely lost.

It has been said (by Wayne Fulton and others) that ordinary color photographic prints have no more than 200 lines (100 line pairs) of resolution per inch.

A Kell factor of 0.65 to 0.7 is probably still valid for still pictures. If a photograph with some juxtaposed details 1/200 inch in size was being scanned into a computer, the scanner needs 286 dpi (dots per inch) to preserve those details. This equals 200 dpi divided by a Kell factor of 0.7. You can round it to 300 dpi. For digital video and computer scanning the Kell factor applies both horizontally and vertically because the displayed picture is divided into pixels in both directions.

Or, if you scan at 200 dpi expecting to realize 200 lines of resolution, details no smaller than 1/140'th of an inch will be reproduced reliably.

In addition if, a scanner has optical resolution of, say, 300 dots per inch, the sensors may well be scanning tracks a little narrower than 1/300 inch and may miss details, or, more likely, may be scanning tracks a little wider than 1/300 inch introducing some blur. Like the video picture whose scan lines were too wide and overlapped, or were too narrow leaving gaps, additional resolution loss may be perceived in the finished picture.

More on scanners and scanning resolution

Redigitizing  and Resampling

If video or a scanned picture is digital, converted to analog, and then digitized a second time (or maybe a third time), generation loss (resulting in more resolution loss )can and probably does occur. The video signal on DVD is recorded as digital. When it is output via component jacks, S-video jack, or composite video jack, it is analog. If the video is then put through a video processor (line doubler or progressive scan converter) that uses digitizing to about the same number of pixels, there will be a noticeable softening of the picture due to additional loss of horizontal resolution. HDMI and other digital connections are used to avoid the need to convert the video to analog to be transmitted to another component.

If video source material is digital, e.g. D1, prior to recording on DVD, it should not be converted back to analog during production or post production. Otherwise generation loss of resolution due to redigitizing will occur there too.

There is no easy way for the consumer to tell what went on in the production process. Every now and then someone comments that "S-video doesn't look any better than composite" or "this DVD movie doesn't look any better than the VHS tape version". It could simply be that the DVD program being viewed suffered resolution loss during production.

Resizing digital video to a different number of pixels or scan lines is a form of redigitizing and also incurs resolution loss. Of course the more pixels are used in the early stages of production, the more resolution the final product will have.

Examples of  Generation Loss From Redigitizing

Again, you be the judge. The top row in each diagram is the original source, the middle row is the representation after the first digitizing, and the lower row is the representation of a reasonable worst case going back to analog and undergoing a second digitizing using the same number of pixels. Remember, these are still pictures; a motion picture such as video will probably appear to suffer less resolution loss.

Regular DVD has a horizontal pixel count of about 720. A typical standard definition line doubler. has a 720 pixel wide video frame. A typical stand alone line doubler (or video processor) can acceptsanalog video input, perform its doubling or de-interlacing digitally, and can output an analog video signal. Therefore the top row might represent the original scene, the middle row might represent a DVD player's output, and the bottom row may represent the line doubler's output. Progressive scan DVD players should not use an analog connection internally from their decoder to their built in doubler (unfortunately not guaranteed) and therefore should have an advantage over the standard DVD player and stand alone doubler combination. The most modern line doublers also have digital (HDMI or DVI) inputs and outputs. You should use the digital connections between video components if possible to avoid or minimize generation loss due to redigitizing.

7 details per 10 pixels

8 details per 10 pixels

8-1/2 details per 10 pixels

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