Hi Jukka,

> 
> If I run gdalinfo against the JPEG2000 image in
> http://kartat.kapsi.fi/files/orto/etrs-tm35fin/mara_v_25000_50/2013/N53/02m
> /1/N5144H.jp2 the JP2ECW driver reports the blocksize as (256x256) and
> JPEG2000OpenJPEG driver reports that the block size is (1024x1024).

Yes for single tiled images, all JPEG2000 drivers will report a block size
of much smaller dimension to avoid GDAL consuming too much memory.

> 
> What interests me would be to know the fact that this image has only one
> JPEG2000 tile with a tilesize of (11754x11754). Is there any
> driver-independent way for getting this information?

You can use the opj_dump utility from openjpeg, or a GDAL Python script
https://svn.osgeo.org/gdal/trunk/gdal/swig/python/samples/dump_jp2.py

$ python swig/python/samples/dump_jp2.py 
/vsicurl/http://kartat.kapsi.fi/files/orto/etrs-tm35fin/mara_v_25000_50/2013/N53/02m/1/N5144H.jp2
 | grep "siz\""

        <Field name="Rsiz" type="uint16" description="Unrestricted 
profile">0</Field>
        <Field name="Xsiz" type="uint32">11754</Field>     <-- image width
        <Field name="Ysiz" type="uint32">11754</Field>     <-- image height
        <Field name="XOsiz" type="uint32">0</Field>
        <Field name="YOsiz" type="uint32">0</Field>
        <Field name="XTsiz" type="uint32">11754</Field>    <-- tile width
        <Field name="YTsiz" type="uint32">11754</Field>    <-- tile height
        <Field name="Csiz" type="uint16">3</Field>


Even

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