WO2014078985A1 - Procédé et appareil de regularisation d'image - Google Patents

Procédé et appareil de regularisation d'image Download PDF

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Publication number
WO2014078985A1
WO2014078985A1 PCT/CN2012/084886 CN2012084886W WO2014078985A1 WO 2014078985 A1 WO2014078985 A1 WO 2014078985A1 CN 2012084886 W CN2012084886 W CN 2012084886W WO 2014078985 A1 WO2014078985 A1 WO 2014078985A1
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image
gradient
directions
blocks
regularization
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PCT/CN2012/084886
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English (en)
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Wenfei JIANG
Hengbin CUI
Zhibo Chen
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Thomson Licensing
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/70—Denoising; Smoothing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/90—Dynamic range modification of images or parts thereof
    • G06T5/94—Dynamic range modification of images or parts thereof based on local image properties, e.g. for local contrast enhancement
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20021—Dividing image into blocks, subimages or windows

Definitions

  • the present invention generally relates to image regularization. More particularly, it relates to total variation (TV)image regularization.
  • TV Total variation
  • image de-noising compression and super resolution. It is a widely-used measure of intensity continuity.
  • TV regularization is based on an inherent property of image data wherein the difference between adjacent pixels is often small. Thus, reducing the TV of an image subject to a close match to the original signal removes noise while preserving real details.
  • V x f(*, y) f(* + l, y) - f(*, y)
  • V y fO, y) fO, y + l) - fO, y)-
  • the TV of the image is defined as the sum of the II or 12 norm of the gradient images for all the pixels, formulated as:
  • TV l2 (f ) ⁇ tj x f(i,jY + V y f(/ ) 2 (2) where i and j are the coordinates of the pixels in the image.
  • f arg min f 7T(f) , s. t.
  • u and f are the input image and output image; andcp(f)is a measuring function that maps the output image to a certain domain to compare with the input image.
  • (p(f) can take the form of a random matrix or a specially designed matrix ⁇ 3 ⁇ 4>, e.g. a full or a partial DCT matrix, multiplying the output image/ i.e. ⁇ /, and the constraint becomes ⁇ u— ⁇ /
  • the real edges are smoothed as little as possible; second, the high-gradient edges are preferably preserved over the low-gradient detail or noise.
  • traditional TV 11112 regularization as defined in Eqn. (1) or Eqn. (2) does not meet the requirement well.
  • the textures and edges are inevitably blurred.
  • the oblique edges are likely to be significantly smoothed since both vertical and horizontal gradient regularizations tend to reduce the gradient across oblique edges.
  • strong edges are not particularly protected during TV 11112 regularization; and TV /2regularization even gives higher priority to keeping trivial details rather than the strong edges. This can be seen from following.
  • This invention is directed to methods and apparatuses for image regularization.
  • a method and an apparatus for regularizing an image comprises calculating a plurality of gradient images for said image; and regularizing said image by modifying pixel values of said image to minimize a function of said image defined as a weighted sum of absolute values of said calculated gradient images, each raised by a power that is less than 1 and greater than 0.
  • a method and an apparatus for regularizing an image comprises dividing the image into a plurality of image blocks; for each of said plurality of image blocks, calculating a plurality of gradient blocks; and regularizing said image by modifying pixel values of said each image block to minimize a function of said image block defined as a weighted sum of absolute values of said calculated gradient blocks, each raised by a power that is less than 1 and greater than 0.
  • Figure 1 illustrates an image regularizer according to an embodiment of the present invention.
  • Figure 2 illustrates an exemplary process of a block or patch based image regularization according to another embodiment of the present invention.
  • Figure 3 shows a set of example candidate directions and the corresponding directional gradients for gradient image/block calculation.
  • Figure 4 shows an example image to illustrate the advantages of the TV W image regularization according to one embodiment of the present invention: (a) regularization results of TV II and TV 12; (b) regularization results of TV/1 ⁇ 2.
  • Figure 5 depicts a block schematic diagram of a system in accordance with the present principles for accomplishing TV W image regularization.
  • An image described in the present application can be a still image, a frame of a video sequence or a block/patch of an image.
  • a plurality of gradient images for an image is calculated.
  • the regularization of the image can be performed by modifying pixel values of the image to minimize a function of the image.
  • the function can be any function that measures changes of the image.
  • the function of the image can be defined as a weighted sum of the absolute values of calculated gradient image coefficients. Each of the absolute values of the coefficients is raised by a power that is less than 1 and greater than 0. Different weights can be assigned to different gradient images, or even different gradient coefficients.
  • the image can be represented in forms such as a ID signal or a 2D matrix. The power for each of the coefficients can be the same or different.
  • the function of the image is a Total Variation TV W .
  • TV w (f) ⁇ i >k w k ⁇ / k f(i,j) ⁇ e (6)
  • V fc f(i,y) is a value of V fc f at position w fc is a weight for the k-th calculated gradient image
  • O ⁇ 0 ⁇ l The K gradient images represent different orientations that are considered in the calculation of TV W .
  • ⁇ V fc f ⁇ ⁇ V x f
  • V y f ⁇ is considered wherein only edges along horizontal and vertical directions are considered.
  • ⁇ V fc f ⁇ can also include diagonal and anti-diagonal directions.
  • ⁇ w k ⁇ assigns different weights to different directions.
  • all ⁇ w k ⁇ are set to 1 to put equal weights on all directions.
  • the image f can be regularized by modifying pixel values of said image to minimize the total variation of the image using the calculated gradient images as formulated in Eqn. (6).
  • the minimization problem can be formulated by a constrained TV minimization problem
  • y(u, f) argmin f 7V ifl (f) + 3 ⁇ 4 y(u, f) (8)
  • u and f are the images before and after the modifying step, respectively;
  • y(u, f) is a measurement of closeness between u and f ; and 1 is a parameter which controls the regularization intensity.
  • y(u, f)
  • u and fare compared pixel by pixel.
  • a bold italic letter, such as / is the one dimensional representation (vector) of the same
  • the total variation TV Woi Eqn. (6) can also be defined on the ID form of the image /.
  • TV W (/) TV W (f).
  • y(u, f) may compare ⁇ (u) and,g (f), where $( ⁇ ) is a function or a transform applied to its argument, or compare g(u— f) with a given value, or may take the form of
  • Fig. 1 illustrates an image regularizer 100, which comprises a gradient image calculator 1 10 and a minimizer 120.
  • the gradient image calculator calculates a plurality of gradient images along different directions.
  • the calculated gradient images and the input image are input to the minimizer 120 to adjust/modify the image pixel value so that the minimization of a function of the image, such as the TV as formulated in Eqn. (7), is achieved.
  • the output is the processed regulated image.
  • the image can be regularized patch by patch, or block by block.
  • Fig. 2 illustrates an exemplary process of such a block or patch based image regularization.
  • the input image is divided into image blocks/patches.
  • gradient images of the image block along several directions, called gradient blocks, are calculated in step 240.
  • the image pixel values of each image block are then adjusted/modified in step 250 by minimizing a function of said image block defined as a weighted sum of absolute values of said calculated gradient block coefficients.
  • Each of the absolute value of the coefficients is raised by a power that is less than 1 and greater than 0.
  • the image regularization of one image block may be affected by the pixel values of its neighboring blocks.
  • the calculation of the gradient at the border of an image block may require the pixel values of its neighbor blocks.
  • the steps 230 to 250 may be repeated iteratively until a termination condition is met at step 260.
  • the terminating condition can be, for example, the improvement of current iteration over the last iteration is smaller than a given threshold.
  • an optional step of pre-processing the input image 210 can be introduced to place the image in a better condition for regularization, for example, by roughly removing noise.
  • the preprocessing step can be performed by the pre-processor 130 shown in Fig. 1.
  • the K gradient image/block can be determined by selecting K gradient directions for an image or an image block. For example, several initial directions can be pre-selected, among which gradient direction(s) that most likely match the orientation of the content of the image or the image block are selected as the set of directions for calculating gradient images/blocks.
  • One embodiment of the present invention is to perform TV /1 ⁇ 2 regularization along the real edge directions.
  • Fig. 3 shows a set of example candidate directions and the corresponding directional gradients.
  • V b fO,y) f(x,y) — f(x— 2,y - 1)
  • V d f(*,y) f(*,y) -f(x-l,y- 2)
  • V f f(*,y) f(*,y) - f 0 + 1, y - 2)
  • V g f(*,y) f(x,y) -f(x + l,y- 1)
  • two most significant directions are picked for the regularization purpose. In different implementations, more directions can be taken into account.
  • the sum of the /1 ⁇ 2 norm of the gradient for each direction can be calculated for an image or an image block/patc
  • the value of the TV /1 ⁇ 2 for the patch/block f f can be calculated by,
  • TV /1 ⁇ 2 is computed by
  • the weights w t ,k are adaptively calculated by normalizing the harmonic mean of Ek,
  • Eqns. (16) and (17) indicate that it is preferred to smooth the image along the small-norm- directions with higher intensity.
  • the TV /1 ⁇ 2 calculation may not be patch-independent.
  • the information of its adjacent patches may be utilized.
  • the image is extended in advance, e.g. by repeating the boundary pixels or by symmetrically copying the boundary pixels, in order to calculate the boundary gradients.
  • f t arg min ft ⁇ 7V i3 ⁇ 4 (f t ) + 1 ⁇ 2 ⁇ u t - ⁇ 3 ⁇ 4>/ t
  • X t is the regularization intensity parameter for the regularization of the input patch f t .
  • f t arg min ft ⁇ 7V i1 ⁇ 2 (f t ) + 1 ⁇ 2 ⁇ u t - / t
  • the solution for the cases with arbitrary reversible measuring matrix ⁇ 3 ⁇ 4> is briefly discussed later.
  • Eqn. (21) can be solved by the Half-Quadratic Splitting method.
  • I k i is substituted by an auxiliary variables d 3 ⁇ 4 which leads to: min, wJldJ! + wp
  • the minimization problem of (22) can be solved by an alternating iterative minimization approach, wherein the minimization problem is decomposed into two subproblems, namely, the f-subproblem and the d subproblem.
  • f-subproblem the minimization problem is decomposed into two subproblems, namely, the f-subproblem and the d subproblem.
  • the f-subproblem seeks for the optimal f given a fixed d 3 ⁇ 4 which is done by minimizing the following cost function:
  • d k * argmin dfc w k ⁇ d k
  • the half-quadratic splitting algorithm is implemented by alternatively solving the f- subproblem and the d subproblem until the following stopping criterion is met,
  • f n andf n+1 are the regulated image lock at n-th iteration and (n+l)-th iteration, respectively.
  • a spatially varying regularization intensity parameter that locally controls the regularization intensity over image regions according to the content can be added.
  • tuning parameter ⁇ it can be updated by,
  • TV /1 ⁇ 2 regularization not only tends to smooth along the low-gradient direction for one pixel, but also prefers to smooth the low-gradient pixels among all pixels in the image.
  • Fig. 4 shows an example of the smoothing results by TV /1 ⁇ 2 regularization on a ID signal.
  • the dash line represents the ID signal before the regularization, and the solid line represents the ID signal after the regularization.
  • Fig. 4(a) shows the regularization results of TV II and TV 12; and Fig. 4(b) shows the regularization results of TV /1 ⁇ 2.
  • Both TV II and 12 regularization have the same result for a ID signal, in which the strong spikes are suppressed more significantly than the trivial spikes.
  • TV /1 ⁇ 2 regularization performs better in retaining the main structure and removing the details.
  • TV /1 ⁇ 2 regularization can be applied to a wide range of image processing applications, such as image denoising, video compression and exposure fusion.
  • TV /1 ⁇ 2 denoising in the spatial domain is discussed here as an example. Nonetheless, the combined TV /1 ⁇ 2 -wavelet idea, i.e. to use wavelet constraintin the regularization ⁇ u— can be implemented.
  • a pre-processing step is introduced to roughly remove the noise of the image. For example, pre-denoising the images with conventional TV regularization, such as TV 11112 as defined in Eqn. (1) and Eqn. (2),can be performed in the pre-processing step.
  • the terminating condition for the iteration can be, for example,
  • thl is a pre-determined threshold.
  • An example value for thl can be 0.001.
  • TV can be used in compressive sensing (CS), which is capable of acquiring and recovering signals that can be sparsely represented by some bases below the Nyquist rate.
  • CS compressive sensing
  • TV /1 ⁇ 2 regularization based on such a principle can be applied to video compression.
  • the reconstruction / decoding method can be formulated as
  • f t argmin ft ⁇ 7V i1 ⁇ 2 (f t ) + 1 ⁇ 2
  • z t is the vector of quantized transform coefficient of the block f t
  • f is the prediction of f t either by motion estimation or intra prediction.
  • ⁇ is a partial DCT matrix, which takes a number of low-frequency measurements of the block.
  • the codec defines a CS mode in which the blocks are represented by T low frequency DCT coefficients, and decoded by (37) can be adaptively determined by the estimation of the sparsity.
  • IDCT Inverse DCT
  • the encoder can choose between a CS mode and the ordinary IDCT mode for each block by rate distortion optimization.
  • the rate distortion (RD) cost is computed with the estimation of the bit cost ? m and the distortion D m ,
  • mode opt min m D m + xR m (38) wherer is the Lagrangian multiplier derived by the quality parameter of the compression.
  • the optimal mode mode opt is the mode whose RD cost is lower.
  • the encoder Since a new CS mode is introduced, the encoder has to transmit a mode flag for each block to the decoder. This can be a large overhead to the compression efficiency, especially for low bit rate coding.
  • the mode information can be transmitted covertly in terms of the parity of the number of nonzero coefficients like watermarks. For example, the number of nonzero coefficients after quantization is made to be odd when CS mode is chosen, and be even when IDCT mode is chosen.
  • the rule above can be easily fulfilled during the quantization step.
  • the encoder simply quantizes the last nonzero coefficient to zero if the parity of the number of nonzero DCT coefficients does not match the reconstruction mode. Considering that the coefficients at the six lowest frequencies have remarkable influence to the visual appearance, they cannot be modified for this mode watermarking. Consequently, a block must be reconstructed in the CS mode if all of its nonzero DCT coefficients are at the 6 lowest frequencies. As will be demonstrated, the compression efficiency benefits a lot from this covert mode communication mechanism.
  • Exposure fusion is a process to compute the desired image by keeping only the "best" parts in the multi-exposure image sequence.
  • An exposure fusion process can be guided by a set of quality measures (contrast, saturation and well-exposedness), which is consolidated into a scalar-valued weight map. Then the fused image is obtained by a weighted blending of input images.
  • Eqn. (39) indicates that all the pixels in one channel of an input image share a saturation weights; Eqn. (40) indicates that each pixel of an input image have one well-exposedness weight for its 3 channels.
  • TV 11 ⁇ 2 regularization can be utilized to extract the structure Struct k and the detail Detail k of the gray-scale version of an input image, G k . Then the intensity of each pixels in the detail image can be used as the contrast weight,
  • the recomposed image F is obtained by the weighted average of the input images .
  • Fig.5 depicts a system 10 in accordance with the present principles for accomplishing image regularization using TV W regularization in the manner discussed in greater detail hereinafter.
  • the system 10 includes a processor 12, in the form of a computer, which executes software that performs image TV / ⁇ regularization.
  • the processor 12 is connected to one or more conventional data input devices for receiving operator input. In practice, such data input devices include a keyboard 14 and a computer mouse 16. Output information generated by the processor undergoes display on a monitor 18. Additionally such output information can undergo transmission to one or more destinations via a network link (not shown).
  • the processor 12 is connected to a database 22 which can reside on a hard drive or other non-volatile storage device internal to, or separate from, the processor.
  • the database 22 can store raw image information as well as processed image information, in addition to storing software and/or data for processor use.
  • the system 10 further includes an image acquisition device 24 for supplying the processor 12 with data associated with one or more incoming images.
  • the image acquisition device 24 can take many different forms, depending on the incoming images. For instance, if the incoming images are "live", the image acquisition device 24 could comprise a television camera. In the event the images were previously recorded, the image acquisition device 24 could comprise a storage device for storing such images. Under circumstances where the images might originate from an another location, the image acquisition device 24 could comprise a network adapter for coupling the processor 12 to a network (not shown) for receiving such images.
  • Fig. 5 depicts the image acquisition device 24 as separate from the processor, depending on how the images originate, the functionality of the image acquisition device 24 could reside in the processor 12.
  • the present invention may be implemented in various forms of hardware, software, firmware, special purpose processors, or a combination thereof.
  • the present invention is implemented as a combination of hardware and software.
  • the software is preferably implemented as an application program tangibly embodied on a program storage device.
  • the application program may be uploaded to, and executed by, a machine comprising any suitable architecture.
  • the machine is implemented on a computer platform having hardware such as one or more central processing units (CPU), a random access memory (RAM), and input/output (I/O) interface(s).
  • CPU central processing units
  • RAM random access memory
  • I/O input/output
  • the computer platform also includes an operating system and microinstruction code.
  • various processes and functions described herein may either be part of the microinstruction code or part of the application program (or a combination thereof), which is executed via the operating system.
  • various other peripheral devices may be connected to the computer platform such as an additional data storage device and a printing device.

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Abstract

L'invention concerne des procédés et des appareils permettant la régularisation d'image. La régularisation de l'image est exécutée par régularisation (TV) lθ par variation totale, 0<θ<1. Dans un mode de réalisation, une image est divisée en blocs d'image. Pour chaque bloc d'image, des directions sont déterminées pour permettre le calcul des blocs de gradients par identification des directions correspondant à l'orientation du contenu du bloc d'image. la régularisation TV lθ est ensuite exécutée pour chaque bloc d'image au moyen des blocs de gradient calculés. Le processus est exécuté de manière itérative afin d'éliminer le problème des blocs voisins non-régularisés affectant la régularisation du bloc en cours. La régularisation TV lθ est applicable aux applications telles que le débruitage des images, la compression vidéo et la
PCT/CN2012/084886 2012-11-20 2012-11-20 Procédé et appareil de regularisation d'image WO2014078985A1 (fr)

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CN104616249A (zh) * 2014-11-24 2015-05-13 南京信息工程大学 一种基于曲率变分的小波变换图像去噪算法
CN104835123A (zh) * 2015-05-04 2015-08-12 中国科学院自动化研究所 基于先验模型的光片显微成像条纹噪声去除方法
CN104851081A (zh) * 2015-05-15 2015-08-19 南京信息工程大学 一种基于gpu的并行拉普拉斯图像锐化方法
CN105872315A (zh) * 2016-04-01 2016-08-17 广西大学 一种针对混合噪声的视频去噪方法
CN107492077A (zh) * 2017-08-03 2017-12-19 四川长虹电器股份有限公司 基于自适应多方向总变分的图像去模糊方法
CN109003233A (zh) * 2018-06-21 2018-12-14 西安理工大学 一种基于自适应权重全变分模型的图像去噪方法
CN109712091A (zh) * 2018-12-19 2019-05-03 深圳市华星光电技术有限公司 图片处理方法、装置及电子设备
CN110084774A (zh) * 2019-04-11 2019-08-02 江南大学 一种增强的梯度传递和总变差最小化融合图像的方法
CN110930331A (zh) * 2019-11-22 2020-03-27 南京信息职业技术学院 一种噪声模糊图像非盲复原方法、系统及存储介质
CN111127347A (zh) * 2019-12-09 2020-05-08 Oppo广东移动通信有限公司 降噪方法、终端及存储介质
CN113112425A (zh) * 2021-04-08 2021-07-13 南京大学 一种四方向相对全变分图像去噪方法

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CN104616249A (zh) * 2014-11-24 2015-05-13 南京信息工程大学 一种基于曲率变分的小波变换图像去噪算法
CN104835123A (zh) * 2015-05-04 2015-08-12 中国科学院自动化研究所 基于先验模型的光片显微成像条纹噪声去除方法
CN104835123B (zh) * 2015-05-04 2018-07-31 中国科学院自动化研究所 基于先验模型的光片显微成像条纹噪声去除方法
CN104851081A (zh) * 2015-05-15 2015-08-19 南京信息工程大学 一种基于gpu的并行拉普拉斯图像锐化方法
CN105872315A (zh) * 2016-04-01 2016-08-17 广西大学 一种针对混合噪声的视频去噪方法
CN107492077A (zh) * 2017-08-03 2017-12-19 四川长虹电器股份有限公司 基于自适应多方向总变分的图像去模糊方法
CN109003233A (zh) * 2018-06-21 2018-12-14 西安理工大学 一种基于自适应权重全变分模型的图像去噪方法
CN109003233B (zh) * 2018-06-21 2021-08-06 西安理工大学 一种基于自适应权重全变分模型的图像去噪方法
CN109712091B (zh) * 2018-12-19 2021-03-23 Tcl华星光电技术有限公司 图片处理方法、装置及电子设备
CN109712091A (zh) * 2018-12-19 2019-05-03 深圳市华星光电技术有限公司 图片处理方法、装置及电子设备
CN110084774A (zh) * 2019-04-11 2019-08-02 江南大学 一种增强的梯度传递和总变差最小化融合图像的方法
CN110930331A (zh) * 2019-11-22 2020-03-27 南京信息职业技术学院 一种噪声模糊图像非盲复原方法、系统及存储介质
CN110930331B (zh) * 2019-11-22 2023-03-03 南京信息职业技术学院 一种噪声模糊图像非盲复原方法、系统及存储介质
CN111127347A (zh) * 2019-12-09 2020-05-08 Oppo广东移动通信有限公司 降噪方法、终端及存储介质
CN113112425A (zh) * 2021-04-08 2021-07-13 南京大学 一种四方向相对全变分图像去噪方法
CN113112425B (zh) * 2021-04-08 2024-03-22 南京大学 一种四方向相对全变分图像去噪方法

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