What is the range of parameters rho and theta in normal equation of a straight line?
I'm implementing Hough Transform in MatLab to detect straight lines in an Image. It uses normal form of a straight line equation
$$x cos(theta) + y sin(theta) = rho$$
I'm interested in the lines which pass through the 1st quadrant only, that too in the rectangle with vertices $(0,0), (M,0), (0,N), (M,N)$ i.e. any line that doesn't pass through this rectangle, I'm not interested in finding the equation of that line. Orientation of the line can be anything. What is the range of values for the parameters $rho$ and $theta$?
If I assume $theta$ varies from $-90^text{o}$ to $90^text{o}$, what is the range of values for $rho$? Can $rho$ be negative?
geometry
edited Nov 18 '18 at 18:21
learner
226
asked Nov 18 '18 at 18:17
Nagabhushan S N
255214
add a comment |
I'm implementing Hough Transform in MatLab to detect straight lines in an Image. It uses normal form of a straight line equation
$$x cos(theta) + y sin(theta) = rho$$
I'm interested in the lines which pass through the 1st quadrant only, that too in the rectangle with vertices $(0,0), (M,0), (0,N), (M,N)$ i.e. any line that doesn't pass through this rectangle, I'm not interested in finding the equation of that line. Orientation of the line can be anything. What is the range of values for the parameters $rho$ and $theta$?
If I assume $theta$ varies from $-90^text{o}$ to $90^text{o}$, what is the range of values for $rho$? Can $rho$ be negative?
geometry
edited Nov 18 '18 at 18:21
learner
226
asked Nov 18 '18 at 18:17
Nagabhushan S N
255214
add a comment |
I'm implementing Hough Transform in MatLab to detect straight lines in an Image. It uses normal form of a straight line equation
$$x cos(theta) + y sin(theta) = rho$$
I'm interested in the lines which pass through the 1st quadrant only, that too in the rectangle with vertices $(0,0), (M,0), (0,N), (M,N)$ i.e. any line that doesn't pass through this rectangle, I'm not interested in finding the equation of that line. Orientation of the line can be anything. What is the range of values for the parameters $rho$ and $theta$?
If I assume $theta$ varies from $-90^text{o}$ to $90^text{o}$, what is the range of values for $rho$? Can $rho$ be negative?
geometry
edited Nov 18 '18 at 18:21
learner
226
asked Nov 18 '18 at 18:17
Nagabhushan S N
255214
I'm implementing Hough Transform in MatLab to detect straight lines in an Image. It uses normal form of a straight line equation
$$x cos(theta) + y sin(theta) = rho$$
I'm interested in the lines which pass through the 1st quadrant only, that too in the rectangle with vertices $(0,0), (M,0), (0,N), (M,N)$ i.e. any line that doesn't pass through this rectangle, I'm not interested in finding the equation of that line. Orientation of the line can be anything. What is the range of values for the parameters $rho$ and $theta$?
If I assume $theta$ varies from $-90^text{o}$ to $90^text{o}$, what is the range of values for $rho$? Can $rho$ be negative?
geometry
geometry
edited Nov 18 '18 at 18:21
learner
226
asked Nov 18 '18 at 18:17
Nagabhushan S N
255214
edited Nov 18 '18 at 18:21
learner
226
asked Nov 18 '18 at 18:17
Nagabhushan S N
255214
edited Nov 18 '18 at 18:21
learner
226
edited Nov 18 '18 at 18:21
learner
226
edited Nov 18 '18 at 18:21
learner
226
226
asked Nov 18 '18 at 18:17
Nagabhushan S N
255214
asked Nov 18 '18 at 18:17
Nagabhushan S N
255214
asked Nov 18 '18 at 18:17
Nagabhushan S N
255214
255214
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
As depicted in the graph we have better split for negative anf for positive values of $theta$.
Thus we must have
$$
left{ {matrix{
{left{ matrix{
- rho /cos theta le M hfill cr
- rho /sin theta le N hfill cr} right.} hfill & {left| {; - pi /2 < theta < 0} right.} hfill cr
{left{ matrix{
rho /cos theta - Ntan theta le M hfill cr
0 le rho hfill cr} right.} hfill & {left| {;0 < theta < pi /2} right.} hfill cr
} } right.
$$
that is
$$
left{ {matrix{
{ - Mcos theta le rho le - Nsin theta } hfill & {left| {; - pi /2 < theta < 0} right.} hfill cr
{0 le rho le Mcos theta + Nsin theta } hfill & {left| {;0 < theta < pi /2} right.} hfill cr
} } right.
$$
answered Nov 19 '18 at 1:21
G Cab
17.9k31237
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%2f3003904%2fwhat-is-the-range-of-parameters-rho-and-theta-in-normal-equation-of-a-straight-l%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
As depicted in the graph we have better split for negative anf for positive values of $theta$.
Thus we must have
$$
left{ {matrix{
{left{ matrix{
- rho /cos theta le M hfill cr
- rho /sin theta le N hfill cr} right.} hfill & {left| {; - pi /2 < theta < 0} right.} hfill cr
{left{ matrix{
rho /cos theta - Ntan theta le M hfill cr
0 le rho hfill cr} right.} hfill & {left| {;0 < theta < pi /2} right.} hfill cr
} } right.
$$
that is
$$
left{ {matrix{
{ - Mcos theta le rho le - Nsin theta } hfill & {left| {; - pi /2 < theta < 0} right.} hfill cr
{0 le rho le Mcos theta + Nsin theta } hfill & {left| {;0 < theta < pi /2} right.} hfill cr
} } right.
$$
answered Nov 19 '18 at 1:21
G Cab
17.9k31237
add a comment |
As depicted in the graph we have better split for negative anf for positive values of $theta$.
Thus we must have
$$
left{ {matrix{
{left{ matrix{
- rho /cos theta le M hfill cr
- rho /sin theta le N hfill cr} right.} hfill & {left| {; - pi /2 < theta < 0} right.} hfill cr
{left{ matrix{
rho /cos theta - Ntan theta le M hfill cr
0 le rho hfill cr} right.} hfill & {left| {;0 < theta < pi /2} right.} hfill cr
} } right.
$$
that is
$$
left{ {matrix{
{ - Mcos theta le rho le - Nsin theta } hfill & {left| {; - pi /2 < theta < 0} right.} hfill cr
{0 le rho le Mcos theta + Nsin theta } hfill & {left| {;0 < theta < pi /2} right.} hfill cr
} } right.
$$
answered Nov 19 '18 at 1:21
G Cab
17.9k31237
add a comment |
As depicted in the graph we have better split for negative anf for positive values of $theta$.
Thus we must have
$$
left{ {matrix{
{left{ matrix{
- rho /cos theta le M hfill cr
- rho /sin theta le N hfill cr} right.} hfill & {left| {; - pi /2 < theta < 0} right.} hfill cr
{left{ matrix{
rho /cos theta - Ntan theta le M hfill cr
0 le rho hfill cr} right.} hfill & {left| {;0 < theta < pi /2} right.} hfill cr
} } right.
$$
that is
$$
left{ {matrix{
{ - Mcos theta le rho le - Nsin theta } hfill & {left| {; - pi /2 < theta < 0} right.} hfill cr
{0 le rho le Mcos theta + Nsin theta } hfill & {left| {;0 < theta < pi /2} right.} hfill cr
} } right.
$$
answered Nov 19 '18 at 1:21
G Cab
17.9k31237
As depicted in the graph we have better split for negative anf for positive values of $theta$.
Thus we must have
$$
left{ {matrix{
{left{ matrix{
- rho /cos theta le M hfill cr
- rho /sin theta le N hfill cr} right.} hfill & {left| {; - pi /2 < theta < 0} right.} hfill cr
{left{ matrix{
rho /cos theta - Ntan theta le M hfill cr
0 le rho hfill cr} right.} hfill & {left| {;0 < theta < pi /2} right.} hfill cr
} } right.
$$
that is
$$
left{ {matrix{
{ - Mcos theta le rho le - Nsin theta } hfill & {left| {; - pi /2 < theta < 0} right.} hfill cr
{0 le rho le Mcos theta + Nsin theta } hfill & {left| {;0 < theta < pi /2} right.} hfill cr
} } right.
$$
answered Nov 19 '18 at 1:21
G Cab
17.9k31237
answered Nov 19 '18 at 1:21
G Cab
17.9k31237
answered Nov 19 '18 at 1:21
G Cab
17.9k31237
answered Nov 19 '18 at 1:21
G Cab
17.9k31237
17.9k31237
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3003904%2fwhat-is-the-range-of-parameters-rho-and-theta-in-normal-equation-of-a-straight-l%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
