{"id":5086,"date":"2021-11-25T15:39:21","date_gmt":"2021-11-25T21:39:21","guid":{"rendered":"https:\/\/sandislandobservatory.com\/?page_id=5086"},"modified":"2021-11-26T06:09:37","modified_gmt":"2021-11-26T12:09:37","slug":"understanding-histograms","status":"publish","type":"page","link":"https:\/\/sandislandobservatory.com\/technical-articles\/understanding-histograms\/","title":{"rendered":"Understanding Histograms"},"content":{"rendered":"<style>\n#ref-doc {\n color:rgb(0,0,150);\n font-size:20px;\n}\n#text-align {\n padding: 0px 50px 0px 10px;\n color:black;\n}\n#image-align {\n padding: 10px;\n float: left;\n}\n<\/style>\n<h2 style=\"padding: 10px;\">Introduction<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Histogram Example 1\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/HistogramExample_1.png\" alt=\"Histogram\" width=\"800\"><\/p>\n<p id=\"text-align\">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.<\/p>\n<p id=\"text-align\">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.<\/p>\n<p id=\"text-align\">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.<\/p>\n<p id=\"text-align\">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.<\/p>\n<h2 style=\"padding: 60px 20px 0px 10px;\">Graph Nomenclature<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Nomenclature\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Nomenclature.png\" alt=\"Nomenclature\" width=\"800\"><\/p>\n<p>Peak &#8211; Point of maximum number of pixels<\/p>\n<p>0% &#8211; Black intensity on graph left side<\/P><\/p>\n<p>25%, 50%, 75% &#8211; Gray intensity on graph center<\/p>\n<p>100% &#8211; White intensity on graph right side<\/p>\n<p>Standard Deviation &#8211; 1\/2 width of curve at half amplitude<\/p>\n<p>Foot &#8211; Point where some pixels have intensity on graph left side<\/p>\n<p>Separation &#8211; Distance from 0% intensity to the foot<\/p>\n<p>Shoulders &#8211; Point where number of pixels are increasing rapidly<\/p>\n<p>Head &#8211; Point here some pixels no longer have intensity on graph right side<\/p>\n<p>Dynamic Range &#8211; Intensity range from Foot to Head<\/p>\n<h2 style=\"padding: 70px 20px 0px 10px;\">Exposure<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Exposure\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Exposure.png\" alt=\"Exposure\" width=\"800\"><\/p>\n<p id=\"text-align\">Exposing the camera the right amount of time is very important so faint detail in the darkest part of the image can be processed later. Check the separation from 0% intensity and the foot. Longer exposures will widen the separation and will also cause very bright objects to saturate.<\/p>\n<p id=\"text-align\">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.<\/p>\n<p>The separation in example to the left is approximately 12%.<\/p>\n<h2 style=\"padding: 270px 20px 0px 10px;\">Background Level<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Background Level\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Background.png\" alt=\"Background Level\" width=\"800\"><\/p>\n<p id=\"text-align\">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.<\/p>\n<p id=\"text-align\">The background level 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.<\/p>\n<h2 style=\"padding: 210px 20px 0px 10px;\">Dynamic Range<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Dynamic Range\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Dynamic Range.png\" alt=\"Dynamic Range\" width=\"800\"><\/p>\n<p id=\"text-align\">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.<\/p>\n<p id=\"text-align\">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.<\/p>\n<h2 style=\"padding:240px 20px 0px 10px;\">Color Channel Offset<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Color Channel Offset\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Color Offset.png\" alt=\"Color Channel Offset\" width=\"800\"><\/p>\n<p id=\"text-align\">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.<\/p>\n<p><img decoding=\"async\" style=\"float: left;\" title=\"Color Balance\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/ColorBalance.png\" alt=\"Color Balance\" width=\"750\"><\/p>\n<p id=\"text-align\">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.<\/p>\n<h2 style=\"padding:30px 20px 0px 10px;\">Black Clipping<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Black Clipping\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Black Clipping.png\" alt=\"Black Clipping\" width=\"800\"><\/p>\n<p id=\"text-align\">Black clipping occurs when the graph is moved too far to the left.<\/p>\n<p id=\"text-align\">Black clippings means a loss of faint details. Avoid black clipping.<\/p>\n<h2 style=\"padding:250px 20px 0px 10px;\">White Clipping<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"White Clipping\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/White Clipping.png\" alt=\"White Clipping\" width=\"800\"><\/p>\n<p id=\"text-align\">White clipping occurs when the graph is moved to far to the right.<\/p>\n<p id=\"text-align\">White clipping means a loss of bright details. Some white clipping is acceptable on very bright stars.<\/p>\n<p>Avoid white clipping on galaxies with bright cores.<\/p>\n<h2 style=\"padding:220px 20px 0px 10px;\">Noise<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Noise\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Noise.png\" alt=\"Noise\" width=\"800\"><\/p>\n<p>The shoulder width is an indication of noise. The wider the width means greater noise.<\/p>\n<p>Noise increases when stretching an image.<\/p>\n<p>Some noise can be smoothed out during post-processing.<\/p>\n<h2 style=\"padding:230px 20px 0px 10px;\">Gaussian Noise<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Gaussian Noise 1\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Gausian 0.01 Noise.png\" alt=\"Gaussian 0.01 Noise\" width=\"800\"><\/p>\n<p>The majority of noise has a Gaussian (bell shaped) curve.<\/p>\n<p id=\"text-align\">As noise levels increase, the width of the curve will increase and the peak can decrease.<\/p>\n<p>This image was injected with 0.01 standard deviation Gaussian noise.<\/p>\n<p>Observe the width of the curve has widen slightly and the peak has reduced by almost 25%.<\/p>\n<h2 style=\"padding:180px 20px 0px 10px;\"> <\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Gaussian Noise 2\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Gausian 0.02 Noise.png\" alt=\"Gaussian 0.02 Noise\" width=\"800\"><\/p>\n<p>This image was injected with twice as much noise.<\/p>\n<p>Observe the width of the curve has widen and the peak has reduced to 40%.<\/p>\n<h2 style=\"padding:250px 20px 0px 10px;\">Uniform Noise<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Uniform Noise\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Uniform Noise.png\" alt=\"Uniform Noise\" width=\"800\"><\/p>\n<p>Uniform noise is evenly distributed across the mean value.<\/p>\n<p>This type of noise results in a flat topped peak.<\/p>\n<h2 style=\"padding:250px 20px 0px 10px;\">Noise Within Noise<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Jitter Noise\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Jitter Noise.png\" alt=\"Jitter Noise\" width=\"800\"><\/p>\n<p>Noise within noise is evident as a jittery curve.<\/p>\n<p>This means pixel intensity deviation due to noise is occurring<\/p>\n<h2 style=\"padding:400px 20px 0px 10px;\">Dark Current Noise<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Dark Current Noise\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Dark Current.png\" alt=\"Dark Current Noise\" width=\"800\"><\/p>\n<p>Dark current noise is the signal produce by a pixel in total darkness.<\/p>\n<p>longer exposures will produce more dark current.<\/p>\n<p>Notice the random spikes in the image. Hot pixels have some intensity value.<\/p>\n<p>Cold pixels have no intensity value.<\/p>\n<h2 style=\"padding:200px 20px 0px 10px;\">Banding Noise<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Banding Noise\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Banding.png\" alt=\"Banding Noise\" width=\"800\"><\/p>\n<p>Banding noise varies in frequency and can be difficult to identify.<\/p>\n<p>Try reducing histogram bit depth (resolution) if possible.<\/p>\n<p>Observe the graph has gaps between peaks.<\/p>\n<h2 style=\"padding:620px 20px 0px 10px;\">Noise Reduction<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Gaussian 0.01 Noise\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Gausian 0.01 Noise.png\" alt=\"Noise Reduction\" width=\"800\"><\/p>\n<p id=\"text-align\">Goal in noise reduction, from the histogram view point, is to reduce standard deviation and width between foot and head.<\/p>\n<p>Several passes of noise reduction will produce smoother results.<\/p>\n<p>Observe the histogram after each pass to evaluate the effectiveness of noise reduction.<\/p>\n<h2 style=\"padding:200px 20px 0px 10px;\">Blocking<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Blocking\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Blocking.png\" alt=\"Blocking\" width=\"800\"><\/p>\n<p>Blocking occurs when standard deviation exceeds the mean value that produces negative ADU values.<\/p>\n<p>Observe left side of graph for blocking as shown in the figure to the left.<\/p>\n<p>Blocking can be corrected with longer exposures or change camera parameters for lower dark current.<\/p>\n<p>Using a light pollution filter can also help.<\/p>\n<h2 style=\"padding:160px 20px 0px 10px;\">Image Acquisition<\/h2>\n<p><img decoding=\"async\" id=\"image-align\" title=\"Final\" src=\"https:\/\/sandislandobservatory.com\/\/\/wp-content\/uploads\/histogram\/Final.png\" alt=\"Final\" width=\"800\"><\/p>\n<p>Avoid excessive gain as that adds noise.<\/p>\n<p>Reduce dark current by cooling the sensor.<\/p>\n<p>Reduce light pollution as much as possible.<\/p>\n<p>Use histogram to evaluate image exposure settings before collecting hours of marginal sub-frames.<\/p>\n<h2 style=\"padding-top:180px; padding-left: 10px;\">References<\/h2>\n<p style=\"padding-left: 10px;\"><a id=\"ref-doc\" href=\"https:\/\/pixinsight.com\/doc\/tools\/HistogramTransformation\/HistogramTransformation.html#usage_009\" rel=\"noopener noreferrer\" target=\"_blank\"><u>PixInsight Histogram Transformation<\/u><\/a><\/p>\n<p style=\"padding-left: 10px;\"><a id=\"ref-doc\" href=\"https:\/\/jonrista.com\/the-astrophotographers-guide\/astrophotography-basics\/signal-noise-and-histograms\" rel=\"noopener noreferrer\" target=\"_blank\"><u>Signal &#038; Noise Histogram Transformation<\/u><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction The histogram is an essential tool for analyzing digital images. We are accustomed to looking at a three-dimensional image:<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2558,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/sandislandobservatory.com\/wp-json\/wp\/v2\/pages\/5086"}],"collection":[{"href":"https:\/\/sandislandobservatory.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sandislandobservatory.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sandislandobservatory.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sandislandobservatory.com\/wp-json\/wp\/v2\/comments?post=5086"}],"version-history":[{"count":0,"href":"https:\/\/sandislandobservatory.com\/wp-json\/wp\/v2\/pages\/5086\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/sandislandobservatory.com\/wp-json\/wp\/v2\/pages\/2558"}],"wp:attachment":[{"href":"https:\/\/sandislandobservatory.com\/wp-json\/wp\/v2\/media?parent=5086"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}