Kortenkamp
- Top of page 53: “collinear” should be “concurrent”.
- Page 75: eq. 6.1 should be
. - Page 75: eq. 6.2 should be
. - Middle of page 77: “
” should be 
.
Here we list possible errata in the readings. In general these may not be confirmed with the author, hence we call them “possible” errata.
We also list some clarifications for possibly tricky sections.
..” should be .
” should be 
.
” should be 
.
” should be 
.
” may be confusing. Here, 
and 
are quaternions, say 
and similarly for . However, for the purposes of taking the dot product 
, they are temporarily considered simply 4-dimensional vectors: 
.
”.
and 
are quaternions but temporarily considered as vectors to evaluate the dot product 
, just as was done for 
on p. 248.
” should be 
, and similar for all the other expansions of 
on the page.
term in the equations for 
should be negative
.
to 
, and change "yielding 
to 
.
matrix 
for each pixel 
according to the equation at the top of p. 318 (note that in this equation 
and 
are the first derivatives of the image in the horizontal resp. vertical directions) and then (2) classify pixel as a corner iff both eigenvalues (there will be two because is ) of are “relatively large”. Harris suggested an approximation to this condition based on the determinant and trace of which saves a little computation vs actually computing the eigenvalues, but later Shi and Tomasi pointed out that it gives better results to actually compute the eigenvalues and verify that the smaller of the two is greater than some threshold.
.
are in units of pixels, and upper-case variables such as 
are in physical units, e.g. millimeters (any choice of physical units works as long as it is used consistently).
is the actual focal length in physical units (e.g. millimeters), and 
and 
are effective horizontal and vertical focal lenghths in pixels. These differ only when the pixels are not actually square, i.e. when 
. In practice, despite what the book says, nowadays most cameras have square pixels, even cheap ones. Also, it is usually possible to get accurate specifications from the camera manufacturer of the designed values of 
and 
. The designed focal length is also often specified, but the actual as-built value may differ somewhat.
and 
. Also, note that all equations on this page are given without derivation or detailed explanation; we’ll just take them at face value. The quantity 
appearing in the equations is defined as the radial distance of the pixel from the optical center 
: 
.
with 
, and note that 
is calculated in object frame coordinates. This is fairly nonstandard, in particular note that the vector here is not the same as the 
vector used later in the chapter (starting on p. 386). The 
matrix is the same though. See further discussion below on a similar issue with the vector on p. 422—423.
, combined with the radial and tangential lens distortion models (equations on p. 376), which are defined by five parameters 
. Perhaps confusingly, “intrinsics matrix” refers only to the matrix 
defined at the top of p. 374, i.e. the pinhole camera model. The discussion of the required number of equations on p. 381 mostly ignores the distortion parameters. Fortunately, the discussion is repeated in more detail, including the distortion parameters, on p. 388.
is measured in physical units (e.g. millimeters) in a coordinate frame 
fixed to the moving object (i.e. the chessboard). Thus, if the chessboard has square cells of side length 
millimeters, its corners would have coordinates of the form 
for integers 
, assuming the chessboard is aligned so that one corner is at the origin of , that the 
axis of is normal to the plane of the chessboard, and that the 
and 
axes are aligned with the rows and columns of the chessboard. The point 
is in units of pixels in the image plane.
with 
.
).Page 391: while technically correct, the block of equations at the top of the page is unnecessarily complicated (this appears to be an artifact of translating the original equations from Zhang’s paper, which handles a slightly more general case). Note that here 
. Using that fact, and also substituting in the expressions in 
variables for the derived quantities and 
in the third and fifth equations, respectively, gives the following simpler set of equations:
.
is not explained. It comes from the fact that if 
is a solution to the equation at the bottom of p. 390, then so is any scalar multiple of . Thus, the returned solution is actually multiplied by some unknown scalar factor . Fortunately, here can be recovered by the above equation. is not necessarily the same as in the first block of equations on the page.
has a typo—rather than depending on 
, depends on 
. Also, it is never explicitly stated, but the coordinates 
are produced by multiplying a point in object frame 
by the now-reconstructed extrinsic transformation matrix 
:
and 
” with "We begin by considering the relationship between 
and 
. used in the section “Essential matrix math” is different from that used later in the chapter. However, this is ok, because each usage is self-consistent. The usage on 422—423 is relatively non-standard, and is similar to that on p. 380 (see above): is an orthonormal basis for the left camera frame in the right camera frame (as would be typical for defining a rigid transform, as we are doing, from left camera coordinates to right camera coordinates), but (this is the nonstandard part) here is the location of the right camera in the left camera frame; normally (i.e. as when forming the right column of a homogenous transformation matrix taking left camera coordinates to right camera coordinates) the translation vector would simply be the location of the left camera in the right camera frame. through…” with “all possible points on a plane through…”.
and 
with and . and in the sentence should be replaced by and . with 
, and replace “(the pixel coordinate)” with “(the camera frame coordinate)”.
in 
should be replaced by 
.Page 428, first footnote: replace the existing text with “Let’s be careful about what these terms mean: and denote the locations of the 3D point in the coordinate system of the left and right cameras, respectively. itself is in an object-relative coordinate frame 
s.t. 
and 
are rigid transforms that take coordinates in to the left resp. right camera frame. 
is a rigid transform that takes coordinates in the left camera frame to the right camera frame; thus encodes the pose of the left camera with respect to the right.”