Mixing
Differences between homography and transformation matrix
$begingroup$
I'm wondering whats the differences between a homography and a transformation matrix?
For me it's kinda look like the same? Or is homography just the more precise word in the area of computer vision and transformation of image plane?
transformation computer-vision
asked Aug 9 '17 at 19:12
user1234user1234
1215
$endgroup$
add a comment |
$begingroup$
I'm wondering whats the differences between a homography and a transformation matrix?
For me it's kinda look like the same? Or is homography just the more precise word in the area of computer vision and transformation of image plane?
transformation computer-vision
asked Aug 9 '17 at 19:12
user1234user1234
1215
$endgroup$
$begingroup$
What would you say is the difference between a linear transformation and a matrix?
$endgroup$
– amd
Aug 9 '17 at 19:14
$begingroup$
@amd thats literally what I'm asking ?!
$endgroup$
– user1234
Aug 21 '17 at 12:01
$begingroup$
A transformation is a function. A matrix is an array of numbers that can represent a transformation. Do you see the difference?
$endgroup$
– amd
Aug 21 '17 at 19:49
$begingroup$
@amd well I wasn't asking for the difference between an transformation and a matrix. I was asking for the difference between a homopgrahy and a transformation matrix. But in the mean time I found the difference on my own
$endgroup$
– user1234
Aug 22 '17 at 20:32
$begingroup$
A homography is a particular type of transformation. The difference between that and a matrix is exactly the same: the latter is one possible representation of the former.
$endgroup$
– amd
Aug 22 '17 at 21:51
add a comment |
$begingroup$
I'm wondering whats the differences between a homography and a transformation matrix?
For me it's kinda look like the same? Or is homography just the more precise word in the area of computer vision and transformation of image plane?
transformation computer-vision
asked Aug 9 '17 at 19:12
user1234user1234
1215
$endgroup$
I'm wondering whats the differences between a homography and a transformation matrix?
For me it's kinda look like the same? Or is homography just the more precise word in the area of computer vision and transformation of image plane?
transformation computer-vision
transformation computer-vision
asked Aug 9 '17 at 19:12
user1234user1234
1215
asked Aug 9 '17 at 19:12
user1234user1234
1215
asked Aug 9 '17 at 19:12
user1234user1234
1215
asked Aug 9 '17 at 19:12
user1234user1234
1215
asked Aug 9 '17 at 19:12
user1234user1234
1215
1215
$begingroup$
What would you say is the difference between a linear transformation and a matrix?
$endgroup$
– amd
Aug 9 '17 at 19:14
$begingroup$
@amd thats literally what I'm asking ?!
$endgroup$
– user1234
Aug 21 '17 at 12:01
$begingroup$
A transformation is a function. A matrix is an array of numbers that can represent a transformation. Do you see the difference?
$endgroup$
– amd
Aug 21 '17 at 19:49
$begingroup$
@amd well I wasn't asking for the difference between an transformation and a matrix. I was asking for the difference between a homopgrahy and a transformation matrix. But in the mean time I found the difference on my own
$endgroup$
– user1234
Aug 22 '17 at 20:32
$begingroup$
A homography is a particular type of transformation. The difference between that and a matrix is exactly the same: the latter is one possible representation of the former.
$endgroup$
– amd
Aug 22 '17 at 21:51
add a comment |
$begingroup$
What would you say is the difference between a linear transformation and a matrix?
$endgroup$
– amd
Aug 9 '17 at 19:14
$begingroup$
@amd thats literally what I'm asking ?!
$endgroup$
– user1234
Aug 21 '17 at 12:01
$begingroup$
A transformation is a function. A matrix is an array of numbers that can represent a transformation. Do you see the difference?
$endgroup$
– amd
Aug 21 '17 at 19:49
$begingroup$
@amd well I wasn't asking for the difference between an transformation and a matrix. I was asking for the difference between a homopgrahy and a transformation matrix. But in the mean time I found the difference on my own
$endgroup$
– user1234
Aug 22 '17 at 20:32
$begingroup$
A homography is a particular type of transformation. The difference between that and a matrix is exactly the same: the latter is one possible representation of the former.
$endgroup$
– amd
Aug 22 '17 at 21:51
$begingroup$
What would you say is the difference between a linear transformation and a matrix?
$endgroup$
– amd
Aug 9 '17 at 19:14
$begingroup$
What would you say is the difference between a linear transformation and a matrix?
$endgroup$
– amd
Aug 9 '17 at 19:14
$begingroup$
@amd thats literally what I'm asking ?!
$endgroup$
– user1234
Aug 21 '17 at 12:01
$begingroup$
@amd thats literally what I'm asking ?!
$endgroup$
– user1234
Aug 21 '17 at 12:01
$begingroup$
A transformation is a function. A matrix is an array of numbers that can represent a transformation. Do you see the difference?
$endgroup$
– amd
Aug 21 '17 at 19:49
$begingroup$
A transformation is a function. A matrix is an array of numbers that can represent a transformation. Do you see the difference?
$endgroup$
– amd
Aug 21 '17 at 19:49
$begingroup$
@amd well I wasn't asking for the difference between an transformation and a matrix. I was asking for the difference between a homopgrahy and a transformation matrix. But in the mean time I found the difference on my own
$endgroup$
– user1234
Aug 22 '17 at 20:32
$begingroup$
@amd well I wasn't asking for the difference between an transformation and a matrix. I was asking for the difference between a homopgrahy and a transformation matrix. But in the mean time I found the difference on my own
$endgroup$
– user1234
Aug 22 '17 at 20:32
$begingroup$
A homography is a particular type of transformation. The difference between that and a matrix is exactly the same: the latter is one possible representation of the former.
$endgroup$
– amd
Aug 22 '17 at 21:51
$begingroup$
A homography is a particular type of transformation. The difference between that and a matrix is exactly the same: the latter is one possible representation of the former.
$endgroup$
– amd
Aug 22 '17 at 21:51
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The term homography is often used in the sense of homography matrix in computer vision. In maths, I guess, the term homography describes the substatial concept, not the matrix. So the question is: What is the difference between homography matrix and transformation matrix?
The mathematical name for homography concept is "projective transformation" (source) and in computer vision it refers to transforming images such as if they were taken under different perspective. This is a much narrower question than any arbitrary transformation and hence homography can be computed by using mathematical tricks (see this question for details), avoiding geometrical computations. The effect of applying the matrix should be the same, but the way to get this matrix is easier.
An example from opencv: we have two images of the same place, taken from different angle. We will compute homography H. If we now select one pixel with coordinates (x1, y1) from the first image and another pixel (x2, y2) that represents the same point on another image, we can transform the latter pixel to have the same viewing perspective as the first one by applying H:
As we see, it is identical to applying transformation matrix, hence homography is just a special case of transformation. Most examples that I have seen, consider homography only for 2D (i.e., for images). Still, homography can be extended to larger dimension (source). Thanks to homography, 3D to 2D planar projection (i.e., mapping coordinates in 3D space to points on 2D plane) reduces to 2D to 2D, i.e., to a less complex problem (source).
While transformation is very general concept and includes all kinds of conversions, including conversion between coordinate frames, homography is a subset of it, mostly only applied when rotation is needed (source). In computer vision it is a technical term that describes above-mentioned case of transformation. You can achieve the same result by using proper geometrical transformation, but it will be more complex.
edited Apr 26 '18 at 11:43
Mårten W
2,57241837
answered Apr 19 '18 at 20:39
MF.OXMF.OX
1011
$endgroup$
add a comment |
Your Answer
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%2f2388259%2fdifferences-between-homography-and-transformation-matrix%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
$begingroup$
The term homography is often used in the sense of homography matrix in computer vision. In maths, I guess, the term homography describes the substatial concept, not the matrix. So the question is: What is the difference between homography matrix and transformation matrix?
The mathematical name for homography concept is "projective transformation" (source) and in computer vision it refers to transforming images such as if they were taken under different perspective. This is a much narrower question than any arbitrary transformation and hence homography can be computed by using mathematical tricks (see this question for details), avoiding geometrical computations. The effect of applying the matrix should be the same, but the way to get this matrix is easier.
An example from opencv: we have two images of the same place, taken from different angle. We will compute homography H. If we now select one pixel with coordinates (x1, y1) from the first image and another pixel (x2, y2) that represents the same point on another image, we can transform the latter pixel to have the same viewing perspective as the first one by applying H:
As we see, it is identical to applying transformation matrix, hence homography is just a special case of transformation. Most examples that I have seen, consider homography only for 2D (i.e., for images). Still, homography can be extended to larger dimension (source). Thanks to homography, 3D to 2D planar projection (i.e., mapping coordinates in 3D space to points on 2D plane) reduces to 2D to 2D, i.e., to a less complex problem (source).
While transformation is very general concept and includes all kinds of conversions, including conversion between coordinate frames, homography is a subset of it, mostly only applied when rotation is needed (source). In computer vision it is a technical term that describes above-mentioned case of transformation. You can achieve the same result by using proper geometrical transformation, but it will be more complex.
edited Apr 26 '18 at 11:43
Mårten W
2,57241837
answered Apr 19 '18 at 20:39
MF.OXMF.OX
1011
$endgroup$
add a comment |
$begingroup$
The term homography is often used in the sense of homography matrix in computer vision. In maths, I guess, the term homography describes the substatial concept, not the matrix. So the question is: What is the difference between homography matrix and transformation matrix?
The mathematical name for homography concept is "projective transformation" (source) and in computer vision it refers to transforming images such as if they were taken under different perspective. This is a much narrower question than any arbitrary transformation and hence homography can be computed by using mathematical tricks (see this question for details), avoiding geometrical computations. The effect of applying the matrix should be the same, but the way to get this matrix is easier.
An example from opencv: we have two images of the same place, taken from different angle. We will compute homography H. If we now select one pixel with coordinates (x1, y1) from the first image and another pixel (x2, y2) that represents the same point on another image, we can transform the latter pixel to have the same viewing perspective as the first one by applying H:
As we see, it is identical to applying transformation matrix, hence homography is just a special case of transformation. Most examples that I have seen, consider homography only for 2D (i.e., for images). Still, homography can be extended to larger dimension (source). Thanks to homography, 3D to 2D planar projection (i.e., mapping coordinates in 3D space to points on 2D plane) reduces to 2D to 2D, i.e., to a less complex problem (source).
While transformation is very general concept and includes all kinds of conversions, including conversion between coordinate frames, homography is a subset of it, mostly only applied when rotation is needed (source). In computer vision it is a technical term that describes above-mentioned case of transformation. You can achieve the same result by using proper geometrical transformation, but it will be more complex.
edited Apr 26 '18 at 11:43
Mårten W
2,57241837
answered Apr 19 '18 at 20:39
MF.OXMF.OX
1011
$endgroup$
add a comment |
$begingroup$
The term homography is often used in the sense of homography matrix in computer vision. In maths, I guess, the term homography describes the substatial concept, not the matrix. So the question is: What is the difference between homography matrix and transformation matrix?
The mathematical name for homography concept is "projective transformation" (source) and in computer vision it refers to transforming images such as if they were taken under different perspective. This is a much narrower question than any arbitrary transformation and hence homography can be computed by using mathematical tricks (see this question for details), avoiding geometrical computations. The effect of applying the matrix should be the same, but the way to get this matrix is easier.
An example from opencv: we have two images of the same place, taken from different angle. We will compute homography H. If we now select one pixel with coordinates (x1, y1) from the first image and another pixel (x2, y2) that represents the same point on another image, we can transform the latter pixel to have the same viewing perspective as the first one by applying H:
As we see, it is identical to applying transformation matrix, hence homography is just a special case of transformation. Most examples that I have seen, consider homography only for 2D (i.e., for images). Still, homography can be extended to larger dimension (source). Thanks to homography, 3D to 2D planar projection (i.e., mapping coordinates in 3D space to points on 2D plane) reduces to 2D to 2D, i.e., to a less complex problem (source).
While transformation is very general concept and includes all kinds of conversions, including conversion between coordinate frames, homography is a subset of it, mostly only applied when rotation is needed (source). In computer vision it is a technical term that describes above-mentioned case of transformation. You can achieve the same result by using proper geometrical transformation, but it will be more complex.
edited Apr 26 '18 at 11:43
Mårten W
2,57241837
answered Apr 19 '18 at 20:39
MF.OXMF.OX
1011
$endgroup$
The term homography is often used in the sense of homography matrix in computer vision. In maths, I guess, the term homography describes the substatial concept, not the matrix. So the question is: What is the difference between homography matrix and transformation matrix?
The mathematical name for homography concept is "projective transformation" (source) and in computer vision it refers to transforming images such as if they were taken under different perspective. This is a much narrower question than any arbitrary transformation and hence homography can be computed by using mathematical tricks (see this question for details), avoiding geometrical computations. The effect of applying the matrix should be the same, but the way to get this matrix is easier.
An example from opencv: we have two images of the same place, taken from different angle. We will compute homography H. If we now select one pixel with coordinates (x1, y1) from the first image and another pixel (x2, y2) that represents the same point on another image, we can transform the latter pixel to have the same viewing perspective as the first one by applying H:
As we see, it is identical to applying transformation matrix, hence homography is just a special case of transformation. Most examples that I have seen, consider homography only for 2D (i.e., for images). Still, homography can be extended to larger dimension (source). Thanks to homography, 3D to 2D planar projection (i.e., mapping coordinates in 3D space to points on 2D plane) reduces to 2D to 2D, i.e., to a less complex problem (source).
While transformation is very general concept and includes all kinds of conversions, including conversion between coordinate frames, homography is a subset of it, mostly only applied when rotation is needed (source). In computer vision it is a technical term that describes above-mentioned case of transformation. You can achieve the same result by using proper geometrical transformation, but it will be more complex.
edited Apr 26 '18 at 11:43
Mårten W
2,57241837
answered Apr 19 '18 at 20:39
MF.OXMF.OX
1011
edited Apr 26 '18 at 11:43
Mårten W
2,57241837
edited Apr 26 '18 at 11:43
Mårten W
2,57241837
edited Apr 26 '18 at 11:43
Mårten W
2,57241837
2,57241837
answered Apr 19 '18 at 20:39
MF.OXMF.OX
1011
answered Apr 19 '18 at 20:39
MF.OXMF.OX
1011
answered Apr 19 '18 at 20:39
MF.OXMF.OX
1011
1011
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%2f2388259%2fdifferences-between-homography-and-transformation-matrix%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
$begingroup$
What would you say is the difference between a linear transformation and a matrix?
$endgroup$
– amd
Aug 9 '17 at 19:14
$begingroup$
@amd thats literally what I'm asking ?!
$endgroup$
– user1234
Aug 21 '17 at 12:01
$begingroup$
A transformation is a function. A matrix is an array of numbers that can represent a transformation. Do you see the difference?
$endgroup$
– amd
Aug 21 '17 at 19:49
$begingroup$
@amd well I wasn't asking for the difference between an transformation and a matrix. I was asking for the difference between a homopgrahy and a transformation matrix. But in the mean time I found the difference on my own
$endgroup$
– user1234
Aug 22 '17 at 20:32
$begingroup$
A homography is a particular type of transformation. The difference between that and a matrix is exactly the same: the latter is one possible representation of the former.
$endgroup$
– amd
Aug 22 '17 at 21:51