int QccWAVTarpEncode(const
QccIMGImageComponent *image, const QccIMGImageComponent *mask, double
alpha, int num_levels, int target_bit_cnt, const QccWAVWavelet *wavelet,
QccBitBuffer *output_buffer);
int QccWAVTarpDecodeHeader(QccBitBuffer
*input_buffer, double *alpha, int *num_levels, int *num_rows, int *num_cols,
double *image_mean, int *max_coefficient_bits);
int QccWAVTarpDecode(QccBitBuffer
*input_buffer, QccIMGImageComponent *image, const QccIMGImageComponent
*mask, double alpha, int num_levels, const QccWAVWavelet *wavelet, double
image_mean, int max_coefficient_bits, int target_bit_cnt);
QccWAVTarpEncode() encodes an image component, image, using the tarp algorithm by Simard et al. The tarp algorithm involves a 2D DWT followed by a progressive "bitplane" coding of the wavelet coefficients using a Parzen-window technique to estimate probability of significance and nonadaptive arithmetic coding to code significance-map and refinement information. See "ALGORITHM" below for more detail.
image is the image component to be coded and buffer is the output bitstream. buffer must be of QCCBITBUFFER_OUTPUT type and opened via a prior call to QccBitBufferStart(3) .
num_levels gives the number of levels of dyadic wavelet decomposition to perform, and wavelet is the wavelet to use for decomposition.
The tarp algorithm performance is determined primarily through the parameter alpha, a value that gives the learning rate of the density-estimation process implemented by the tarp filter. Simard et al. originally used a value of alpha = 0.6.
The bitstream output from the tarp encoder is embedded, meaning that any prefix of the bitstream can be decoded to give a valid representation of the image. The tarp encoder essentially produces output bits until the number of bits output reaches target_bit_cnt, the desired (target) total length of the output bitstream in bits, and then it stops. Note that this is the bitstream length in bits, not the rate of the bitstream (which would be expressed in bits per pixel).
QccTarpEncode() optionally supports the use of a shape-adaptive DWT (SA-DWT) rather than the usual DWT. That is, QccTarpEncode() can call QccWAVSubbandPyramidShapeAdaptiveDWT(3) as the wavelet transform rather than the usual QccWAVSubbandPyramidDWT(3) . The use of a SA-DWT is indicated by a non-NULL mask; if mask is NULL, then the usual DWT is used. In the case of a SA-DWT, mask gives the transparency mask which indicates which pixels of the image are non-transparent and thus have data that is to be transformed. Refer to QccWAVSubbandPyramidShapeAdaptiveDWT(3) for more details on the calculation of this SA-DWT, and see "ALGORITHM" below for how the shape-adaptive mask is employed in the tarp algorithm.
QccWAVTarpDecodeHeader() decodes the header information in the bitstream in the input buffer (which must be of QCCBITBUFFER_INPUT type and opened via a prior call to QccBitBufferStart(3) ). The header information is returned in alpha (the learning-rate parameter of the density-estimation process), num_levels (number of levels of wavelet decomposition), num_rows (vertical size of image), num_cols (horizontal size of image), image_mean (the mean value of the original image), and max_coefficient_bits (the number of bits used to represent the magnitude of the coefficient with largest absolute value).
QccWAVTarpDecode() decodes the bitstream buffer, producing the reconstructed image component, image. The bitstream must already have had its header read by a prior call to QccWAVTarpDecodeHeader() (i.e., you call QccWAVTarpDecodeHeader() first and then QccWAVTarpDecode()). If target_bit_cnt is QCCENT_ANYNUMBITS, then decoding stops when the end of the input bitstream is reached; otherwise, decoding stops when target_num_bits from the input bitstream have been decoded.
If a SA-DWT was used in tarp encoding, then the original transparency mask should be passed to QccWAVTarpDecode() as mask. That is, mask should be the same transparency mask (in the spatial domain) that was passed to QccWAVTarpEncode(). Note that QccWAVTarpDecode() will transform this mask via a Lazy wavelet transform, and then pass the transformed mask to QccWAVSubbandPyramidInverseShapeAdaptiveDWT(3) . If the usual DWT was used in encoding, then mask should be a NULL pointer.
The embedded tarp coder as implemented in QccPack involves a 2D DWT followed by a progressive encoding of the bitplanes of wavelet coefficients. As is common with bitplane-based embedded coders, the encoder of the tarp algorithm codes significance information in a significance pass followed by refinement-bit information in a refinement pass. The significance pass determines the significance of a wavelet coefficient against a given threshold, while the refinement pass codes the bits of those coefficients previously determined to be significant.
The unique aspect of the tarp algorithm is in the significance pass. The tarp algorithm employs a density-estimation process based upon Parzen windows to determine the probability that each currently insignificant coefficient becomes significant in the current significance pass. This probability is passed to a two-symbol, nonadaptive arithmetic coder to code the actual significance value of the current coefficient. The alpha parameter to the algorithm determines the shape of the Parzen windows employed, effectively determining the learning rate of the density-estimation process. The actual density estimation is implemented as an efficient set of filtering operations that create a causal 2D filter that looks like a canvas propped up by a pole at the current coefficient, hence the name "tarp" filter. That's it - no runlength coding, no zerotrees - just a simple density estimation.
The refinement pass codes refinement bits using the same nonadaptive arithmetic coder used in the significance pass except that the refinement bits are assumed equally likely, and thus a uniform density is used by the nonadaptive arithmetic coder.
There are several ways to handle the overlapping of the 2D causal tarp filter beyond the image boundaries. Simard et al. proposed boundary initial conditions that attempt to spread prior knowledge accumulated during the filtering along the boundary. In contrast, the implementation here takes the simpler route of merely assuming all values beyond the image boundaries are insignificant. It is unlikely that either approach differs much from the other in terms of rate-distortion performance.
As proposed by Fowler, to handle shape-adaptive coding (not originally considered by Simard et al.), the implementation here merely skips over the transparent regions, maintaining the current probability estimate unchanged.
Finally, we note that Tian and Hemami proposed a variant of tarp coding somewhat similar to what is implemented here in that they use the tarp filter to code significance information. However, their approach is somewhat more sophisticated in that fraction bitplanes are used in the significance pass to achieve a higher degree of embeddedness.
Lenna
------------------------------------
| Rate | PSNR (db) |
| (bpp) | Tarp SPIHT |
------------------------------------
| 0.2 | 32.83 | 32.94 |
| 0.5 | 36.74 | 37.11 |
| 1.0 | 39.85 | 40.28 |
------------------------------------
Average difference = 0.22 dB
Barbara
------------------------------------
| Rate | PSNR (db) |
| (bpp) | Tarp SPIHT |
------------------------------------
| 0.2 | 26.48 | 26.48 |
| 0.5 | 31.07 | 31.33 |
| 1.0 | 35.90 | 36.43 |
------------------------------------
Average difference = 0.11 dB
Goldhill
------------------------------------
| Rate | PSNR (db) |
| (bpp) | Tarp SPIHT |
------------------------------------
| 0.2 | 29.62 | 29.68 |
| 0.5 | 32.97 | 32.96 |
| 1.0 | 36.16 | 36.37 |
------------------------------------
Average difference = 0.12 dB
P. Simard, D. Steinkraus, and H. Malvar, "On-Line Adaptation in Image Coding with a 2-D Tarp Filter", in Proceedings of the IEEE Data Compression Conference, J. A. Storer and M. Cohn, Eds., Snowbird, UT, April 2002, pp. 422-431.
J. E. Fowler, "Shape-Adaptive Tarp Coding," in Proceedings of the International Conference on Image Processing, Barcelona, Spain, September 2003, vol. 1, pp. 621-624.
C. Tian and S. S. Hemami, "An Embedded Image Coding System Based on Tarp Filter with Classification," in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Montreal, Canada, May 2004, to appear.