Why it is said that "convolution of an image in spatial domain is equal to multiplication in frequency domain" ? Could anyone please explain it briefly?
Why convolution in spatial domain equal to multiplication in frequency domain?
2.9k views Asked by Linkon At
1
There are 1 answers
Related Questions in IMAGE-PROCESSING
- Add additional fields to Linq group by
- couldn't copy pdb file to another directory while consuming wcf web service
- Why are the aliases for string and object in lowercase?
- WPF MessageBox Cancel checkbox check
- Resolve object using DI container with object instance
- Creating a parametrized field name for a SELECT clause
- Does compiler optimize operation on const variable and literal const number?
- Get data from one form to another form in C#
- Writing/Overwriting to specific XML file from ASP.NET code behind
- Deleting Orphans with Fluent NHibernate
Related Questions in LINEAR-ALGEBRA
- Add additional fields to Linq group by
- couldn't copy pdb file to another directory while consuming wcf web service
- Why are the aliases for string and object in lowercase?
- WPF MessageBox Cancel checkbox check
- Resolve object using DI container with object instance
- Creating a parametrized field name for a SELECT clause
- Does compiler optimize operation on const variable and literal const number?
- Get data from one form to another form in C#
- Writing/Overwriting to specific XML file from ASP.NET code behind
- Deleting Orphans with Fluent NHibernate
Related Questions in CONVOLUTION
- Add additional fields to Linq group by
- couldn't copy pdb file to another directory while consuming wcf web service
- Why are the aliases for string and object in lowercase?
- WPF MessageBox Cancel checkbox check
- Resolve object using DI container with object instance
- Creating a parametrized field name for a SELECT clause
- Does compiler optimize operation on const variable and literal const number?
- Get data from one form to another form in C#
- Writing/Overwriting to specific XML file from ASP.NET code behind
- Deleting Orphans with Fluent NHibernate
Related Questions in FREQUENCY-DOMAIN
- Add additional fields to Linq group by
- couldn't copy pdb file to another directory while consuming wcf web service
- Why are the aliases for string and object in lowercase?
- WPF MessageBox Cancel checkbox check
- Resolve object using DI container with object instance
- Creating a parametrized field name for a SELECT clause
- Does compiler optimize operation on const variable and literal const number?
- Get data from one form to another form in C#
- Writing/Overwriting to specific XML file from ASP.NET code behind
- Deleting Orphans with Fluent NHibernate
Popular Questions
- How do I undo the most recent local commits in Git?
- How can I remove a specific item from an array in JavaScript?
- How do I delete a Git branch locally and remotely?
- Find all files containing a specific text (string) on Linux?
- How do I revert a Git repository to a previous commit?
- How do I create an HTML button that acts like a link?
- How do I check out a remote Git branch?
- How do I force "git pull" to overwrite local files?
- How do I list all files of a directory?
- How to check whether a string contains a substring in JavaScript?
- How do I redirect to another webpage?
- How can I iterate over rows in a Pandas DataFrame?
- How do I convert a String to an int in Java?
- Does Python have a string 'contains' substring method?
- How do I check if a string contains a specific word?
Popular Tags
Trending Questions
- UIImageView Frame Doesn't Reflect Constraints
- Is it possible to use adb commands to click on a view by finding its ID?
- How to create a new web character symbol recognizable by html/javascript?
- Why isn't my CSS3 animation smooth in Google Chrome (but very smooth on other browsers)?
- Heap Gives Page Fault
- Connect ffmpeg to Visual Studio 2008
- Both Object- and ValueAnimator jumps when Duration is set above API LvL 24
- How to avoid default initialization of objects in std::vector?
- second argument of the command line arguments in a format other than char** argv or char* argv[]
- How to improve efficiency of algorithm which generates next lexicographic permutation?
- Navigating to the another actvity app getting crash in android
- How to read the particular message format in android and store in sqlite database?
- Resetting inventory status after order is cancelled
- Efficiently compute powers of X in SSE/AVX
- Insert into an external database using ajax and php : POST 500 (Internal Server Error)
StackOverflow, unfortunately, doesn't support MathJaX hence it is hard to show the math here.
One way to explain is that Convolution is Linear Invariant Operator.
As you know, Linear Time / Spatially Invariant Systems basically do one thing - Delay and Scaling.
The Eigen Functions of Delay and Scaling are the Harmonic Functions.
Which means that give a signal described by harmonic signals (Practically its Fourier Transform) Linear Time / Spatially Invariant Operator only scales it by complex number (Scaling and shifting by phase) which is what you do in the Fourier Domain.
It is similar to Diagonalization in Linear Algebra.
For instance let's thing of the Filter we apply on the image as an operator -
A.So the output of the system is
y = A x.If
Ais diagonalizable asA = P^T D PwhereDis diagonal matrix andP P^T = I, namely Unitary Matrix.So
y = A x = P^T D P xhence by definingz = P xandt = P ywe gett = D znamely we only need to multiply each element intand not the whole matrix multiplication.If you think about
Pas the Fourier Transom operator then instead of doing Matrix Multiplication you can have element wise multiplication in other domain - Fourier Domain.