Discrete Cosine Transform (DCT)
Definition
A mathematical transform that expresses a block of pixel values as a sum of cosine functions at different frequencies. JPEG applies the DCT to 8x8 pixel blocks. The resulting 64 DCT coefficients represent the spatial frequency content of the block, with low-frequency terms in the top-left of the coefficient matrix and high-frequency terms in the bottom-right.
Related terms
- Block grid phase
- The horizontal and vertical offset of the 8x8 encoding grid relative to the image coordinate origin. A phase of (0,0) means the...
- Blocking artifact
- A visual discontinuity at the boundary between two adjacent 8x8 blocks in a JPEG image, caused by independent quantisation of each block....
- Compression floor
- The stable low-residual state that a JPEG region approaches after many successive saves at the same quality. Once the DCT coefficients are...
- Double JPEG compression
- The situation where an image has been JPEG-encoded, decoded to a bitmap, and then JPEG-encoded again. The second quantisation step leaves a...
- Double quantisation effect
- The statistical artefact that appears in DCT coefficient histograms when a video or image is quantised twice with different step sizes. The...
- ELA residual
- The pixel-level absolute difference at a given location after re-compression. High residual means the pixel value moved substantially on re-compression, indicating the...
- Error Level Analysis (ELA)
- A technique that re-compresses a JPEG at a controlled quality setting and maps the pixel-level difference between the re-compressed and original images....
- Intra-frame vs inter-frame coding
- Intra-frame (I-frame) coding compresses each frame independently using DCT quantisation, like a JPEG image. Inter-frame (P-frame or B-frame) coding stores only the...
- JPEG ghost
- A visualisation technique introduced by Farid (2009) that reveals regions compressed at a quality factor different from the rest of the image....
- Macroblock
- The fundamental coding unit in most video codecs: a 16x16 pixel block in luma (brightness) and the corresponding chroma samples. Macroblocks are...
- Quantisation
- The step in lossy compression where DCT coefficients are divided by a quantisation parameter and rounded to integers. Higher quantisation parameters produce...
- Quantisation parameter (QP)
- A per-block or per-slice value that controls the coarseness of the DCT coefficient rounding step in H.264 and H.265. Higher QP means...
Explained in these topics
- DCT Block Boundaries and Quantisation Grid AnalysisA mathematical transform that expresses a block of pixel values as a sum of cosine functions at different frequencies. JPEG applies the DCT to 8x8 pixel blocks...
- JPEG Compression Artifacts and Error Level AnalysisThe mathematical transform JPEG uses to convert each 8x8 pixel block from the spatial domain into frequency coefficients. Higher-frequency coefficients represe...
- Double Compression Analysis in VideoA mathematical transform applied to pixel blocks in most video codecs. It converts spatial pixel values into frequency coefficients. Most of the signal energy...