Mixing
Finding Transformation Matrix from source/destination vector pairs dataset
$begingroup$
I have a color processing problem I'm trying to solve. When we convert RGB colors to different colorspaces, we use 3x3 matrices. For example if s is a source RGB color vector, M is a 3x3 colorspace transformation matrix, and d is the result RGB color vector, the equation would look like this:
M*s = d
My problem:
I have a dataset of source/destination RGB color pairs that come from a colorspace conversion and am trying to find a "best fit" transformation matrix. Basically I'm trying to reverse-engineer the colorspace conversion and figure out what 3x3 transformation matrix was used. How would I go about solving this?
linear-algebra
asked Oct 31 '14 at 1:08
Greg CottenGreg Cotten
61
$endgroup$
add a comment |
$begingroup$
I have a color processing problem I'm trying to solve. When we convert RGB colors to different colorspaces, we use 3x3 matrices. For example if s is a source RGB color vector, M is a 3x3 colorspace transformation matrix, and d is the result RGB color vector, the equation would look like this:
M*s = d
My problem:
I have a dataset of source/destination RGB color pairs that come from a colorspace conversion and am trying to find a "best fit" transformation matrix. Basically I'm trying to reverse-engineer the colorspace conversion and figure out what 3x3 transformation matrix was used. How would I go about solving this?
linear-algebra
asked Oct 31 '14 at 1:08
Greg CottenGreg Cotten
61
$endgroup$
add a comment |
$begingroup$
I have a color processing problem I'm trying to solve. When we convert RGB colors to different colorspaces, we use 3x3 matrices. For example if s is a source RGB color vector, M is a 3x3 colorspace transformation matrix, and d is the result RGB color vector, the equation would look like this:
M*s = d
My problem:
I have a dataset of source/destination RGB color pairs that come from a colorspace conversion and am trying to find a "best fit" transformation matrix. Basically I'm trying to reverse-engineer the colorspace conversion and figure out what 3x3 transformation matrix was used. How would I go about solving this?
linear-algebra
asked Oct 31 '14 at 1:08
Greg CottenGreg Cotten
61
$endgroup$
I have a color processing problem I'm trying to solve. When we convert RGB colors to different colorspaces, we use 3x3 matrices. For example if s is a source RGB color vector, M is a 3x3 colorspace transformation matrix, and d is the result RGB color vector, the equation would look like this:
M*s = d
My problem:
I have a dataset of source/destination RGB color pairs that come from a colorspace conversion and am trying to find a "best fit" transformation matrix. Basically I'm trying to reverse-engineer the colorspace conversion and figure out what 3x3 transformation matrix was used. How would I go about solving this?
linear-algebra
linear-algebra
asked Oct 31 '14 at 1:08
Greg CottenGreg Cotten
61
asked Oct 31 '14 at 1:08
Greg CottenGreg Cotten
61
asked Oct 31 '14 at 1:08
Greg CottenGreg Cotten
61
asked Oct 31 '14 at 1:08
Greg CottenGreg Cotten
61
asked Oct 31 '14 at 1:08
Greg CottenGreg Cotten
61
61
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Assuming there is a linear transformation mapping $S$ to $D$, you can do one thing. Take three input vectors $S = [s_1, s_2, s_3]$ and corresponding output vectors $D = [d_1, d_2, d_3]$. Now you can easily use matrix algebra to get the transformation $M$, you can do $M = DA^{-1}$.
If you take more than three vectors, you can use pseudo inverse of $A$, but for unique $3×3$ matrix estimation, having three vectors is enough.
edited Jan 3 at 5:29
Saad
19.7k92352
answered Jan 3 at 4:44
SukuyaSukuya
32
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f999231%2ffinding-transformation-matrix-from-source-destination-vector-pairs-dataset%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Assuming there is a linear transformation mapping $S$ to $D$, you can do one thing. Take three input vectors $S = [s_1, s_2, s_3]$ and corresponding output vectors $D = [d_1, d_2, d_3]$. Now you can easily use matrix algebra to get the transformation $M$, you can do $M = DA^{-1}$.
If you take more than three vectors, you can use pseudo inverse of $A$, but for unique $3×3$ matrix estimation, having three vectors is enough.
edited Jan 3 at 5:29
Saad
19.7k92352
answered Jan 3 at 4:44
SukuyaSukuya
32
$endgroup$
add a comment |
$begingroup$
Assuming there is a linear transformation mapping $S$ to $D$, you can do one thing. Take three input vectors $S = [s_1, s_2, s_3]$ and corresponding output vectors $D = [d_1, d_2, d_3]$. Now you can easily use matrix algebra to get the transformation $M$, you can do $M = DA^{-1}$.
If you take more than three vectors, you can use pseudo inverse of $A$, but for unique $3×3$ matrix estimation, having three vectors is enough.
edited Jan 3 at 5:29
Saad
19.7k92352
answered Jan 3 at 4:44
SukuyaSukuya
32
$endgroup$
add a comment |
$begingroup$
Assuming there is a linear transformation mapping $S$ to $D$, you can do one thing. Take three input vectors $S = [s_1, s_2, s_3]$ and corresponding output vectors $D = [d_1, d_2, d_3]$. Now you can easily use matrix algebra to get the transformation $M$, you can do $M = DA^{-1}$.
If you take more than three vectors, you can use pseudo inverse of $A$, but for unique $3×3$ matrix estimation, having three vectors is enough.
edited Jan 3 at 5:29
Saad
19.7k92352
answered Jan 3 at 4:44
SukuyaSukuya
32
$endgroup$
Assuming there is a linear transformation mapping $S$ to $D$, you can do one thing. Take three input vectors $S = [s_1, s_2, s_3]$ and corresponding output vectors $D = [d_1, d_2, d_3]$. Now you can easily use matrix algebra to get the transformation $M$, you can do $M = DA^{-1}$.
If you take more than three vectors, you can use pseudo inverse of $A$, but for unique $3×3$ matrix estimation, having three vectors is enough.
edited Jan 3 at 5:29
Saad
19.7k92352
answered Jan 3 at 4:44
SukuyaSukuya
32
edited Jan 3 at 5:29
Saad
19.7k92352
edited Jan 3 at 5:29
Saad
19.7k92352
edited Jan 3 at 5:29
Saad
19.7k92352
19.7k92352
answered Jan 3 at 4:44
SukuyaSukuya
32
answered Jan 3 at 4:44
SukuyaSukuya
32
answered Jan 3 at 4:44
SukuyaSukuya
32
32
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f999231%2ffinding-transformation-matrix-from-source-destination-vector-pairs-dataset%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
