{"id":443,"date":"2016-12-25T15:02:29","date_gmt":"2016-12-25T15:02:29","guid":{"rendered":"http:\/\/www.rangakrish.com\/?p=443"},"modified":"2016-12-25T15:07:08","modified_gmt":"2016-12-25T15:07:08","slug":"checking-image-overlap-with-mathematica-part-2","status":"publish","type":"post","link":"https:\/\/www.rangakrish.com\/index.php\/2016\/12\/25\/checking-image-overlap-with-mathematica-part-2\/","title":{"rendered":"Checking Image Overlap with Mathematica – Part 2"},"content":{"rendered":"

In the previous post<\/a>, we discussed one technique to check the overlap between two given images of equal dimensions. In today\u2019s post, let us look at another idea that uses Mathematica\u2019s ImageCorrespondingPoints<\/a><\/strong><\/em>\u00a0function.<\/p>\n

As per the documentation, the ImageCorrespondingPoints<\/a><\/strong><\/em> function finds a set of matching interest points between two given images and returns their coordinates. Internally it uses the ImageKeyPoints<\/a><\/strong><\/em>\u00a0function to determine the key points of each image.<\/p>\n

First, let us write a function that will highlight the corresponding points on a given pair of images.<\/p>\n

\"Corresponding<\/a>
Corresponding Points<\/strong><\/figcaption><\/figure>\n

When applied to our image sets, we get the highlighted pairs as below:<\/p>\n

\"Corresponding<\/a>
Corresponding Points Highlighted<\/strong><\/figcaption><\/figure>\n

As expected, this technique shows very little overlap between image1 and image4 (in contrast to the previous technique).<\/p>\n

An interesting variation of highlighting is to number the matching points so that we can see exactly which point is where in each image. Here is the function to do that (we restrict the number of points shown in order to prevent clutter):<\/p>\n

\"Numbering<\/a>
Numbering Points<\/strong><\/figcaption><\/figure>\n

The corresponding visualization of two images is here:<\/p>\n

\"Visualize<\/a>
Visualize Numbered Points<\/strong><\/figcaption><\/figure>\n

Let us now write a function to compute the overlap:<\/p>\n

\"Compute<\/a>
Compute Overlap<\/strong><\/figcaption><\/figure>\n

I have chosen the scale factor<\/strong><\/em> constant to bring the actual ratio close to what is perceived visually. This is a trial and error process.<\/p>\n

Here is the computed overlap percentage for the different image pairs:<\/p>\n

\"Overlap<\/a>
Overlap Percentages<\/strong><\/figcaption><\/figure>\n

I feel this technique gives a better estimate of image overlap compared to the technique we saw in the previous post.<\/p>\n","protected":false},"excerpt":{"rendered":"

In the previous post, we discussed one technique to check the overlap between two given images of equal dimensions. In today\u2019s post, let us look at another idea that uses Mathematica\u2019s ImageCorrespondingPoints\u00a0function. As per the documentation, the ImageCorrespondingPoints function finds a set of matching interest points between two given images and returns their coordinates. Internally […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[85,72,17],"tags":[88,86,87,43],"class_list":["post-443","post","type-post","status-publish","format-standard","hentry","category-image-processing","category-mathematica","category-programming","tag-image-overlap","tag-imagecorrespondingpoints","tag-imagekeypoints","tag-mathematica"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p9OLnF-79","jetpack-related-posts":[{"id":425,"url":"https:\/\/www.rangakrish.com\/index.php\/2016\/12\/05\/checking-image-overlap-with-mathematica\/","url_meta":{"origin":443,"position":0},"title":"Checking Image Overlap with Mathematica","author":"admin","date":"December 5, 2016","format":false,"excerpt":"Recently I had to solve a seemingly simple problem: Given two images, can we find out if there is any overlap between the two? Where does such a requirement arise? One use case is in photogrammetry, where in order to build an orthomosaic from multiple\u00a0images, there must be at least\u2026","rel":"","context":"In "Image Processing"","block_context":{"text":"Image Processing","link":"https:\/\/www.rangakrish.com\/index.php\/category\/image-processing\/"},"img":{"alt_text":"Sample Images","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/12\/Sampleimages.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/12\/Sampleimages.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/12\/Sampleimages.png?resize=525%2C300 1.5x"},"classes":[]},{"id":457,"url":"https:\/\/www.rangakrish.com\/index.php\/2017\/01\/16\/checking-image-overlap-with-mathematica-part-3\/","url_meta":{"origin":443,"position":1},"title":"Checking Image Overlap with Mathematica \u2013 Part 3","author":"admin","date":"January 16, 2017","format":false,"excerpt":"This is the\u00a0 third and the last in the series of articles on checking image overlap using Mathematica. Let us take a quick look at the images that we are using as samples (image1 and image3 in the first row, image3 and image4 in the second row): The first technique\u2026","rel":"","context":"In "Image Processing"","block_context":{"text":"Image Processing","link":"https:\/\/www.rangakrish.com\/index.php\/category\/image-processing\/"},"img":{"alt_text":"Sample Images","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2017\/01\/Sampleimages.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2017\/01\/Sampleimages.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2017\/01\/Sampleimages.png?resize=525%2C300 1.5x"},"classes":[]},{"id":348,"url":"https:\/\/www.rangakrish.com\/index.php\/2016\/09\/26\/computer-vision-with-mathematica\/","url_meta":{"origin":443,"position":2},"title":"Computer Vision with Mathematica","author":"admin","date":"September 26, 2016","format":false,"excerpt":"Over the past several weeks, I have been discussing many interesting features of Mathematica. As a continuation, today, I would like to show some cool functionality in the domain of computer vision and machine learning. The function ImageIdentify[] tries to identify the object in the given image. According to the\u2026","rel":"","context":"In "Machine Learning"","block_context":{"text":"Machine Learning","link":"https:\/\/www.rangakrish.com\/index.php\/category\/machine-learning\/"},"img":{"alt_text":"A Truck","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/09\/truck-fig.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":870,"url":"https:\/\/www.rangakrish.com\/index.php\/2018\/03\/25\/question-answering-in-mathematica\/","url_meta":{"origin":443,"position":3},"title":"Question Answering in Mathematica","author":"admin","date":"March 25, 2018","format":false,"excerpt":"About 10 days ago, I received an update for Mathematica. The latest version is 11.3.0. As usual, I looked through the list of new features\u00a0in this release. There are several new features, but one of them attracted my attention immediately: There is a new function FindTextualAnswer\u00a0that, given a piece of\u2026","rel":"","context":"In "Mathematica"","block_context":{"text":"Mathematica","link":"https:\/\/www.rangakrish.com\/index.php\/category\/mathematica\/"},"img":{"alt_text":"Example 1","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2018\/03\/Example1.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2018\/03\/Example1.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2018\/03\/Example1.png?resize=525%2C300 1.5x"},"classes":[]},{"id":364,"url":"https:\/\/www.rangakrish.com\/index.php\/2016\/10\/11\/cloud-computing-with-mathematica\/","url_meta":{"origin":443,"position":4},"title":"Cloud Computing with Mathematica","author":"admin","date":"October 11, 2016","format":false,"excerpt":"Mathematica provides excellent support for cloud computation, and most of the time, it is a very simple and intuitive process. Today, let us look at some examples of cloud deployment. For using Mathematica\u2019s cloud capabilities, you need an appropriate subscription. I use Mathematica Desktop, which comes with some free cloud\u2026","rel":"","context":"In "Mathematica"","block_context":{"text":"Mathematica","link":"https:\/\/www.rangakrish.com\/index.php\/category\/mathematica\/"},"img":{"alt_text":"FormFunction","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/10\/FormFunction1.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/10\/FormFunction1.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/10\/FormFunction1.png?resize=525%2C300 1.5x"},"classes":[]},{"id":328,"url":"https:\/\/www.rangakrish.com\/index.php\/2016\/09\/11\/natural-language-processing-in-mathematica\/","url_meta":{"origin":443,"position":5},"title":"Natural Language Processing in Mathematica","author":"admin","date":"September 11, 2016","format":false,"excerpt":"Welcome back. Today I am going to share with you some of the nice capabilities of Mathematica in the area of Natural Language Processing (NLP). Let us start with words. What if we wish to know\u00a0the various definitions of the word image?\u00a0Here is the answer. Mathematica gives the various senses\u2026","rel":"","context":"In "Mathematica"","block_context":{"text":"Mathematica","link":"https:\/\/www.rangakrish.com\/index.php\/category\/mathematica\/"},"img":{"alt_text":"Word Definition","src":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/09\/word-data1-1024x238.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/09\/word-data1-1024x238.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/09\/word-data1-1024x238.png?resize=525%2C300 1.5x, https:\/\/i0.wp.com\/www.rangakrish.com\/wp-content\/uploads\/2016\/09\/word-data1-1024x238.png?resize=700%2C400 2x"},"classes":[]}],"_links":{"self":[{"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/posts\/443","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/comments?post=443"}],"version-history":[{"count":0,"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/posts\/443\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/media?parent=443"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/categories?post=443"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rangakrish.com\/index.php\/wp-json\/wp\/v2\/tags?post=443"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}