We present the design, implementation, and application of several families of fast multiplierless approximations of the discrete cosine transform (DCT) with the lifting scheme called the binDCT. These binDCT families are derived from Chen's (1977) and Loeffler's (1989) plane rotation-based factorizations of the DCT matrix, respectively, and the design approach can also be applied to a DCT of arbitrary size. Two design approaches are presented. In the first method, an optimization program is defined, and the multiplierless transform is obtained by approximating its solution with dyadic values. In the second method, a general lifting-based scaled DCT structure is obtained, and the analytical values of all lifting parameters are derived, enabling dyadic approximations with different accuracies. Therefore, the binDCT can be tuned to cover the gap between the Walsh-Hadamard transform and the DCT. The corresponding two-dimensional (2-D) binDCT allows a 16-bit implementation, enables lossless compression, and maintains satisfactory compatibility with the floating-point DCT. The performance of the binDCT in JPEG, H.263+, and lossless compression is also demonstrated.

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Fast multiplierless approximations of the DCT with the lifting scheme

A compression and decompression system in which a reversible wavelet filter are used to generates coefficients from input data, such as image data. The reversible wavelet filter is an efficient transform implemented with integer arithmetic that has exact reconstruction. The present invention uses the reversible wavelet filter in a lossless system (or lossy system) in which an embedded codestream is generated from the coefficients produced by the filter. An entropy coder performs entropy coding on the embedded codestream to produce the compressed data stream.

Method and apparatus for compression using reversible wavelet transforms and an embedded codestream

A digital segmentation method and apparatus determines foreground and/or background within at least one portion of a captured image. The determining includes comparing a captured image to a pre-captured or post captured reference image of nominally the same scene. One of the images is taken with flash and the other without. The system can be implemented as part of a digital camera acquisition chain having effective computation complexity.

Foreground/Background Segmentation in Digital Images with Differential Exposure Calculations

Compression/decompression using reversible embedded wavelets

Many consumer digital color cameras use a single light sensitive sensor and a color filter array (CFA) with each pixel element recording intensity information of one color component. The captured data is interpolated into a full color image, which is then compressed in many applications. Carrying out color interpolation before compression introduces redundancy in the data. In this paper we discuss methods and issues involved in the compression of CFA data before full color interpretation. The compression methods described operate on the same number of pixels as the sensor data. To obtain improved image quality, median filtering is applied as post-processing. Furthermore, to assure low complexity, the CFA data is compressed by JPEG. Simulations have demonstrated that substantial improvement in image quality is achievable using these new schemes.

New efficient methods of image compression in digital cameras with color filter array

In this paper, reversible subband coding of images are proposed. The high-band signals of conventional one-dimensional reversible filter banks were extrapolative prediction error signals or interpolative ones of which number of levels became four times that of the input signals. Therefore, we design reversible filter banks that generate interpolative prediction error signals of which number of levels becomes twice that of the input signals. We also design nonseparable filter banks. It is shown that the proposed methods have the better performance than the conventional reversible subband coding and that the separable method with low-pass filter has little aliasing in the reduced images.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Reversible subband coding of images

In this paper a reversible discrete cosine transform (RDCT) is presented. The N-point reversible transform is firstly presented, then the 8-point RDCT is obtained by substituting the 2 and 4-point reversible transforms for the 2 and 4-point transforms which compose the 8-point discrete cosine transform (DCT), respectively. The integer input signal can be losslessly recovered, although the transform coefficients are integer numbers. If the floor functions are ignored in RDCT, the transform is exactly the same as DCT with determinant=1. RDCT is also normalized so that we can avoid the problem that dynamic range is nonuniform. A simulation on continuous-tone still images shows that the lossless and lossy compression efficiencies of RDCT are comparable to those obtained with reversible wavelet transform.

Reversible discrete cosine transform

Since the lossless DCT is compatible with JPEG or MPEG, it is expected to play an important role in unified lossless/lossy image coding. However, there is a problem that the difference between the transform coefficients of the lossless DCT and those of the (lossy) DCT is not very small. We present the design of a two dimensional lossless DCT based on a 4-point two dimensional lossless WHT and indicate that its number of rounding off becomes smaller than that of the one dimensional lossless DCT and, as a result, the difference between its transform coefficients and those of the DCT becomes small.

2D lossless discrete cosine transform

SUMMARY Lossless block transforms and filter banks that map integers to integers are important for unified lossless and lossy image coding systems. In this paper, we present simple yet effective methods for designing lossless versions of block transforms and FIR filter banks. First, an N-point lossless transform and a lossless interpolative prediction are introduced. Next, we demonstrate that filter banks can be decomposed into 2-point transforms or interpolative predictions. Lastly, lossless versions of block transforms and filter banks are obtained by replacing every constituent module by the corresponding lossless version. Lossless versions of 8-point discrete cosine transform (DCT), 8point Walsh-Hadamard transform (WHT) and several filter banks are designed and their lossless compression performance is evaluated.

Design of Lossless Block Transforms and Filter Banks for Image Coding

The 64-point separable lossless two dimensional (2D) WHT is composed of the 8-point lossless one dimensional WHT. The latter is obtained by first decomposing the 8-point WHT into 2-point WHTs and then replacing every 2-point WHT by a ladder network. Since the coefficients in the ladder network then become real, the advantage of being multiplier-free vanishes. This paper therefore proposes a 64-point nonseparable lossless 2D WHT without multiplication as follows. First, the 64-point separable 2D WHT is decomposed into 4-point 2D WHTs. Second, every 4-point 2D WHT is replaced by a 2D ladder network which is multiplier-free. It is also shown that the transform coefficients of the proposed transform are closer to those of the 64-point lossy 2D WHT than those of the 64-point separable lossless 2D WHT.

Kunitoshi Komatsu

Papers

Reversible subband coding of images

Reversible discrete cosine transform

2D lossless discrete cosine transform

Design of Lossless Block Transforms and Filter Banks for Image Coding

Lossless 2D discrete Walsh-Hadamard transform