تبدیل صفحک: یک موجک هندسی مناسب برای فشرده‌سازی تصاویر عمق دوربین‌های شبه‌کینکت

تبدیلات گوک (wedgelet) و شیبک (platelet) که پیش ازاین در خانواده موجک های هندسی وفقی برای بازنمایی تصاویر روشنایی مطرح شده اند، توانایی بازنمایی تنک تصاویر قطعه ای ثابت، و تصاویر قطعه ای خطی را دارند؛ اما کارایی آن ها در بازنمایی تصاویر قطعه ای غیرخطی مانند تصاویر عمق بهینه نیست. در این مقاله تبدیل صفحک[1] به عنوان عضو جدیدی از خانواده موجک های هندسی برای بازنمایی بهینه تصاویر عمق قطعه ای صفحه گون ارائه شده است. برخلاف موجک های هندسی پیشین که تنها از مدل های خطی و ثابت برای توصیف هر ناحیه هموار در تصویر استفاده می کنند، تبدیل صفحک برای تقریب هر ناحیه صفحه گون از یک مدل غیرخطی مبتنی بر توابع گویا بهره می گیرد. آزمایش ها بر روی تصاویر عمق واقعی نشان دادند که در نرخ بیت bpp 0.03 استفاده از کدگذار مبتنی بر صفحک در فشرده سازی تصاویر عمق نسبت به موجک هندسی گوک به طور میانگین تا db 2.7 کیفیت را افزایش می دهد. همچنین در شرایط مشابه، در مقایسه با کدگذارهای مدرن jpeg2000 و h.264، استفاده از کدگذار عمق مبتنی بر صفحک به ترتیب منجر به db 2.59 و db 1.56 افزایش در کیفیت تصاویر بازسازی شده می شود.[1] planelet transform

Planelet Transform: A New Geometrical Wavelet for Compression of Kinect-like Depth Images

With the advent of cheap indoor RGBD sensors, proper representation of piecewise planar depth images is crucial toward an effective compression method. Although there exist geometrical wavelets for optimal representation of piecewise constant and piecewise linear images (i.e. wedgelets and platelets), an adaptation to piecewise linear fractional functions which correspond to depth variation over planar regions is still missing. Such planar regions constitute major portions of the indoor depth images and need to be well represented to allow for desirable ratedistortion tradeoff.In this paper, secondorder planelet transform is introduced as an optimal representation for piecewise planar depth images with sharp edges along smooth curves. Also, to speed up the computation of planelet approximation of depth images, an iterative estimation procedure is described based on nonlinear least squares and discontinuity relaxation. The computed approximation is fed to a ratedistortion optimized quadtree based encoder; and the pruned quadtree is encoded into the bitstream. Spatial horizontal and vertical plane prediction modes are also introduced to further exploit geometric redundancy of depth images and increase the compression ratio. Performance of the proposed planeletbased coder is compared with wedgelets, platelets, and general image encoders on synthetic and realworld Kinectlike depth images. The synthetic images dataset consists of 30 depth images of different scenes which are manually selected from eight video sequences of ICLNUIM RGBD Benchmark dataset. The dataset of realworld images also includes 30 depth images of indoor scenes selected from Washington RGBD Scenes V2 dataset captured by Kinectlike cameras. In contrast to former geometrical wavelets which approximate smooth regions of each image using constant and linear functions, planelet transform exploits a nonlinear model based on linear fractional functions to approximate every smooth region. Visual comparisons by 3D surface reconstruction and visualization of the decoded depth images as surface plots revealed that at a specific bitrate the planeletsbased coder better preserves the geometric structure of the scene compared with the former geometric wavelets and the general images coders. Numerical evaluations showed that compression of synthetic depthimages by planelets results in a considerable PSNR improvement of 0.83 dB and 6.92 dB over platelets and wedgelets, respectively. Due to absence of the noise, the plane prediction modes were very successful on synthetic images and boosted the PSNR gap over platelets and wedgelets to 5.73 dB and 11.82 dB, respectively. The proposed compression scheme also performed well on the realworld depth images. Compared with wedgelets, planeletsbased coder with spatial prediction achieved noticeable quality improvement of 2.7 dB at the bitrate of 0.03 bpp. It also led to 1.46 dB quality improvement over platelets at the same bitrate. In this experiment, application of planeletsbased coder led to 2.59 dB and 1.56 dB increase in PSNR over JPEG2000 and H.264 general image coders. Similar results are also achieved in terms of SSIM metric.