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ImageMagick's JPEG-2000 image formats, JP2 and JPC, accept a plethora of encoding options as detailed below. As an example, suppose you are interested in these options:

Use this command:

$magick> convert wizard.png -define jp2:cblkwidth=64 -define jp2:cblkheight=32 \
-define jp2:nomct -define jp2:numrlvls=4 -define jp2:rate=0.015625 wizard.jpc

Here is a complete list of JPEG-2000 encoding options:

imgareatlx=x
Set the x-coordinate of the top-left corner of the image area to x.
imgareatly=y
Set the y-coordinate of the top-left corner of the image area to y.
tilegrdtlx=x
Set the x-coordinate of the top-left corner of the tiling grid to x.
tilegrdtly=y
Set the y-coordinate of the top-left corner of the tiling grid to y.
tilewidth=w
Set the nominal tile width to w.
tileheight=h
Set the nominal tile height to h.
prcwidth=w
Set the precinct width to w. The argument w must be an integer power of two. The default value is 32768.
prcheight=h
Set the precinct height to h. The argument h must be an integer power of two. The default value is 32768.
cblkwidth=w
Set the nominal code block width to w. The argument w must be an integer power of two. The default value is 64.
cblkheight=h
Set the nominal code block height to h. The argument h must be an integer power of two. The default value is 64.
mode=m
Set the coding mode to m. The argument m must have one of the following values:
Value Description
int integer mode
real real mode
If lossless coding is desired, the integer mode must be used. By default, the integer mode is employed. The choice of mode also determines which multicomponent and wavelet transforms (if any) are employed.
rate=r
Specify the target rate. The argument r is a positive real number. Since a rate of one corresponds to no compression, one should never need to explicitly specify a rate greater than one. By default, the target rate is considered to be infinite.
ilyrrates=r0[,r1,. . . ,rN]
Specify the rates for any intermediate layers. The argument to this option is a comma separated list of N rates. Each rate is a positive real number. The rates must increase monotonically. The last rate in the list should be less than or equal to the overall rate (as specified with the rate option).
prg=p
Set the progression order to p. The argument p must have one of the following values:
Value Description
lrcp layer-resolution-component-position (LRCP) progressive (i.e., rate scalable)
rlcp resolution-layer-component-position (RLCP) progressive (i.e., resolution scalable)
rpcl resolution-position-component-layer (RPCL) progressive
pcrl position-component-resolution-layer (PCRL) progressive
cprl component-position-resolution-layer (CPRL) progressive
By default, LRCP progressive ordering is employed. Note that the RPCL and PCRL progressions are not valid for all possible image geometries.
nomct
Disallow the use of any multicomponent transform.
numrlvls=n
Set the number of resolution levels to n. The argument n must be an integer that is greater than or equal to one. The default value is 6.
sop
Generate SOP marker segments.
eph
Generate EPH marker segments.
lazy
Enable lazy coding mode (a.k.a. arithmetic coding bypass).
termall
Terminate all coding passes.
segsym
Use segmentation symbols.
vcausal
Use vertically stripe causal contexts.
pterm
Use predictable termination.
resetprob
Reset the probability models after each coding pass.
numgbits=n
Set the number of guard bits to n.