The principal component analysis (PCA) is widely used for data decorrelation and dimensionality reduction. However, the use of PCA may be impractical in real-time applications, or in situations were energy and computing constraints are severe. In this context, the discrete cosine transform (DCT) becomes a low-cost alternative to data decorrelation. This paper presents a method to derive computationally efficient approximations to the DCT. The proposed method aims at the minimization of the angle between the rows of the exact DCT matrix and the rows of the approximated transformation matrix. The resulting transformations matrices are orthogonal and have extremely low arithmetic complexity. Considering popular performance measures, one of the proposed transformation matrices outperforms the best competitors in both matrix error and coding capabilities. Practical applications in image and video coding demonstrate the relevance of the proposed transformation. In fact, we show that the proposed approximate DCT can outperform the exact DCT for image encoding under certain compression ratios. The proposed transform and its direct competitors are also physically realized as digital prototype circuits using FPGA technology.

The ecological apparency hypothesis seeks to understand the dynamics of use that a particular species has through its availability in vegetation areas. According to this hypothesis, apparent plants are the most collected and used by humans. This hypothesis was tested in the rural community of Santa Rita, municipality of Congo, in Cariri microregion (Paraíba state, Northeast Brazil). We calculated the use value (UV) for each species. For the phytosociological inventory, we adopted the point-quadrant method, plotting 500 points distributed in the vegetation areas of the community, registering the perimeter measurements and height of 2000 plants. Interviews were conducted with householders, totaling 98 informants (41 men and 57 women), and 24 species, 21 genera, and 11 families were recorded. The cited species were grouped into 11 utility categories. The Spearman correlation coefficient was used to correlate phytosociological and ethnobotanical data. The use values of the species did not correlate with phytosociological parameters. Regarding the use categories, there were positive correlations for fuel (UV with dominance and basal area), construction (UV with all phytosociological parameters), fodder (UV with all parameters), and poison/abortion categories (UV with density and frequency). Ecological apparency significantly explained the local importance of useful plants in fuel, construction, and fodder categories, and less significantly for poison/abortion.

An orthogonal 16-point approximate discrete cosine transform (DCT) is introduced. The proposed transform requires neither multiplications nor bit-shifting operations. A fast algorithm based on matrix factorization is introduced, requiring only 44 additions-the lowest arithmetic cost in literature. To assess the introduced transform, computational complexity, similarity with the exact DCT, and coding performance measures are computed. Classical and state-of-the-art 16-point low-complexity transforms were used in a comparative analysis. In the context of image compression, the proposed approximation was evaluated via PSNR and SSIM measurements, attaining the best cost-benefit ratio among the competitors. For video encoding, the proposed approximation was embedded into a HEVC reference software for direct comparison with the original HEVC standard. Physically realized and tested using FPGA hardware, the proposed transform showed 35% and 37% improvements of area-time and area-time-squared VLSI metrics when compared to the best competing transform in the literature. IntroductionThe discrete cosine transform (DCT) [1, 2] is a fundamental building-block for several image and video processing applications. In fact, the DCT closely approximates the Karhunen-Loève transform (KLT) [1], which is capable of optimal data decorrelation and energy compaction of first-order stationary Markov signals [1].This class of signals is particularly appropriate for the modeling of natural images [1,3]. Thus, the DCT finds applications in several contemporary image and video compression standards, such as the JPEG [4] and the H.26x family of codecs [5][6][7]. Indeed, several fast algorithms for computing the exact DCT were proposed [8][9][10][11][12][13][14][15]. However, these methods require the use of arithmetic multipliers [16,17], which are time, power, and hardware demanding arithmetic operations, when compared to additions or bit-shifting operations [18].

This paper introduced a matrix parametrization method based on the Loeffler discrete cosine transform (DCT) algorithm. As a result, a new class of 8-point DCT approximations was proposed, capable of unifying the mathematical formalism of several 8-point DCT approximations archived in the literature. Pareto-efficient DCT approximations are obtained through multicriteria optimization, where computational complexity, proximity, and coding performance are considered. Efficient approximations and their scaled 16- and 32-point versions are embedded into image and video encoders, including a JPEG-like codec and H.264/AVC and H.265/HEVC standards. Results are compared to the unmodified standard codecs. Efficient approximations are mapped and implemented on a Xilinx VLX240T FPGA and evaluated for area, speed, and power consumption.