Introduction

The histogram is an essential tool for analyzing digital images. We are accustomed to looking at a three-dimensional image: Width, Height, Intensity. However, the histogram graph is a two-dimensional representation of a digital image. The histogram horizontal x-axis represents image intensity from black on the left side to white on the right side. The histogram vertical y-axis represents the total number of pixels at each intensity.

The digital intensity of jpg images has a range of 2^8 (256) unique values. An astrophotography raw digital image could have 2^16 (65536) unique values. The range of plotted histogram intensity values on the x-axis is typically 256 values. Intensity values from a raw digital image may have to be compressed to fit the unique values into 256 possibilities. Some histogram applications permits the user to adjust the range of plotted intensity values.

For example, a raw image that has 2^10 (1024) intensities is compressed 4:1 to fit 1024 intensities into 256 possible intensity values for the histogram.

Another example, a raw image that has 2^16 (65536) intensities is compressed 256:1 to fit 65536 intensities into 256 possible intensity values for the histogram.

Graph Nomenclature

Peak – Point of maximum number of pixels

0% – Black intensity on graph left side

25%, 50%, 75% – Gray intensity on graph center

100% – White intensity on graph right side

Standard Deviation – 1/2 width of curve at half amplitude

Foot – Point where some pixels have intensity on graph left side

Separation – Distance from 0% intensity to the foot

Shoulders – Point where number of pixels are increasing rapidly

Head – Point here some pixels no longer have intensity on graph right side

Dynamic Range – Intensity range from Foot to Head

Exposure

Exposing the camera the right amount of time is very important so faint detail in the darkest part of the image can later be processed. Check the separation from 0% intensity and the foot. Longer exposures will widen the separation and will also cause very bright objects to saturate.

Some separation is better than none so very faint detail can be extracted later. A saturated star will not look that bad, unless it is severely saturated.

The separation in example to the left is approximately 12%.

Background Level

The peak point represents the maximum number of pixels that typically defines the intensity level of the background signal, sometimes called sky-fog due to light pollution. For many astronomy images the peak point will be true background level because the majority of the pixels are at that intensity. Images taken will filters can cause the peak point to vary considerably. If all the pixels were at the same intensity, the graph would just be a vertical line for the background level. It is normal for the graph to have some width between the shoulders due to Gaussian distribution of light.

Background Value

The background value in ADU can be extracted from the graph. The peak is approx. 19%. If histogram has 256 intensity levels, then multiply 0.19 by 256 to get 48.6. Image was 16-bit so multiply 48.6 by 256 since the image is being compressed 256:1. Final answer is 1555 ADU.

Dynamic Range

The peak point represents the maximum number of pixels that typically defines the intensity level of the background signal, sometimes called sky-fog due to light pollution. For many astronomy images the peak point will be true background level because the majority of the pixels are at that intensity. Images taken will filters can cause the peak point to vary considerably. If all the pixels were at the same intensity, the graph would just be a vertical line for the background level. It is normal for the graph to have some width between the shoulders due to Gaussian distribution of light.

The example to the left has a dynamic range from 12% to 94%. There is some room left to stretch the image and extend the dynamic range.

Color Channel Offset

An offset occurs when the peak point of each color channel is not aligned with each other. For neutral sky background, these peaks should occur at the same intensity.

Color Channel Offset

Aligning the colors left and right will change the color balance. Graph color will change where the curves overlap each other. White is produced where all 3 colors overlap. The goal is to fit align all 3 channels for the correct color balance. This can be challenging at times.

Black Clipping

Black clipping occurs when the graph is moved too far to the left. Black clippings means a loss of faint details. Avoid black clipping.

White Clipping

White clipping occurs when the graph is moved to far to the right. White cliping means a loss of bright details. Some white clipping is acceptable on very bright stars. Avoid white clipping on galaxies with bright cores.

Noise

The shoulder width is an indication of noise. Wider the width means higher noise. Noise increases when stretching an image. Noise can be smoothed out during post-processing.

Gaussian Noise

The majority of noise is Gaussian (bell shaped curves). As noise levels increase, the width of the curve will increase and the peak can decrease. The image on the left was injected with 0.01 standard deviation Gaussian noise. Observe the width of the curve widen slightly and the peak has reduced by almost 25%.

Gaussian Noise

Twice as much noise was injected on the next image. Observe the width of the curve has widen and the peak has reduced to 40%.

Uniform Noise

Uniform noise is evenly distributed across the mean value that results in a flat topped peak as seen in the figure to the left.

Noise Within Noise

Noise within noise is evident as a jittery curve. This means pixel intensity deviation due to noise is occurring

Dark Current Noise

Dark current noise is the result of pixels that are not responding to the exposed light. Random spikes occur in the image to the left. Hot pixels have some intensity value. Cold pixels have no intensity value.

Banding Noise

Banding noise varies in frequency and can be difficult to identify. Try reducing histogram bit depth (resolution) if possible. Observe graph for gaps between peaks.

Noise Reduction

Goal in noise reduction from the histogram vie point is to reduce standard deviation and width between foot and head. Several passes of noise reduction will produce smoother results. Observe the histogram after each pass to evaluate the effectiveness of noise reduction.

Blocking

Blocking occurs when standard deviation exceeds the mean value that produces negative ADU values. Observe left side of graph for blocking as shown in the figure to the left. Blocking can be corrected with longer exposures or change camera parameters for lower dark current. Using a light pollution filter can also help.

Image Acquisition

Avoid excessive gain as that adds noise. Reduce dark current by cooling the sensor. Reduce light pollution as much as possible. Use histogram to evaluate image exposure settings before collecting hours of marginal sub-frames.

References

PixInsight Histogram Reference Document

Histogram Transformation Documentation

Histogram Signal To Noise

Astrophotography Basics: Signal, Noise and Histograms

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