dip_image
Object
The Contents
Images used by this toolbox are encapsulated in an object called
dip_image
. Objects of this type are unlike regular MATLAB arrays in
some ways, but behave similarly most of the time. This chapter explains
the usage of these objects.
For more information on the functions mentioned in this chapter (and
elsewhere) use the MATLAB help system. At the MATLAB command prompt, type
help <function_name>
.
Creating a dip_image
object
To create a dip_image
object, the function dip_image
must be used.
It converts any numeric array into an image object. The optional second
argument indicates the desired data type for the image. The pixel data
will be converted to this type if possible, or else an error will be
generated (for example, it is illegal to convert complex data to a real
type, since there are many ways this can be accomplished; it is
necessary to do this explicitly). The valid data types are listed in
the table below. This table also lists some alternative names
that are mapped to the names on the left; these are just to make
specifying the data type easier.
Data type  Description  Other allowed names 

bin 
binary (in 8bit integer)  
uint8 
8bit unsigned integer  
uint16 
16bit unsigned integer  
uint32 
32bit unsigned integer  
uint64 
64bit unsigned integer  
sint8 
8bit signed integer  int8 
sint16 
16bit signed integer  int16 
sint32 
32bit signed integer  int32 
sint64 
64bit signed integer  int64 
sfloat 
single precision float  single 
dfloat 
double precision float  double 
scomplex 
single precision complex  
dcomplex 
double precision complex 
For example,
a = dip_image(a,'sfloat');
will convert the data in a
to single
(4byte) floats before creating
the dip_image
object. The variable a
now behaves somewhat
differently than you might be used to. The following sections explain
its behavior.
To convert a dip_image
object back to a MATLAB array use the function
dip_array
. It simply returns the data array stored inside the
dip_image
object. The functions double
, single
, uint8
, etc.
convert the dip_image
object to a MATLAB array of the specified class.
There are also some commands to create an image from scratch. newim
is
equivalent to the zeros
function, but returns a dip_image
object.
a = newim(256,256);
creates an image with 256x256 pixels set to zero. An additional
parameter (as in the table above) can be used to specify the
data type of the new image. The default is 'sfloat'
. If b
is an
object of type dip_image
, then
a = newim(b);
creates an image of the same size (this is the same as
newim(imsize(b))
). The functions xx
, yy
, zz
, rr
and phiphi
all
create an image containing the coordinates of its pixels, and can be
used in formulas that need them. For example, rr([256,256])<64
creates a
binary image with a disk of radius 64. The expression
a = (yy('corner'))*sin((xx('corner'))^2/300)
generates a nice test pattern with increasing frequency along the
xaxis, and increasing amplitude along the yaxis. All these functions
have 256x256 pixels as the default output size, and allow as a parameter
either the size of an image, or an image whose size is to be copied. For
example, a*xx(a)
is an image multiplied by its xcoordinates.
Displaying dip_image
objects
When a MATLAB command does not end with a semicolon, the display method
is called for the resulting values, if any. This method defaults to
calling the disp
method, which displays all the values in matrices.
For the dip_image
objects, the display method has been overloaded to
call dipshow
instead. dipshow
displays the image in a figure window
(see The dipshow
function for more information on this
function). Before display, dipshow
first calls squeeze
(see
Dimensions and Indexing pixels),
meaning that a 4x1x6 image will be displayed as if it were a 4x6 image.
The disp
method shows only the image size and data type instead. If
you want display
to call disp
instead of dipshow
, you can change
the 'DisplayToFigure'
preference using dipsetpref
(see
Toolbox preferences: dipsetpref
and dipgetpref
and Other settings).
For images that cannot be displayed by dipshow
, (e.g. zerodimensional
and empty images, tensor images, etc.), display
always calls disp
.
There exist overloaded methods to query image properties, such as size
and ndims
, and some methods that are specific to dip_image
objects,
such as imsize
, ntensordims
and datatype
.
Operations on dip_image
objects
All mathematical operations have been overloaded for the dip_image
object. The matrix multiplication (*
)
does a pixelbypixel multiplication, just as the array multiplication
(.*
) (the difference between these two operators becomes relevant
when we introduce tensor images, see Tensor images).
The same applies to the other matrix operations. Relational
operations return binary images. Binary operations on nonbinary images
treat any nonzero value in those images as true and zero as false. For
example, to do a threshold we do not need a special function, since we
have the relational operators:
b = a > 100;
A double threshold would be (note MATLAB‘s operator precedence):
b = a > 50 & a < 200;
When the two images in the operation do not have the same number of
dimensions, images are expanded to match each other. This is called
singleton expansion. For example, if image a
is 10x12x15, and
image b
is 10x12, then image b
is expanded along the third dimension
by replication to compute a+b
, resulting in an image the same size as
a
. If image a
is 10x1, and image b
is 1x12, the result of a+b
is
10x12. Only dimensions of size one (and nonexisting dimensions) will be
expanded. If image a
is 10x12, and image b
is 1x6, a+b
will
produce an error.
A note is required on the data types of the resulting images. The
“higher” data type always determines this result, but we have chosen
never to return an integer type after any arithmetic operation. Thus,
adding two integer images will result in a 4byte floatingpoint image;
an 8byte floatingpoint (double
) image is returned only if any of the
two inputs is double
.
Many of the arithmetic functions have also been defined for objects of
type dip_image
(see the two tables below for a complete listing).
The basic difference between these and their MATLAB counterpart is that by
default they work on the image as a whole, instead of on a percolumn basis.
For example, the function sum
returns a row
vector with the sum over the columns when applied to a numeric matrix,
but returns a single number when applied to an image. An additional argument
can be provided to compute a sum projection. Besides these,
there are some other functions that are only defined for objects of type
dip_image
. See Overloaded methods with different behavior to learn about these
functions. That section also lists some functions that behave
differently than usual when applied to images.
Arithmetic functions defined for objects of type dip_image (image in, image out) 


abs 
acos 
and , & 
angle 
asin 
atan 

atan2 
besselj 
ceil 
complex 
conj 
cos 

erf 
exp 
fix 
floor 
hypot 
imag 

log 
log10 
log2 
mod 
not , ~ 
or ,  

phase 
pow10 
pow2 
real 
round 
sign 

sin 
sqrt 
tan 
xor 
 
+ 

* 
.* 
./ 
/ 
\^ 
.^ 

== 
~= 
> 
>= 
< 
<= 
Arithmetic functions defined for objects of type dip_image (image in, scalar out) 


all 
any 
max 
mean 
median 
min 

percentile 
prod 
std 
sum 
var 
Dimensions
MATLAB arrays have at least 2 dimensions. This is not true for an image
in a dip_image
object, which can also have 0 or 1 dimension. That is,
for images there is an explicit distinction between a 2D image of size
256 by 1 pixels, and a 1D image of size 256. Even though both images
have the same number of pixels and their MATLAB array representation is
identical, these two images behave differently in many aspects. For
example, the imsize
method (which is specific to dip_image
objects,
and returns the image size) will return two numbers for the first image,
but only one for the second; similarly, it will return an empty array for
a 0D image (whereas the corresponding MATLAB matrix has a size of 1by1).
The method size
(which is overloaded from the common MATLAB function)
behaves more similarly to what you’re used to, as it always returns at
least two values. This method is implemented because MATLAB requires
it for displaying information with whos
, we recommend you always use
imsize
with dip_image
objects.
Use the function ndims
to obtain the number of dimensions in an image.
The 2D image in the example above has a singleton dimension. A singleton
dimension is any dimension of size 1. In MATLAB arrays, trailing
singleton dimensions are removed if the array has more than two
dimensions. That is, an array of size 4x1x6x1 is silently converted to
an array of size 4x1x6. This never happens with dip_image
objects.
As in MATLAB, operations between two images require that both images have compatible sizes. Singleton expansion is applied to make the two images equal in size. Singleton trailing dimensions can be applied to one of the images before singleton expansion, meaning that the images do not need to have the same dimensionality.
Indexing pixels
In image processing, it is conventional to index images starting at (0,0) in the upperright corner, and have the first index (usually x), index into the image horizontally. Unfortunately, MATLAB is based on matrices, which are indexed starting at one, and indicating the row number first. By encapsulating images in an object, we were allowed to redefine the indexing. We chose not to follow MATLAB‘s default indexing method. This might be confusing at first, and special care must be taken to check the class of a variable before indexing.
dip_image
objects are indexed from 0 to end
in each dimension, the
first being the horizontal. The imsize
function also returns the image
width as the first number in the array. Any portion of a dip_image
object, when extracted, is still a dip_image
object, and of the same
dimensionality, even if it is just a single pixel. Thus, if a
is a 3D
dip_image
object, a(0,0,0)
is also a 3D dip_image
object, even
though it only has a single pixel. To get a pixel value as a MATLAB
array, use double(a(0,0,0))
. To remove these singleton dimensions use
squeeze
. For example, a(:,:,2)
is a 3D image with a singleton
dimensions, whereas squeeze(a(:,:,2))
is a 2D image.
Any numeric type can be assigned into a dip_image
object, without
changing the image data type (that is, the element assigned into the
image is converted to the image data type). For example,
b(:,0) = 0;
sets the top row of the image in b
to 0. Note that indexing
expressions can become as complicated as you like. For example, to
subsample the image by a factor 3, we could write
b = b(1:3:end,1:3:end);
Instead of using full indexing (indexing each dimension separately), it
is also possible to index using a single (linear) index. As with standard
MATLAB arrays, the indices increase in the vertical direction, which is
how pixels are stored in memory. However they start at 0 for dip_image
objects (). The output is always a 1D image.
Finally, it is also possible to index using a mask image. Any binary image (or logical array) can be used as mask, but it must be of the same size as the image into which is being indexed. For example,
a(m) = 0;
sets all pixels in a
, where m
is one, to zero. A very common
expression is of the form
a(a<0) = 0;
(which sets all negative pixels to zero).
Note that the expression a(m)
above returns a onedimensional image,
with all pixels selected by the mask. It is equivalent to a(find(m))
,
where find
returns an array of indices where m
is one. This array is
then used as a linear index into a
.
Tensor images
Some image data benefits from assigning multiple values to each pixel. The most common example is a multichannel image, such as an RGB color image. The multichannel image is a form of vector image, where each pixel is a vector of values. Similarly, you could think of each pixel being a matrix. This concept can be generalized using tensors. A tensor can be a scalar value (0rank tensor), a vector (1rank tensor), a matrix (2rank tensor), etc. In DIPimage (and DIPlib) we currently limit the tensor rank to 2, simply because we never came across a use for higherrank tensor images.
The function newtensorim
creates a new tensor image filled with zeros:
A = newtensorim([2,2],[256,256])
creates a 2by2 tensor image of 256 by 256 pixels.
Note that a scalar image (with one component) is also a tensor
image (istensor
returns true). The function isscalar
returns true
when there is only one tensor component. Additionally, the function
isvector
returns true if the tensor has rank 1. Relevant similar
functions are iscolumn
, isrow
.
Some arithmetic operations behave differently for nonscalar images than
for scalar images. For example, the *
operator, which behaves
identically to the .*
operator for scalar images, actually applies
a matrix multiplication between each corresponding pair of pixels. For
example, the following code applies a matrix multiplication to the
2vector image b
, yielding a 2by2 matrix image c
:
a = readim('trui'); b = gradient(a) % yields a 2vector c = b * b' % yields a 2by2 matrix
The pixels of a tensor image can be indexed like a normal image,
returning a new tensor image. It can also be indexed using curly
braces ({}
) to select one or more tensor elements (channels). Indexing
into the tensor dimension is identical to indexing into a MATLAB
matrix: the first index goes down, and indices start at 0. For
example, c{1,1}
is a scalar image with the first tensor element of
each matrix in the image c
.
A single index uses linear indexing: c{1}
also is the first tensor element.
It is possible to combine spatial and tensor indexing, but the curly
braces have to come first (this is a limitation of the MATLAB parser).
Thus, write c{1}(0,0)
, not c(0,0){1}
.
Because of limitations in the MATLAB language, it is impossible to know,
for the overloaded end
method, if it is being used inside curly or
round braces (i.e. whether the last element of the image array is
requested, or the last pixel of the image is requested). The solution we
have adopted is to always assume round braces (()
). Never use end
within curly braces ({}
). You can use tensorsize
or numtensorel
to compute indices from the end for tensor indexing:
a{end}; % doesn't work! a{numtensorel(a)}; % returns the last tensor component
Note here that the image c
above is a special type of matrix image:
it is symmetric. That is because c{1,2}
and c{2,1}
are the result of
the same operation: b{1}*b{2}
. The *
operator recognizes that the two
inputs are transposed versions of each other (because they point at the
same data block), and thus knows not to compute the same thing twice.
The image c
actually only contains 3 tensor elements, even though it
represents a 2by2 matrix. Therefore, c{4}
is an outofbounds error,
whereas c{2,2}
returns the result of b{2}.^2
, and is identical to
c{3}
. There are special representations for the columnmajor matrix
(the default), rowmajor matrix (obtained by transposing a matrix, which
therefore doesn’t need to copy any data), symmetric matrix, and upper
and lower triangular matrices. How the elements are stored is described
in the DIPlib API documentation, but if you always access matrix
elements using the twoindex form then there is no need to know how
these are stored.
The method numtensorel
returns the number of tensor elements, and
the method tensorsize
returns the size of the tensor.
To get the array at a single pixel, use the double
function:
c(0,0)
is a tensor image with a single pixel, and double(c(0,0))
is
a MATLAB array with the tensor values at the first pixel.
Functions defined specifically for tensor images are summarized in the following table. See Overloaded methods with different behavior.
Functions defined for tensor images  

cross 
curl 
det 
diag 
divergence 
dot 

eig 
eye 
inv 
norm 
pinv 
rotate 

svd 
trace 
* 
.' 
' 
Color images
A color image is represented in a dip_image
object by a tensor image
with some extra information on the color space in which the pixel values
are to be interpreted. A color image must have more than one channel, so
the tensor image that represents it should have at least two components.
Use the colorspace
function to add this color space information to a
tensor image:
C = colorspace(A,'RGB')
A color space is any string recognized by the system. See help colorspace
for currently known color spaces.
Images with a color space will be displayed by dipshow
, which will
convert them to RGB for a correct representation.
To convert an image from one color space to another, use the
colorspace
function. Converting to a colorspaceless tensor image is
done by specifying the empty string as a color space. This action only
changes the color space information, and does not change any pixel
values. Thus, to change from one color space to another without
converting the pixel values themselves, change first to a
colorspaceless tensor image, and then to the final color space.
The function joinchannels
combines two or more images into a color
image using the specified color space:
C = joinchannels('RGB',a,b,c)
The function newcolorim
creates a new color image of the given
color space, filled with zeros:
C = newcolorim([256,256],'RGB');
All operations that are defined for tensor images can be applied to color images. These operations simply ignore the color space. Thus, adding two images with different color spaces does not cause one to be converted to the other color space. Typically, the output image will have the color space of the first input image with a color space and whose number of tensor elements matches that of the output image.
Manipulating the image shape
Functions used in MATLAB to manipulate array dimensions have been overloaded to do the same thing with images. They are listed in the table below.
Dimension manipulation functions defined for objects of type dip_image 


cat 
circshift 
expanddim 
flipdim 
fliplr 
flipud 

permute 
repmat 
reshape 
rot90 
shiftdim 
squeeze 

swapdim 
tensortospatial 
spatialtotensor 
A few of these functions are unique to dip_image
objects.
The function expanddim
adds trailing singleton dimensions, and swapdim
is a simpler interface to the more general permute
, and allows to
swap two image dimensions.
spatialtotensor
takes a spatial dimension of a scalar image and converts
it to the tensor dimension, returning a vector image. tensortospatial
does
the reverse, returning a scalar image.
When not specifying which spatial dimension to use, both these functions pick
the dimension that requires no copying of data: 2. If you specify any other
dimension, the data must be copied (and reordered). Thus, by using dimension 2,
it is possible to exchange image shapes very efficiently, for example to
apply functions such as max
or sum
along the tensor dimension.
Note that reshape
and squeeze
never copy image data (but see
A note on the reshape and squeeze methods), and thus preserve the
linear indexing order (the linear indexing order is related to storage in memory).
Because linear indexing order matches the MATLAB storage order, dimension 2
is the most rapidly changing dimension. This means that squeezing an image of
size [1,10,20,30]
leads to an image of size [20,10,30]
, not [10,20,30]
,
as one would expect.
A note on the reshape and squeeze methods
reshape
and squeeze
have a different behavior in DIPimage 3 than they
had in earlier versions of the toolbox. The behavior was changed for consistency,
though the new behavior can be surprising at times.
In older versions of the toolbox, reshape
and squeeze
often reordered the
data (i.e. incurred the cost of a data copy), whereas the methods applied to a
normal array never do so, these methods are supposed to be essentially free.
reshape
was implemented to fill the output image rowwise with pixels taken
rowwise from the input image. But because MATLAB stores matrices columnwise,
the data copy was necessary. However, this behavior was inconsistent with
linear indexing, which wasn’t translated to use that same ordering. That is,
linear indexing used the memory order of the pixels to translate an index to
pixel coordinates, in the same way that it works for normal array. Thus,
applying reshape
(or squeeze
, which applies a reshape
to remove singleton
dimensions) would change the pixels accessed at a given linear index, which is
counterintuitive. For example, in the following program a
and b
are
different values:
img = dip_image(rand(10,11,8)); a = img(200); img = reshape(orig,[11,8,10]); b = img(200);
DIPimage 3 changed this behavior, such that reshape
and squeeze
are
essentially free like they are for normal MATLAB arrays. Reshaping or squeezing
an image is consistent with linear indexing (i.e. a
and b
above have the
same value). However, this causes a different surprising behavior: squeeze
reorders dimensions!
MATLAB’s array memory layout is such that a dip_image
‘s dimensions are ordered
in memory like so: [2, 1, 3, 4, …]. If squeeze
were to remove dimension number
1, subsequent dimensions would move left, meaning that dimension number 3 ends up
in the location of dimension 1, but 2 stays where it was. An image of size 1x20x30,
when squeezed, becomes an image of size 30x20, not 20x30 as one would expect.
Similarly, removing dimension 2 would move dimension 1 to its place, and dimension
3 to the place of 1. Thus, an image of size 20x1x30 becomes a image of size 30x20,
not 20x30 as one would expect.
Setting the preference CheapSqueeze
to 'off'
changes the behavior of squeeze
to match its old behavior,
possibly incurring a data copy. In essence, when the setting is 'off'
,
then squeeze
is implemented through permute
, whereas when it is 'on'
(the default), it is implemented through reshape
.
Overloaded methods with different behavior
Most overloaded methods behave in a consistent manner with the builtin
MATLAB functions that they overload. However, due to differences of
the dip_image
object, some behave somewhat differently. We summarize
these functions here.
find
, findcoord
find
works similarly to the base version, except it is not possible
to obtain [I,J]
indices as output. The indices returned are always
linear indices. An optional second output argument receives the nonzero
values. To obtain the coordinates of nonzero values, use findcoord
instead. It returns the coordinates of the pixels with nonzero values
as a single array, with as many columns as dimensions in the input
image, and one row for every nonzero pixel. Note that this matrix
cannot be used directly to index an image.
gradient
The overloaded version of gradient
returns a vector image, instead of
multiple outputs. The derivatives are computed using Gaussian
derivatives by default.
ind2sub
, sub2ind
These functions have the same function as their base counterparts, but
instead of using subscripts specified with one array for each dimension,
they take and return a single coordinate array, compatible to that
returned by findcoord
. Also, instead of a size array, they take an
image as input.
isscalar
, isvector
, isrow
, iscolumn
, ismatrix
These functions examine the tensor shape, not the image shape. A scalar
image (it has a single channel) tests true with isscalar
, no matter
how many spatial dimensions it has.
max
, min
, mean
, median
, std
, var
, prod
, sum
, all
, any
The builtin MATLAB versions of these always operate along matrix columns, yielding a row vector where each element is the max/min/mean/etc. of the corresponding column. This is a max/min/mean/etc. projection. It is possible to have them work along a different array dimension, and only since R2018b along multiple dimensions.
The overloaded versions of these functions that operate on dip_image
objects can work along any number of dimensions simultaneously. By default,
they operate on all dimensions, such that max(a)
returns the maximum
value of the image a
. And max(a,[],[2,3])
, if a
is a 3D image, returns
a 3D image with two singleton dimensions, where each pixel i
contains the
maximum over a(i,:,:)
.
Note there is a second argument to max
that we didn’t use above. The
projection functions all take a mask image as an optional second argument.
The projection is taken only over those pixels selected by the mask. For
example,
mean(a,a>0,1)
computes the mean projection along the first dimension (x axis), but only computes the mean over the positive pixels.
The function percentile
is also projection function, but does not have a
counterpart for MATLAB arrays (unless you have the statistics toolbox).
ndims
This method can return 0 or 1 (for 0D and 1D images, respectively).
For normal MATLAB arrays it always returns at least 2. Note that
ndims(a)
is not necessarily equal to length(size(a))
, but it is
equal to length(imsize(a))
.
numel
The overloaded numel
is the number of samples in the image. Note that
prod(size(a))
is not equal to numel(a)
, as it is for regular arrays.
Instead, the following relations hold:

prod(size(a)) == numpixels(a)

prod(tensorsize(a)) == numtensorel(a)

numpixels(a) * numtensorel(a) == numel(a)
rotate
The overloaded method rotate
has nothing to with MATLAB‘s rotate
(a handle graphics function).
Applied to a 3vector image, it rotates the vectors around an axis
given by a second vector image or vector.
Review of the differences between a dip_image
and a MATLAB array
As we have seen, objects of type dip_image
have some differences with
respect of regular MATLAB arrays. The main difference is in indexing. We
start counting pixels from 0, and the first index counts from left to
right. This ordering is also used by functions such as imsize
, in which
the first number is the image width and the second one the height.
Finally, ndims
can return 0 or 1, which it never does for MATLAB
arrays. The reason is that zerodimensional and onedimensional images are
allowed, and are not seen as a special case of twodimensional images.
Furthermore, singleton dimensions at the end are not ignored.
Another major difference is that one of the dimensions is not a spatial
dimension, and is not included in the result of imsize
and ndims
, or
accessible using normal indexing. This dimension represents a tensor at
each image pixel. tensorsize
and numtensorel
are relevant here, as
is indexing using curly braces ({}
) as in cell array indexing.
Color images are images with multiple tensor elements (i.e. channels),
and color space information.
When a MATLAB command results in an object of type dip_image
, and it
is not ended with a semicolon, the image is displayed to a figure
window, instead of having its pixel values shown in the command window.
This is the default behavior, but can be overridden.
All operators work on a pixelbypixel basis. For example, the transpose
operators '
and .'
transpose the vector or matrix at each pixel,
not the image itself, and the multiplication operator *
applies matrix
multiplication to each of the corresponding pixel pairs.
All functions that work on the columns of numeric arrays (such as sum
and max
) work on the image as a whole when applied to a dip_image
object.
Objects of type dip_image
cannot be used in functions of the
MathWorks’ Image Processing Toolbox. Although most of MATLAB‘s functions
work on dip_image
objects, not every function will work as expected.
Use the functions dip_array
, double
or uint8
to convert the image
to a format recognizable by these functions.