# Talk:Pinhole camera model

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The geometry of a pinhole camera

## Untitled

In this figure we see two similar triangles, both having parts of the projection line (green) as their hypotenuses. The catheti of the left triangle are $-y_1$ and f and the catheti of the right triangle are $x_1$ and $x_3$. Since the two triangles are similar it follows that

$\frac{-y_1}{f} = \frac{x_1}{x_3}$ or $y_1 = -\frac{f \, x_1}{x_3}$

Is this correct? Since the triangle is similar, the angles are equal. However, the sides are in a proportion to one another, and are not equal but rather in a fixed ratio. damien--198.151.13.15 14:24, 3 August 2007 (UTC)
It's correct. The equations given express precisely what you have described: the sides are in a proportion to one another, not equal. The constant of proportionality between $-y_1$ and $x_1$ is $f/x_3$.--Srleffler (talk) 05:11, 11 November 2008 (UTC)
However, I have a problem with $-y_1$. The coordinate of Q is $y_1$ as described earlier in the article. I don't understand why it changed. In my opinion the coordinates of Q should be $-y_1,-y_2$. There are too many signs appearing and desappearing in this article :). — Preceding unsigned comment added by LucasThePatator (talkcontribs) 09:06, 12 August 2011 (UTC)

## Citations needed

I copied this here from my talk page so that others can see my responses (indented) and join in. Dicklyon 14:55, 28 September 2007 (UTC)

Hi, I missed your point about the necessity to provide more specific references in the Pinhole camera model article.

• The article, as it is, is on a rather introductory level, the geometry is "elementary" and self-explanatory and it is perhaps only the terminology which needs to be verified relative the literature. Any of the textbooks which are included in the reference list provides a similar presentation with some variation (described in the article) in the terminology. As far as I know, there are also no "first references" which can be used for the "citation needed" tags you have inserted, any of the textbook will do.
Then cite one or more of the textbooks there. Having them listed, without saying what they verify, isn't nearly as good.
• One could possibly stack the citations to all of the current refs, for example, at the end of the lead section or the end of the article, but I don't see the point if there is a reference section which is clearly visible. Also, I have to confess that since the current implementation of the ref makes a mess and clutters the edit text, I don't use it unless it is really necessary.
• Is there some policy or guideline which can be of any help here? I haven't seen that the ref tags are compulsory.
See WP:V, note 1.
• I couldn't even figure out the reason for your "citation needed" tags at the places where they are. There must be a few more dozen of statements which are equally "uncited" and we can't have a cite on each and every such statement?

Regards --KYN 12:48, 28 September 2007 (UTC)

Generally speaking, having a cite on almost every statement, or every paragraph, is a good idea. But for ones that follow trivially from what comes before them, it's not really necessary. But the final derived relationship should be cited, so that one can verify that that's the result the experts get, without trying to check every step in the deriviation. Citations are also required to verify assertions about what something is called in the literature. That's why I picked the particular set of things to tag, which are really there just as a first guess of where inline citation would be useful.
Dicklyon 14:55, 28 September 2007 (UTC)

## Relation to Pinhole camera

I'm new to Wikipedia and would like to contribute material to this article. To begin with the term "photography" should appear since the purpose of a pinhole camera is to make pinhole photos. More to the point, there is at least one individual of whom I am aware who is a recognized expert on pinhole photography. Wiley Sanderson was head of the photography school at the University of Georgia. Among other things, he required all beginning students to construct and use a pinhole camera during their first year. I'm neither a photographer nor an academic, but he made such a deep impression on me over forty years ago that I never forgot him and what he taught about taking pictures. I told the story at my blog, Hootsbuddy's Place. Any Google search for "Wiley Sanderson" will bring up the link. I would appreciate any feedback. —Preceding unsigned comment added by Hootsbuddy (talkcontribs) 22:14, 18 August 2008 (UTC)

Have you seen the article on pinhole camera? I'm guessing that this is what you are interested in? This article describes the mathematical model of an ideal pinhole camera, and the pinhole camera article describes the implementation of this model. I'v added a link to the pinhole camera article in the See also section. --KYN (talk) 07:18, 19 August 2008 (UTC)

## Projective representation Section

I'm having some problems with the following statement in the "Projective representation" section:

$\mathbf{y} \sim \mathbf{C} \, \mathbf{x}$

where $\mathbf{C}$ is the $3 \times 4$ camera matrix and the $\, \sim$ sign implies that the left and right hand sides are equal up to a non-zero scalar multiplication.

The left and right-hand side are equal, not just under a non-zero scalar multiplication. The fact that a non-zero scale multiplication of $\mathbf{y}$ would keep $\mathbf{y}$ in the same homogeneous equivalence class is irrelevant for this section.

Also, I'm wondering whether the "Projective representation" section shouldn't be called "Homogeneous Coordinates". Naming the section "Projective representation" would imply that the above sections are not a representing a projection. The original author was most likely talking about representation in projective geometry, but it sound slightly vague this way.

Wim (talk) 16:04, 14 March 2009 (UTC)

I changed to "homogeneous coordinates" which is a better heading, and also modified the description on the tilde sign. Hope this solves your problems. --KYN (talk) 07:17, 18 March 2009 (UTC)

## focal length

Currently the article states "f is also referred to as the focal length of the pinhole camera." This usage is quite distinct from the strict 'optics' definition currently given in focal length. If we had a reliable source to justify it, it would be very helpful to add this 'alternative' definition to the focal length article. --Redbobblehat (talk) 15:52, 7 February 2011 (UTC)

Try any of the following:

• Xu and Zhang, Epipolar Geometry in Stereo, Motion, and Object Recognition, Kluwer 1996 (page 8)
• Ma, Soatto, Košecká and Sastry, An invitation to 3-D Vision, Springer 2006 (page 49)
• Shapiro and Stockman, Computer Vision, Prentice Hall 2001 (page 423)
• Sonka, Hlavac and Boyle, Image Processing, Analysis, and Machine Vision, Thomson 2008 (page 563)
• Hartley and Zisserman, Multiple View Geometry in Computer Vision, Cambridge 2003

--KYN (talk) 16:32, 7 February 2011 (UTC)

You can find such definitions in many books, such as this one, but they do not apply to lenses. This definition is "quite distinct" in some respects, as you note, since a pinhole doesn't have a rear nodal point per se; but in other respects, in terms of the imaging magnification of distant objects (mm per radian), it's the usual defining relationship for focal length. Or take any point in the region of the pinhole that all the image rays pass through (in the case of the pinhole model, that's a unique point) and call it the rear nodal point and you'll have the same result. Dicklyon (talk) 16:33, 7 February 2011 (UTC)
I glanced at KYN's first, second and fifth references (googlebooks). These authors seem to be using the analogy of a pinhole camera to describe a traditional approach to geometrical perspective projection. They clearly borrow vocabulary ("principal point", "focal plane", "pan", "tilt", etc) from the optics /photographic traditions. As far as I could tell, they are not offering a new concept. (Unfortunately I don't know if there is a specific term in optics for the distance from exit pupil to image.) It would be easy to argue that the "alternative meaning" is simply a misuse of photographic/optics terminology, on the basis that the conceptual framework is thẞe same. Using these reference sources, for example, I don't think you would get this "alternative definition" into a standard dictionary! but it might be admissible to wikipedia as an "academic consensus" under WP:RS/AC ? --Redbobblehat (talk) 22:27, 7 February 2011 (UTC)
"The effective focal length of a pinhole aperture is simply its distance from the film plane" is certainly more definitive! I'm just not so sure that the Eastman Kodak's "More Joy of Photography - 100 Techniques For More Creative Photographs" (LOL priceless!) would qualify as a WP:SOURCE - even at best it's a very tertiary source. It's not difficult to imagine that this "alternative definition" would be challenged by serious scholars. I think it's prudent to treat it as an "exceptional claim" under WP:REDFLAG, so IMO we need something more solid - rigorous - before advocating its general use to the wikipedia community ? --Redbobblehat (talk) 22:27, 7 February 2011 (UTC)
It's hardly an exceptional claim, and lots of secondary and tertiary sources support it directly. Dicklyon (talk) 00:29, 8 February 2011 (UTC)
KYN's sources are more about the pinhole model in graphics, which is what this article is about; but if you want photography refs, you might want to read Lord Rayleigh's 1891 paper on Pin-hole Photography, or many others since then. He freely refers to the pinhole distance as focal length. Most people use it more as an analogy. In terms of camera models, this focal length is what makes the model act like a camera using a lens of that focal length, at least for distant objects. Dicklyon (talk) 22:52, 7 February 2011 (UTC)
There is no specific term for the distance from exit pupil to image plane. The specific term for distance from rear nodal point to image plane, when focused at infinity, is focal length. Dicklyon (talk) 22:54, 7 February 2011 (UTC)
Here are lots of books that discuss focal length in the context of the pinhole camera. Dicklyon (talk) 00:28, 8 February 2011 (UTC)
I just noticed that in Jähne and Hauẞecker (Eds), Computer Vision and Applications, Academic Press 2000, focal length is described in sec 3.3 as the distance between the lens and the point of converging rays and in sec 6.5, where the projective aspect of a pinhole camera is discussed, the calibrated focal length is defined as the distance between the perspective center and the image plane. As far as I can see there is no discussion about a possible relation between the two, and the two sections are written by different authors. --KYN (talk) 08:40, 8 February 2011 (UTC)
Thanks Dick, I did enjoy the Rayleigh read :-) Rayleigh, 1891 Lord Rayleigh on Pin-hole Photography in Philosophical Magazine, vol.31, pp. 87-99 certainly uses "focal length" as the pinhole to image distance - a tradition amongst pinholers that lasts to this day! Even the OED might buy this one ! --Redbobblehat (talk) 01:31, 10 February 2011 (UTC)

## "Focal point"

This page mentions "focal point" twice, and Camera matrix links focal point to this page via a redirect. I think the author is trying to talk about the camera center. If so, that's misleading at best. In as much as a pinhole camera models a real camera, the focal point would better be the principal point. Either way, I've never heard "focal point" used with precise meaning in computer vision/graphics. Shall we replace "focal point" with more-precise language? —Ben FrantzDale (talk) 15:14, 14 July 2011 (UTC)