Question

How do i find the image height and width in SOF marker Segment( the Xthumbnail and Ythumbnail are all 0)?

Which is the resolution of the image

ff d8 ff e0 00 10 4a 46 49 46 00 01 01 01 00 c8
 00 c8 00 00 ff db 00 43 00 02 02 02 02 02 01 02
 02 02 02 02 02 02 03 03 06 04 03 03 03 03 07 05
 05 04 06 08 07 08 08 08 07 08 08 09 0a 0d 0b 09
 09 0c 0a 08 08 0b 0f 0b 0c 0d 0e 0e 0e 0e 09 0b
 10 11 0f 0e 11 0d 0e 0e 0e ff db 00 43 01 02 02
 02 03 03 03 06 04 04 06 0e 09 08 09 0e 0e 0e 0e
 0e 0e 0e 0e 0e 0e 0e 0e 0e 0e 0e 0e 0e 0e 0e 0e

here is the image link: http://jeff.cis.cabrillo.edu/datasets/uc-seal.jpg

Answer 1

Regarding the above problem specification,

All tags in JPEG files start with the value 0xFF. If the value 0xFF is ever needed in a JPEG file, it must be escaped by immediately following it with 0x00 which is called "byte stuffing".

So knowing that markers are 0xFF followed by anything other than 0x00, it becomes easy to start pulling apart JPEG files.

xxd -c16 -g1 -u testimg.jpg | grep --color=always -C999 FF

00000000: FF D8 FF E0 00 10 4A 46 49 46 00 01 01 00 00 01 ......JFIF......

00000010: 00 01 00 00 FF DB 00 43 00 08 06 06 07 06 05 08 .......C........

00000020: 07 07 07 09 09 08 0A 0C 14 0D 0C 0B 0B 0C 19 12 ................

00000030: 13 0F 14 1D 1A 1F 1E 1D 1A 1C 1C 20 24 2E 27 20 ........... $.'

00000040: 22 2C 23 1C 1C 28 37 29 2C 30 31 34 34 34 1F 27 ",#..(7),01444.'

00000050: 39 3D 38 32 3C 2E 33 34 32 FF DB 00 43 01 09 09 9=82<.342...C...

00000060: 09 0C 0B 0C 18 0D 0D 18 32 21 1C 21 32 32 32 32 ........2!.!2222

00000070: 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 2222222222222222

00000080: 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 2222222222222222

00000090: 32 32 32 32 32 32 32 32 32 32 32 32 32 32 FF C0 22222222222222..

000000a0: 00 11 08 00 95 00 E3 03 01 22 00 02 11 01 03 11 ........."......

000000b0: 01 FF C4 00 1F 00 00 01 05 01 01 01 01 01 01 00 ................

000000c0: 00 00 00 00 00 00 00 01 02 03 04 05 06 07 08 09 ................ ...

All markers but two are immediately followed by a 2-byte size. The size never includes the 2-byte marker itself, but always includes the 2-byte size. This means the data in a marker is limited to 64KiB - 2 bytes. However, a marker may appear multiple times, and one particular marker -- the one with the actual image data -- works slightly differently to accomodate a payload of any size.

SOF0 (start of frame) - 0xFFC0

xxd -c16 -g1 -u testimg.jpg | grep --color=always -C2 "FF C0"
0000090: 32 32 32 32 32 32 32 32 32 32 32 32 32 32 FF C0 22222222222222..
00000a0: 00 11 08 00 95 00 E3 03 01 22 00 02 11 01 03 11 ........."......
00000b0: 01 FF C4 00 1F 00 00 01 05 01 01 01 01 01 01 00 ................

Description:

0xFF, 0xC0, // SOF0 segement
0x00, 0x11, // length of segment depends on the number of components
0x08, // bits per pixel
0x00, 0x95, // image height
0x00, 0xE3, // image width
0x03, // number of components (should be 1 or 3)
0x01, 0x22, 0x00, // 0x01=Y component, 0x22=sampling factor, quantization table number
0x02, 0x11, 0x01, // 0x02=Cb component, ...
0x03, 0x11, 0x01 // 0x03=Cr component, ...

The 2-byte image height and width fields explains why a JPEG is limited to 65535 x 65535 in size.

Hope this helps.

Thank you.