Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T3/00—Geometric image transformations in the plane of the image
  • G06T3/40—Scaling of whole images or parts thereof, e.g. expanding or contracting
  • G06T3/4053—Scaling of whole images or parts thereof, e.g. expanding or contracting based on super-resolution, i.e. the output image resolution being higher than the sensor resolution

Definitions

• This invention relates to a method for performing super-resolution of single images, and to an apparatus for performing super-resolution of single images.
• SR Super-resolution
• HR high-resolution
• LR low-resolution
• HR means high pixel density in an image, hence an HR image provides more clear and detailed contents to the viewer.
• a number of real-world applications utilizes SR algorithms, as SR provides a relatively low-cost software solution to this inverse problem when compared to high-cost hardware enhancements in optics and sensors technology.
• Exemplar-based methods have been developed to overcome limitations of classical multi-image SR. These methods assume that the missing high-frequency information is explicitly available in other natural images and it can successfully be retrieved from exemplar LR and HR patch pairs.
• LR and HR patch pairs are collected from other natural images, and low- and high-frequency relations of these patches are learned via a Markov network.
• This method has later been simplified in [6] with a sequence of estimations of HR patches by a nearest neighbor (NN) search from the database of exemplars, i.e. examples.
• NN nearest neighbor
• a manifold learning based SR approach has been proposed in [7].
• each LR patch is first reconstructed from its K nearest neighbors ( -NN) taken from the exemplar database.
• the HR patch is then hallucinated (or estimated) with the corresponding HR exemplar patches by considering geometric similarities of LR and HR patch spaces (manifolds).
• a sparse representations based SR method has been proposed in [8]. This method jointly learns two connected dictionaries by enforcing the similarity between sparse representations of exemplar LR and HR patch pairs. In this way, the sparse representation of a given LR patch over the learned LR dictionary can be applied with the learned HR dictionary to hallucinate the unknown HR patch.
• the present invention provides an improved self-contained and exemplar-based framework for single-image SR relying on multi-scale and locally-optimized neighbor embeddings of LR and HR patches. Following the recurrence property of similar patches across different scales of an image, it uses only the observed LR image and its appropriately downscaled versions for SR. Given a LR patch, its size is gradually increased by relying on local geometric similarities of low- and high-resolution patch spaces under small scaling factors. In each step of the algorithm, the local geometry of the given patch and its K-NN patches is characterized using locally linear embedding (LLE) [13]. In order to assure the local image compatibility, the parameter K is locally optimized.
• LLE locally linear embedding
• the invention allows averaging overlaps between adjacent patches, which improves the smoothness of the target HR image.
• the global consistency between the output HR image and the input LR image is enforced by using an iterative back projection (IBP) [2] with a non-local means (NLM) [14] kernel.
• IBP iterative back projection
• NLM non-local means
• the proposed algorithm can easily be ported and parallelized on GPU processors.
• an advantage confirmed by experimental results is that it produces more natural looking textures together with cleaner and sharper edges in the resulting HR images, compared to other known SR methods.
• the present invention provides a method for performing super-resolution of single images. In another embodiment, the present invention provides an apparatus for performing super-resolution of single images. In one embodiment, the invention provides a computer readable medium having executable instructions to cause a computer to perform said method for performing super-resolution of single images.
• a method for performing super-resolution of a single image comprises steps of downsampling Si a LR input image by a first factor, separating the LR input image into overlapping blocks x, , and for each of the blocks x, searching similar blocks in the downsampled LR image, determining blocks Ci,i ,Ci,2,Ci,3 at corresponding positions in the LR input image, locally optimizing S 4 the blocks by linear approximation to obtain locally optimized patches , downsampling S 5 the locally optimized patches by the first factor to obtain a downsampled locally optimized patch z d , comparing the downsampled locally optimized patch z d with the input block x 0 l and optimizing the number and/or weights w, ,i ,Wi,2,Wi,3 of the determined blocks Ci,i ,Ci,2,Ci,3 , wherein a locally optimized patch is obtained, and repeating the above steps with different sampling factors, wherein for each repetition the locally optimized patch xf
• the full (or at least a more sophisticated) super-resolution processing is done only for blocks with high texture, while a simplified super- resolution processing is applied for blocks with low texture.
• the super-resolution processing is done only for blocks with high texture, while it is skipped for blocks with low texture.
• Fig.1 how exemplar LR and HR patch pairs are collected directly from the input LR image and its appropriately downscaled version
• Fig.2 a flow-chart (part 1 ) of the method in a first embodiment of the invention
• Fig.3 a flow-chart (part 2) of the method in the first embodiment of the invention
• Fig.4 a flow-chart (part 3) of the method in the first embodiment of the invention
• Fig.5 an overview of the method in one embodiment of the invention.
• Fig.6 an apparatus according to one embodiment of the invention
• Fig .1 1 a flow-chart of a method in one embodiment of the invention where highly textured blocks and lowly textured blocks are treated different;
• Fig.12 an apparatus according to one embodiment of the invention, where highly textured blocks and lowly textured blocks are treated different.
• the aim of single-image SR is to recover a HR image which is consistent with the given LR image according to an image generation model.
• the observed LR image X of size N x M is assumed to be a blurred and downscaled version of the unknown HR image Y (of size SN x SM), hence the image generation model can be written as
• ⁇ X— (Y * H) I is the data term with regard to eq. (1 )
• R(Y) is an applicable regularization term based on a prior knowledge on Y and ⁇ is a parameter controlling the contribution of the prior on the solution.
• ⁇ is a parameter controlling the contribution of the prior on the solution.
• R(Y) is usually chosen to penalize the variation of Y.
• the above SR optimization is solved in two successive steps; first, by calculating an initial estimate Yo of the HR image to satisfy a patch- based local constraint through a prior R(Y) as
• exemplar patch pairs from a single image are considered.
• the underlying main idea is based on the assumption that small image patches are very likely to repeat themselves within and across different scales of an image [9].
• exemplar LR and HR patch pairs are collected directly from the given LR image and its appropriately downscaled version by matching LR patches (located in the downscaled image) and their spatially corresponding HR parents (suited in the input LR image).
• Fig.1 shows how exemplar LR and HR patch pairs are collected directly from the input LR image 10 and its appropriately downscaled version 1 1 .
• LR patch 13 and HR patch 15 are a (LR and HR) patch pair
• LR patch 14 and HR patch 15 are a patch pair.
• Each LR patch in the downscaled image 1 1 has a corresponding HR patch in the input image 10.
• the input LR image is downscaled with a sufficiently reasonable ratio in order to extract LR and HR patch pairs of greater relevance, and moreover, to maintain the local geometric similarities of LR and HR patch spaces (as explained further below).
• the size of a given LR patch is increased gradually by Ph pixels in horizontal dimension and by p v pixels in vertical dimension (p h not equal p v ) in at least one step of the algorithm.
• Ph usually Ph equals p v .
• the patches in between these offsets are related to each other in sub-pixel precision. So, there is a partial lack of translation invariance, as there is no one-to-one correspondence between all kinds of translations of patches in both images.
• the two images are translation invariant just with suitable offsets. This is actually related with phase information of pixels. According to the invention, the reduction of the number of exemplars is compensated by creating different downsampled images with different phases.
• each local HR patch should resemble its neighboring (similar) patches taken from the given exemplar set.
• the regularization term is formulated with a neighbor embedding optimization such that each HR patch xf v, at step t can optimally be hallucinate timated or modeled) as a weighted linear c
• R(xf) (5)
• VIA,* denote f x .
• the second term in eq. (5) represents a sum-to-one constraint on the weighting coefficients. This constraint enforces the approximation of xf to lie in the sub-space spanned by its K-NN, and the invariance to translations of the data point and its neighbors.
• the invention benefits from the local geometric similarities of LR and HR patch spaces, and relates the intrinsic geometric properties of local LR and HR patch neighborhoods using the neighbor embedding assumption.
• the calculated weights ⁇ w i>k ⁇ would not be the optimum for hallucinating the HR patch x ⁇ in (7).
• the local prior R (x - -1 ) in (6) does not put any constraint on the estimated values of x - except the initial neighbor embedding assumption between LR and HR patch spaces.
• Rixt 1 Rixt 1 ) + ⁇
• h is a low-pass kernel
• P c is the inverse operator of P
• an iterative algorithm based on an optimization on the number of used NN patches is used.
• the method proceeds as follows. For each given LR patch x - -1 , first a K-NN search in the given exemplar set of LR patches is made. Denote the obtained LR patches and their HR correspondences as ⁇ , ⁇ _ . Then vary the number ⁇ of used NN patches from 1 to K and optimize R (xf -1 ) for each distinct value of ⁇ independently. As a result, K ossible estimations ⁇ x ' K ⁇ K i of the HR signal x ⁇ are obtained, i.e.
• equation (4) is solved by employing the known IBP algorithm.
• Yo the initial HR image as recovered above.
• the update equation for IBP is given as
• Y m Y m-1 + [(X - (Ym-i * H) Is) ⁇ S] * P (1 1 )
• Y m the estimated HR image at iteration m
• m 1 ...M
• ⁇ S represents the upscaling (with a factor of S) operator
• P is a back-projection kernel.
• P is chosen to be a fixed isotropic kernel (isotropic kernel is a 2D filter which is symmetric in all dimensions, or circularly symmetric).
• edges usually have anisotropic structures, and the content of the projected data is dynamic along the iterations of IBP. As a result, this kind of kernel often produces results with jaggy and ringing artifacts especially around edges.
• Figs.2-4 show an exemplary flow-chart according to one embodiment of the invention.
• first iteration S1-S6, second iteration Si'-Se' and third iteration Si"-S6 it is also possible to use more or less iterations, depending on a desired scaling factor and on a maximum scaling factor per iteration.
• the size of an LR patch is gradually increased (e.g., 1 -pixel at a time or per iteration), until the required scale is reached.
• the LR image is downscaled with non-integer factors and example patches are collected, taking the phase information into account.
• the K value (for K-nearest neighbor or K-NN search) is optimized by checking the compatibility of the HR patch at each step.
• a back-projection method with non-local means based kernel is used.
• the super-resolution processing is simplified or skipped for low textured portions of the image.
• super- resolution of a single image is performed by downsampling Si a LR input image by a first small factor (e.g. 3 ⁇ 4) several times with different phases to obtain several different downsampled LR images ⁇ - ⁇ , separating the LR input image into overlapping blocks (e.g. 3x3 pixels each) x,, for each of the blocks x, searching one or more similar (preferably equal, or substantially equal) blocks of same size bi,i,bi,2,bi,3 in one or more or each of the downsampled LR images, and
• blocks Ci,i ,Ci,2,Ci,3 at corresponding positions in the LR input image (wherein the blocks in the LR image are upsampled by the reciprocal of the first small factor, e.g. 4/3 so that they have a size of e.g. 4x4 pixels; they are determined just by their position).
• These blocks are locally optimized S 4 by linear approximation as described above to obtain locally optimized patches and then downsampled S 5 by the same small factor as previously (e.g. 3 ⁇ 4) to obtain .
• This patch is then compared to the original patch x 0 l and optimized to minimize the SSD (sum of squared distances) by varying the number of used patches b,,i, b,,2, bi,3 , or the weights Wi,i ,Wi,2,Wi, 3 of the used patches bi,i,bi,2,bi,3, or both (one or more of) the patches bi,i,bi,2,bi,3 and (one or more of) their weights Wi,i ,Wi,2,Wi, 3 .
• FIG.1 1 A flow-chart of one embodiment of the invention is shown in Fig .1 1 .
• blocks with higher texture are treated different from blocks with lower texture.
• Each block is determined to be either highly textured or lowly textured.
• Super-resolution of a single image is performed by downsampling Si a LR input image by a first small factor (e.g. 3 ⁇ 4) several times with different phases to obtain several different downsampled LR images ⁇ - ⁇ , separating the LR input image into overlapping blocks (e.g. 3x3 pixels each) x,, and determining highly textured blocks and lowly textured blocks respectively among the overlapping blocks x,.
• a first small factor e.g. 3 ⁇ 4
• the method further includes for each of the lowly textured blocks Xi performing a simplified upsampling method, and for each of the highly textured blocks x, searching one or more similar (preferably equal, or substantially equal) blocks of same size bi,i,bi,2,bi,3 in one or more or each of the downsampled LR images, and determining blocks Ci,i,Ci,2,Ci,3 at corresponding positions in the LR input image (wherein the blocks in the LR image are upsampled by the reciprocal of the first small factor, e.g. 4/3 so that they have a size of e.g. 4x4 pixels; they are determined just by their position).
• the first small factor e.g. 4/3
• These blocks are locally optimized S 4 by linear approximation as described above to obtain locally optimized patches and then downsampled S 5 by the same small factor as previously (e.g. 3 ⁇ 4) to obtain z d .
• This patch is then compared to the original patch x 0 l and optimized to minimize the SSD (sum of squared distances) by varying the number of used patches b,,i, b,,2, b,,3 , or the weights Wi,i ,Wi,2,Wi, 3 of the used patches bi,i,bi,2,bi,3, or both (one or more of) the patches bi,i,bi,2,bi,3 and (one or more of) their weights
• Wi,i ,Wi,2,Wi, 3 are examples of Wi,i ,Wi,2,Wi, 3 .
• any simplified upsampling method can be used that reduces the computation effort.
• linear, bilinear, cubic or bi-cubic interpolation can be used for the lowly textured blocks.
• the upsampling method for lowly textured blocks is similar to the upsampling method of the highly textured blocks, except at least one of the following: for each of the lowly textured blocks x, , searching less blocks (than for the highly textured blocks) of same size bi,i,bi,2,bi,3 that are similar or substantially similar to the lowly textured block, searching in less of the downsampled LR images (than for the highly textured blocks), using simplified local optimization as compared with the local optimization for the highly textured blocks, and using less patches b,,i, b,,2, bi,3 or using a limited range of weights Wi,i ,Wi,2,Wi, 3 for the used patches bi,i,bi,2,bi,3, or both, in the optimization to minimize the SSD,
• the above-described procedure is then repeated at least once.
• the patches are super-imposed and averaged Ss, as described above, and the IBP S9 is performed to obtain the HR output image S10. It is a super- resolution version of the LR input image.
• the above-mentioned searching one or more similar blocks of same size i,i,bi,2,bi,3 in one or more or each of the downsampled LR images can use any commonly known search algorithm, e.g. as used in motion estimation (e.g. SSD).
• the accumulating and averaging Ss comprises, for each pixel, counting overlapping patches that contribute to the pixel, adding values of overlapping patches that contribute to the pixel and dividing the accumulated values by the number of overlapping patches.
• each iteration there are several downscaled images (e.g. ⁇ - ⁇ i n tne fi rst iteration S1-S6), since the input image is downscaled with non-integer values.
• These downscaled images correspond to different phases of pixels caused by this non- integer downsampling. These provide the "neighbors" of the neighbor embedding.
• steps ⁇ , ⁇ ', ⁇ " a simple norm calculation is performed. It may be SSD (sum of squared distance). Optimization can be done by minimizing this norm (SSD).
• Exemplary upscaling factors shown in Fig.2-5 are 3:4, 4:5 and 5:6, i.e. one additional pixel in each dimension per iteration.
• p is considerably smaller than the block size, e.g. not more than 1 ⁇ 2 of the block size.
• n block size
• the patch size is increased by p pixels until the required scaling is reached.
• factors would be 3/5, 5/7, 7/9, i.e. two additional pixel in each dimension per iteration.
• step S 7 the algorithm simply stops if the required scaling has been reached and y, is assigned to the final result.
• Non-local means kernel in step Sg is a well-known adaptive filter for denoising applications.
• the back-projection kernel was changed with the Non-local means kernel, as it gives better results than using a Gaussian filter.
• Back projection is generally well known, but here it is a part of the algorithm and the kernel is NLM-based. In another embodiment however, back- projection kernel may be used instead.
• Fig.6 shows, in one embodiment, an apparatus for performing super-resolution of a single image, comprising a separator SEPi for separating the LR input image into overlapping blocks x, , one or more (here three) cascaded upscaling units CAU1-3, a HR image assembling unit IAU, and an IBP unit IU.
• Each cascaded upscaling unit provides its output x[, x , x 3 l as input to the next upscaling unit.
• Each cascaded upscaling unit CAUi-3 comprises one or more first downsamplers DUi for downsampling a LR input image by a first factor several times with different phases to obtain several different downsampled LR images ⁇ - ⁇ , a first selector SEL1 for selecting a current block x 0 l , one or more first search units SUi for searching, for each current block x 0 l of all the blocks x, , one or more similar blocks of same size bi , i ,bi , 2,bi,3 of a current block x 0 l in one or more or each of the downsampled LR images, one or more first position determining units PDU1 for determining blocks Ci , i ,Ci , 2,Ci,3 at corresponding positions in the LR input image, wherein the blocks in the
• a second downsampler DU2 for downsampling the locally optimized patches by the first factor to obtain a down- sampled locally optimized patch z d
• a first comparator CUi for comparing the downsampled locally optimized patch z£ d with the input block x 0 l
• a first control unit CTR1 for optimizing the number and/or weights w, ,i ,Wi,2,Wi,3 of the determined blocks Ci,i ,Ci , 2,Ci,3 , wherein the Sum-of-Square-Distance between the downsampled locally optimized patch z£ d with the input block x 0 l is minimized and wherein a locally optimized patch x ⁇ is obtained.
• the first and second downsampler DUi .Dlb and up-samplers UPS use a different factor (and its reciprocal) per each of the one or more cascaded upscaling units (e.g. 3 ⁇ 4 for downsampling and 4/3 for upsampling in the first upscaling unit CAUi , 4/5 for downsampling and 5/4 for upsampling in the second upscaling unit CAU2, and 5/6 for downsampling and 6/5 for upsampling in the third upscaling unit CAU3).
• the last of the cascaded upscaling units CAU3 provides its output to the HR image assembling unit IAU.
• the HR image assembling unit IAU in one
• an optimal number K of patches i.e. a number K that is optimal for a current block to be upsampled
• an optimal number K of patches is obtained by downsampling the reconstructed (or upsampled) block, and computing an error between a current block and the downsampled/reconstructed block. Different numbers K of patches are tested, and the number K is selected that leads to a minimization of the error.
• the error is the sum of absolute differences.
• the error is the square distance or square difference. In the following, a separation of the blocks into highly textured and lowly textured blocks is described.
• the separation of the blocks into highly textured and lowly textured blocks is done according to the blocks' energy.
• the gradient energy is used.
• the gradient energy can be determined, for example, as a sum of squared spatial differences of luminance values within the block, or as a sum of horizontal and vertical gradients within the block. The higher the gradient energy, the higher the texturization of the block.
• the block's energy is determined as the difference between a minimum and a maximum luminance value within the block. Then, the separation of the blocks into highly textured and lowly textured blocks is done according to the difference between a minimum and a maximum luminance value within the block. The higher the difference, the higher the texturization of the block.
• a threshold is defined for determining whether a block is highly textured or lowly textured. If the block energy is below the threshold, a simplified upscaling is used. In one embodiment, a pre-defined fixed threshold is used. A typical value (for block energy calculated according to min-max luminance difference) would be 5, i.e. if luminance ma x - luminance m i n > 5 , the block is considered as highly textured. In one embodiment, an adaptive threshold is used. Since the threshold selection has an impact on both processing power and image quality, it may be adaptive with respect to available processing power (with a lower threshold for more available processing power), with respect to required image quality (with a lower threshold for higher image quality), or both.
• threshold selection e.g. image size, bit amount per pixel etc.
• the threshold may be in a range of 3-7 instead of 5. Note that the threshold needs to be scaled according to the employed energy measure, such that a reasonable amount of blocks is classified in each of high and low texture.
• Fig .1 1 shows a flow-chart of a method, in one embodiment of the invention, where highly textured blocks are treated different from lowly textured blocks.
• a method for performing super-resolution of a single image comprises steps of downsampling Si a LR input image by a first factor several times with different phases to obtain several different downsampled LR images ⁇ - ⁇ , separating the LR input image into overlapping blocks x, , and for each of the blocks determining S1 .1 a measure of its texture or a degree of its texturization, and determining S1 .2 according to the measure of its texture whether the block has high texture or low texture. Then, for each of the blocks having high texture, the following steps are performed:
• the simplified upsampling is one of linear interpolation, bilinear interpolation, cubic interpolation and bi-cubic interpolation.
• the simplified upsampling for blocks with low texture comprises steps of
• the step of determining S1 .1 for a block a measure of its texture or a degree of its texturization comprises measuring the block's energy according to a maximum luminance difference within the block, or according to a sum of luminance gradients within the block.
• the step of determining S1 .2 for a block whether it has high texture or low texture comprises comparing an energy measure of the block with a threshold, and a block having an energy measure above the threshold is determined to have high texture and a block having an energy measure below the threshold is determined to have low texture.
• Fig.12 shows an apparatus according to one embodiment of the invention, where highly textured blocks are treated in a different way than lowly textured blocks. Additionally to the above-described apparatus, the apparatus in this embodiment further comprises a block energy measure determining unit EM for determining a measure of the current block's texture or a degree of its texturization, and a comparison and decision unit ECD for comparing the measure of texture with a threshold so as to determine according to the measure of its texture whether the current block has high texture or low texture.
• EM block energy measure determining unit EM for determining a measure of the current block's texture or a degree of its texturization
• ECD comparison and decision unit
• the one or more first search units SUi , one or more first position determining units PDUi , first optimizer ⁇ , second downsampler DU2 , first comparator CUi and first control unit CTRi are operative for only those current blocks that have high texture x 0 l HT , as determined to the comparison and decision unit ECD.
• the simplified upsampling unit SUP comprises one or more secondary first search units SUi' for searching one or more similar blocks of same size bi,i ,bi,2,bi,3 of a current block x 0 l in one or more or each of the downsampled LR images, wherein less blocks are searched than for blocks with high texture, or the number of downsampled LR images in which the searching is done in less than for blocks with high texture, one or more secondary first position determining units PDUi' for determining blocks Ci , i ,Ci,2,Ci,3 at corresponding positions in the LR input image, wherein the blocks in the LR image are upsampled by the reciprocal of the first factor, secondary first optimizer OPTY for locally optimizing S 4 the blocks by linear approximation to obtain locally optimized patches ,
• secondary second downsampler DU2' for downsampling the locally optimized patches by the first factor to obtain a downsampled locally optimized patch z , , and secondary first comparator CUi' for comparing the downsampled locally optimized patch z d with the input block x 0 l and optimizing the number and/or weights w, ,i ,Wi , 2,Wi,3 of the determined blocks Q,i ,Ci , 2,Ci,3 , wherein the Sum-of- Square-Distance between the downsampled locally optimized patch z£ d with the input block x 0 l is minimized and wherein a locally optimized patch is obtained.
• the block energy measure determining unit EM for
• determining for a block a measure of its texture or a degree of its texturization comprises means, e.g. a processor, for measuring or calculating the block's energy according to a maximum luminance difference within the block, or according to a sum of luminance gradients within the block.
• the comparison and decision unit ECD for determining for a block whether it has high texture or low texture comprises a comparison unit, e.g. comparator, for comparing an energy measure of the block with a threshold, and a determining unit, e.g. switch, for determining blocks having an energy measure above the threshold to have high texture and blocks having an energy measure below the threshold to have low texture.
• a comparison unit e.g. comparator
• a determining unit e.g. switch
• Fig.7 demonstrates a comparison between our result (right) and a result in [10] (left) for the "koala" image.
• Figs.8-10 compare more results on different images for an upscaling factor of four.
• Fig.8 (upper: [9], lower: present invention) shows the efficiency of using the NLM kernel for reducing the jaggy and ringing artifacts, e.g., in the ridge of the chip. From Fig.9 (left: [1 1], right: present invention) and Fig.10 (upper: bi-cubic; lower: present invention), also sharper and cleaner edges can be observed, compared to the different other methods.
• the method for performing super-resolution of a single image comprises a step of determining for each of the overlapping blocks x, whether a current block has high or low texture, and simplifying or skipping the subsequent steps if a current block has low texture.
• the determining of blocks with high or low texture is done, in one embodiment, immediately after the step of separating the LR input image into overlapping blocks Xi.
• the step of determining blocks with high or low texture is performed initially, before said step of downsampling Si a LR input image.
• the blocks need not necessarily coincide with the overlapping blocks Xi, into which the image is separated later.
• highly or lowly textured regions are initially determined, there is a step of determining for each of the overlapping blocks x, whether or not it belongs to a highly or lowly textured region.
• each block has either high texture or low texture, so that determining one type of blocks implicitly yields also the other type.
• a self-contained SR method based on optimized neighbor embed- ding of patch pairs is described. While making use of the recurrence property (i.e. self-similarity) of similar patches across different scales of an image, the given patch is gradually expanded, relying on geometric similarities of LR and HR patch spaces at small scaling ratios. Together with an adaptive IBP, the invention provides more natural looking textures and sharper edges with less artifacts when compared to other known methods. The invention is applicable e.g. for a complete GPU-oriented and totally localized implementation. As an advantage, it is faster or achieves higher performance respectively.

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