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## Topaz-Denoise: general deep denoising models for cryoEM and cryoET

### Abstract

Cryo-electron microscopy (cryoEM) is becoming the preferred method for resolving protein structures. Low signal-to-noise ratio (SNR) in cryoEM images reduces the confidence and throughput of structure determination during several steps of data processing, resulting in impediments such as missing particle orientations. Denoising cryoEM images can not only improve downstream analysis but also accelerate the time-consuming data collection process by allowing lower electron dose micrographs to be used for analysis. Here, we present Topaz-Denoise, a deep learning method for reliably and rapidly increasing the SNR of cryoEM images and cryoET tomograms. By training on a dataset composed of thousands of micrographs collected across a wide range of imaging conditions, we are able to learn models capturing the complexity of the cryoEM image formation process. The general model we present is able to denoise new datasets without additional training. Denoising with this model improves micrograph interpretability and allows us to solve 3D single particle structures of clustered protocadherin, an elongated particle with previously elusive views. We then show that low dose collection, enabled by Topaz-Denoise, improves downstream analysis in addition to reducing data collection time. We also present a general 3D denoising model for cryoET. Topaz-Denoise and pre-trained general models are now included in Topaz. We expect that Topaz-Denoise will be of broad utility to the cryoEM community for improving micrograph and tomogram interpretability and accelerating analysis.

### Introduction

Visualization of micrographs from cryo-electron microscopy (cryoEM) of biological specimens is primarily limited by the phase contrast of proteins, the low electron dose conditions required due to radiation damage accrued by the proteins, and the thickness of the ice. As researchers push towards smaller and smaller proteins, these issues hinder downstream analyses because these proteins become increasingly difficult to distinguish from noise. Certain orientations of large, non-globular proteins can also have low signal, leading to missing views. The typical signal-to-noise ratio (SNR) of a cryoEM micrograph is estimated to be only as high as 0.11, amongst the lowest in any imaging field, and no ground truth exists. Nonetheless, several steps during collection and processing of micrographs in single particle cryoEM rely on properly human-inspecting micrographs, identifying particles, and examining processed data. Conventional cryoEM methods for improving contrast in micrographs include downsampling, bandpass filtering, and Wiener filtering2,3. However, these methods do not address the specific noise properties of micrographs and often do not provide interpretable results, which increasingly hinders attempts to resolve small and non-globular proteins4,5.

At the same time, there is a push in the field to fund large research facilities for high-throughput cryoEM. These and smaller facilities are moving towards the synchrotron model of data collection and need to increase their throughput to meet rising demand. One approach to speed up collection would be to collect shorter micrograph exposures. However, reducing total dose would exacerbate SNR-related analysis problems. Better micrograph denoising provides the opportunity to reduce total dose and increase collection throughput without compromising interpretability or downstream results.

Image denoising has long been a topic of significant interest in the computer vision and signal processing community6, but has recently seen a surge in interest from the machine learning community. Advances in deep neural networks have enabled substantial improvements in image restoration and inpainting (i.e. filling in missing pixels) by learning complex, non-linear priors over the applied image domain. However, these methods require ground truth images to provide supervision for learning the denoising model7,8, and are hence limited to domains where ground truth is available. To overcome this barrier, Lehtinen et al.9 presented a general machine learning (ML) framework, called Noise2Noise, for learning denoising models from paired noisy images rather than paired noisy and ground truth images. This method has been followed by several others for learning denoising models without ground truth10,11,12. These methods offer new approaches for training deep neural network models for denoising in challenging domains. In cryoEM, neural network denoising software has only just started to emerge for dataset-by-dataset cryo-electron tomogram (cryoET) denoising13,14 and single particle micrograph denoising15. However, there have not been any systematic evaluations of these methods to date nor have pre-trained general denoising models been developed.

Here, we develop Topaz-Denoise, large-scale, publicly available denoising models for cryoEM and cryoET. Conventional cryoEM and cryoET denoising methods are ad-hoc filters that do not model the complex image generative process. To address this, our goal is to learn the denoising process directly from data. However, deep denoising models typically require ground truth signal which is not available in cryoEM. We make the key insight that the individual movie frames collected by modern direct detector devices (DDD) are many independent observations of the same underlying signal and, hence, can be used to learn denoising models directly via the Noise2Noise framework. Trained on thousands of micrographs from DDD - K2, Falcon II, and Falcon III - across a variety of imaging conditions, these general models (also called pre-trained models) provide robust denoising without the need to train on a dataset-by-dataset basis. We test and compare these denoising models on several micrographs of typical particles and of small particles, study improvements in SNR, and use denoising combined with Topaz particle picking16 to obtain 3D single particle cryoEM structures of clustered protocadherin, an elongated particle with previously-elusive views and a putative new conformation. We also show that denoising enables more rapid data collection by allowing micrographs to be collected with a lower electron total dose (10–25% typical exposure times) without sacrificing interpretability or downstream processing. Shorter exposure times allow for higher throughput microscope usage, which reduces research cost and increases research efficiency. In addition, we develop a general 3D denoising model for cryoET tomograms, trained on dozens of cryoET tomograms, and show that our general denoising model performs comparably to models trained on a dataset-by-dataset basis. These models are integrated into Topaz allowing easy access to the community, along with the denoising framework that allows users to train their own cryoEM and cryoET denoising models.

Topaz-Denoise source code is freely available as part of Topaz (http://topaz.csail.mit.edu) and can be installed through Anaconda, Pip, Docker, Singularity, and SBGrid17, and is now integrated into CryoSPARC18, Relion19, Appion20 and Scipion21. As with Topaz, Topaz-Denoise is designed to be modular and can easily be integrated into other cryoEM software suites. Topaz-Denoise includes several pre-trained models and the ability for the user to train their own models. Topaz-Denoise 2D training and inference runs efficiently on a single GPU computer, while 3D training and inference runs efficiently on multi-GPU systems. Both 2D and 3D denoising are integrated into the standalone Topaz GUI to assist with command generation.

### Denoising with Topaz improves micrograph interpretability and SNR

We develop a general cryoEM micrograph denoising model by training a neural network using the Noise2Noise framework on dozens of representative datasets of commonly used imaging conditions (Fig. 1, “Methods”). By learning the denoising model directly from data, we avoid making specific assumptions about the noise-generating process leading to superior denoising performance.

Denoising with Topaz improves micrograph interpretability by eye on several datasets and improves SNR measurements in quantitative analyses. Our model correctly smoothes background areas while preserving structural features better than conventional methods (i.e. affine or low-pass filtering) (Fig. 1 and Supplementary Figs. 1–4). Given this known smoothing behavior of micrograph areas containing primarily noise, we find that denoising allows for the identification of structured background features from noise. Figure 1 shows two micrographs where the background areas between particles are flattened after denoising, while Supplementary Fig. 5 shows microtubules with known small proteins in background areas properly retained after denoising. Our denoising model has the combined advantage of reducing ambiguity as to whether the background of a micrograph is generally free from contamination, allowing researchers to identify small and/or low density particle views, for example as applied to micrographs from Mao et al.22 (Supplementary Figs. 6 and 7). In these types of scenarios, visual assessment of denoised micrographs compared to raw micrographs increases protein density confidence, increases confidence of background content, and reduces eye strain for researchers.

We quantitatively assess denoising performance by measuring the SNR of raw micrographs, micrographs denoised with our model, and micrographs denoised with conventional methods. We chose to measure SNR using real cryoEM micrographs because the denoising models were trained on real micrographs generated under real-world conditions that no software accurately simulates. Due to the lack of ground truth in cryoEM, SNR calculations are estimates (Methods). We manually annotated paired signal and background regions on micrographs from 10 different datasets (Supplementary Fig. 8). We then calculated the average SNR (in dB) for each method using these regions23. We present a comparison of four different denoising model architectures (affine, FCNN, U-net (small), and U-net) trained with L1 and L2 losses on either the small or large datasets (Supplementary Table 1). Note that the L2 affine filter is also the Wiener filter solution. We find only minor differences between L1 and L2 models, with L1 loss being slightly favored overall. Furthermore, we find that the training dataset is important. Intriguingly, the affine, FCNN, and U-net (small) models all perform better than the full U-net model when trained on the small dataset and perform better than the same models trained on the large dataset. The best performing model overall, however, is the full U-net model trained on the large dataset. This model also outperforms conventional low-pass filtering denoising on all datasets except for one, where they perform equivalently (EMPIAR-1000524).

A summary comparison is presented in Table 1, where we report SNR results on each dataset for the best overall performing low-pass filter (16x binning) with the L2 U-net trained on the large dataset and the L1 affine model trained on the small dataset. Our pre-trained U-net model improves SNR by >2 dB on average over low-pass filtering and improves SNR by roughly 20 dB (100 fold) over the raw micrographs. The model generalizes well across different imaging conditions, improving SNR on micrographs collected on K2, Falcon II, and Falcon III cameras as well as micrographs collected in super-resolution and counting modes.

To explore the broadness of our general U-net denoising model, we applied the model to several samples across several non-DDD cameras from two screening microscopes and analyzed them visually (Supplementary Fig. 9). The pixelsizes for these datasets are about twice that of the training data and camera hardware binning by two has also been applied. Despite the differing noise characteristics of these cameras relative to the DDD cameras used for training the U-net denoising model, our general denoising model performs well. We see improvements similar to those noted above. Background is reasonably smoothed while the contrast of protein densities is greatly increased in the proteasome and two apoferritin micrographs. The glutamate dehydrogenase micrograph shows slight artifacts around some proteins, but contrast is substantially improved and denoising allows for clear identification of particle aggregates. These improvements demonstrate that our pre-trained denoising model even generalizes well to micrographs collected on screening microscopes and may enable increased cryoEM screening efficiency.

### Denoising with the general model enables more complete picking of difficult particle projections

We denoised micrographs of particles with particularly difficult-to-identify projections, clustered protocadherin (EMPIAR-1023425), to test whether denoising enables these views and others to be picked more completely than without denoising. Figure 2 shows a representative micrograph before and after denoising. Before denoising, many particle top-views were indistinguishable by eye from noise (Fig. 2a, left inset). After denoising, top-views in particular became readily identifiable (Fig. 2a, right inset and circled in green).

We manually picked 1,023 particles while attempting to balance the percentage of side, oblique, and top-views of the particle in our picks. Using these picks, we trained a Topaz16 picking model as described in the “Methods”. The resulting model was used to infer a total of 23,695 particles after CryoSPARC18 2D classification, 3D heterogeneous refinement to identify two conformations, and 3D homogeneous refinement using “gold standard” FSC refinement on each conformation (Fig. 2b, right). A closed conformation consisting of 13,392 particles confirmed the previous structure obtained using sub-tomogram alignment (EMD-9197)25. A putative partially open conformation consisting of 8134 particles was obtained (Fig. 2b, yellow map), which exhibits a dislocation on one end of the dimer and an increased twist of the whole structure relative to the closed conformation. We confirm that these conformations are not random reconstruction anomalies by repeating the reconstruction process six times independently, all of which produce the same two conformations (Supplementary Fig. 10). In comparison, using only the raw micrographs for initial manual picking, the data owner picked 1540 particles to train a Topaz model as described in Brasch et al.25 that inferred 10,010 particles in the closed conformation after CryoSPARC 2D classification and 3D homogeneous refinement using “gold standard” FSC (Fig. 2, left). Using Topaz-Denoise to help identify particles manually enabled us to resolve a putative novel conformation of clustered protocadherin from single particles, resulted in 2.15x more real particles picked, and substantially increased the percentage of top- and oblique-views (Fig. 2c, Supplementary Fig. 11). We substantially improve over the previous best resolution single particle cryoET structure of this protein complex (12 Å vs. 35 Å), yet near atomic resolution single particle structures remain a distant goal. ResLog analysis suggests that millions of particles are required to reach near atomic resolution26 (Supplementary Fig. 11d).

Interestingly, CryoSPARC ab initio reconstruction using a minimal set of denoised particles is less reliable than using the same set of raw particles (Supplementary Fig. 12). Four or five of the six ab initio reconstructions using the raw particles resulted in the correct overall structure, while only one of the six ab initio reconstructions using the denoised particles resulted in the correct overall structure.

### Denoising with the general model enables shorter exposure imaging

We simulated short exposure times at the microscope by truncating frames of several datasets used during frame alignment and summed to the first 10%, 25%, 50%, and 75% of the frames. These datasets were collected with a total dose of between 40 and 69 e-/Å2. We denoised each short exposure with our general U-net model and compared both visually and quantitatively to low-pass filtering and to the raw micrographs without denoising.

Figure 3 shows denoised and low-pass filtered example micrographs of each subset along with the raw micrographs. Visual analysis and our SNR analysis suggests that between 10% and 25% of the exposure time is comparable to the full, raw micrographs (Fig. 3 and Supplementary Fig. 13 for FFT, Supplementary Figs. 14–17). This corresponds to between 4.0 and 16.7 e-/Å2. 3D reconstructions of frame titrations of identical apoferritin particles from 19jan04d suggests that a total dose of ~16.7 e-/Å2 is required for accurate CTF estimation (Supplementary Fig. 18). Remarkably, reconstructions from these low-dose particle stacks reach resolutions surpassing that of the full dose particle stacks. This suggests that Topaz-Denoise can enable low-dose collection, particle identification, and thus high-resolution reconstruction in practice. Furthermore, roughly double the electron dose is required for low-pass filtering to match the SNR of our neural denoised micrographs. This could allow a factor of two or more savings in exposure time. Such a significant reduction in exposure time substantially increases the efficiency of cryoEM collection sessions, allowing for microscopes to operate at higher throughput.

To account for real-world collection overhead, we tested the optimal exposure dose for 19jan04d (~17 e-/Å2) compared to a normal exposure dose (~66 e-/Å2) on both a Titan Krios + Gatan K2 system and a Titan Krios + Gatan K3 system for a typical stage shift collection (1 exposure per hole) and a typical image shift collection (4 exposures per hole). Table 2 shows the results. On the K2 system with stage shift collection, using the optimal exposure dose is about 65% more efficient than using the normal exposure dose (178 exposures per hour compared vs. 108). With image shift collection, using the optimal exposure dose is about 57% more efficient than using the normal exposure dose (190 exposures per hour compared vs. 121). On the K3 system with stage shift collection, using the optimal exposure dose is ~25% more efficient than using the normal exposure dose (242 exposures per hour compared vs. 195). With image shift collection, using the optimal exposure dose is ~15% more efficient than using the normal exposure dose (273 exposures per hour compared vs. 237). These results show that using the Topaz-Denoise general model to optimize exposure dose can allow for on the order of 1000 more exposures per day to be collected on K2 and K3 systems.

### Generalized 3D cryoET tomogram denoising markedly improves contrast, SNR, and interpretability

We converted the 2D Noise2Noise framework used in the previous sections to 3D for the purpose of creating a pre-trained general denoising model for cryo-electron tomograms (Methods). To train a general denoising model, we split 32 aligned cryoET tilt-series from FEI Titan Krios + Gatan K2 BioQuantum systems of cellular and reconstituted biological environments into even/odd frame tilt-series, binned each tilt-series by 2, reconstructed each tilt-series, and trained the neural network for over one month (“Methods”). The average pixelsize of the trained model, called Unet-3d-10a in the Topaz-Denoise package, is 10 Å. To further increase the broadness of 3D denoising in Topaz-Denoise, we trained a second general 3D denoising model called Unet-3d-20a using the same data as the Unet-3d-10a model, except with all training tomograms binned by another factor of 2 in Fourier space (ie. 20 Å pixelsize tomograms). Both general 3D denoising models are included in Topaz-Denoise.

To evaluate the resulting general 3D denoising model, we applied the model to one tomogram from each of the datasets used in the training and compared the results to models trained specifically on each test tomogram (“self-trained”), in addition to low-pass filtered tomograms (Supplementary Table 2). Comparisons were made both by SNR calculations using even/odd tomograms (Supplementary Table 2, “Methods”), and visually. Our pre-trained 3D U-net model (Unet-3d-10a) improves SNR by >3 dB over raw tomograms and improves SNR by about 1 dB on average over the best low-passed tomograms. Self-trained models showed only a marginal improvement in SNR over Unet-3d-10a. Figure 4a and Supplementary Movie 1 show a visual comparison of one of the yeast tomograms used for training and testing. The Unet-3d-10a and self-trained models show a marked improvement in contrast and detail of ribosomes, RNA, ER proteins, mitochondrial transmembrane proteins, and aggregates over the raw and low-passed tomograms, while flattening background similar to the 2D U-net model for micrographs.

We next applied the Unet-3d-10a model to a sample unlike those it was trained on in several respects: an 80 S ribosome single particle unbinned tomogram with a pixelsize of 2.17 Å and defocus of 4 microns, over four times less than the average pixelsize and half the average defocus of the tomograms used for training. A visual comparison of the applied model along with binned and Gaussian low-pass filtered tomograms is shown in Fig. 4b and Supplementary Movie 2. As with the previous 2D and 3D Topaz-Denoise general model results, the Unet-3d-10a model properly flattens background while increasing contrast of proteins relative to binning and low-pass filters. The increased contrast without tomogram resampling allows for visual delineation of objects of interest while retaining their higher-resolution information, and does not require ad-hoc parameter adjustment or training required by filtering methods more complicated than low-pass filtering. Furthermore, we show that applying a Gaussian filter after denoising further increases contrast, but at the expense of higher-resolution information (Fig. 4b and Supplementary Movie 2, last tomogram). This may be useful if researchers wish to further increase contrast and do not require all frequencies to be visualized.

### Discussion

CryoEM has long been hampered by the ability for researchers to confidently identify protein particles in all represented orientations from behind sheets of noise. Several bottlenecks in the general cryoEM workflow may preclude protein structure determination due to low SNR, such as differentiating protein from noise during picking, picking homogeneous subsets of particles, picking sufficient numbers of particles in all represented orientations, and obtaining a sufficient number of particles for 3D refinement. The initial stages of de novo protein structure determination are particularly affected by these issues.

To ameliorate these potentially critical issues, we present Topaz-Denoise, a Noise2Noise-based convolutional neural network for learning and removing noise from cryoEM images and cryoET tomograms. By employing a network trained on dozens of datasets to account for varying sample, microscope, and collection parameters, we achieve robust general denoising for cryoEM. We show empirically that our U-net denoising models result in higher SNR relative to affine models and low-pass filters. Topaz-Denoise enables visual identification of low SNR particle views, as exemplified by the clustered protocadherin dataset where denoising allows for more representative and complete 3D reconstructions, significantly more particles picked, and a putative new conformation. This putative partially “open” conformation suggests the possibility that assembly of protocadherin cis-dimers are preformed on membranes allowing rapid assembly of lattices and triggering of an avoidance signal when two cell surfaces with identical protocadherin complements come into contact. We note that these proteins are known to form flexible complexes in situ25, but multiple confirmations were not previously identifiable in single particle cryoEM due to the difficulty in analysing these micrographs. Increased confidence in particle identification using Topaz-Denoise enables novel structures to be obtained from cryoEM data due to substantially increased particle picking completeness. Moreover, due to the considerable increase in SNR of denoised single particle micrographs, exposure time may be reduced without sacrificing the ability to pick particles reliably or perform downstream processing, thus enabling an increase in collection efficiency. Finally, implementing the same Noise2Noise-based network in 3D enables denoising of cryo-electron tomograms in minutes. As shown in both cellular tomograms and single particle tomograms, the 3D general denoising model in Topaz-Denoise properly smooths areas without signal and increases contrast of areas with signal without reducing the visual resolvability of features. This results in substantially higher SNR features both visually and quantitatively. Together, the U-net model for cryoEM and the Unet-3d models for cryoET in Topaz-Denoise offer superior denoising capabilities that are broadly applicable across instruments and sample types.

Conceptually, the Noise2Noise method as applied to micrographs in Topaz-Denoise trains a neural network to transform each denoised half-micrograph into the paired raw half-micrograph, and performs this training over thousands of half-micrograph pairs. We note that this is effectively learning an SNR maximizing transformation. This follows from the relationship between the SNR of a micrograph and the correlation coefficient between paired independent measurements, which has been known and used in cryoEM since at least 19751,27. This relationship, SNR = CCC/(1-CCC), where CCC is the correlation coefficient, has direct connection with the Noise2Noise objective in which we seek to find a transformation of the micrograph such that the error between transformed micrographs and the paired independent micrograph is minimized. In particular, the choice of L2 loss can be motivated through direct connection with the correlation. When both the denoised micrograph and raw micrograph are normalized to have mean zero and standard deviation one, the mean squared error (MSE) and correlation coefficient (CCC) are related by MSE = 2 − 2 × CCC. This suggests a direct link between the MSE objective and SNR under the framework of Frank and Al-Ali27.

Practically in our experience, because the general models were trained on large datasets from popular DDDs (Gatan K2, FEI Falcon II, and FEI Falcon III), these models provide the best visual results on comparable DDDs. For micrographs from microscopes and detectors used in the training dataset, we find that denoising typical featureful objects, such as proteins, continuous carbon, carbon/gold edges, and crystalline ice, increases their visual contrast, while denoising amorphous objects such as vitrified water results in visual flattening (Fig. 1b, c and Supplementary Fig. 13 for FFTs). Micrographs from non-DDD cameras still fare well compared to DDDs in our experience (Supplementary Fig. 9) despite differing physical characteristics of the microscopes and detectors. This suggests that the general U-net model in Topaz-Denoise is robust to micrographs collected on equipment outside of the training dataset. Since non-DDD cameras are often used on screening microscopes, denoising these micrographs may increase screening throughput by allowing for more rapid analysis of micrographs, thereby increasing the efficiency of grid preparation steps. These results highlight three of the main advantages of our general denoising model: (1) users do not have to spend additional time training specific denoising models using their data, (2) for cameras that do not record frames, such as most screening microscope systems, acquiring data for training is not practical, thus a general denoising model is greatly prefered, and 3) the general model enables real-time denoising during data collection because denoising takes only seconds per micrograph.

The 3D cryoET denoising model included in Topaz-Denoise, and the framework which allows users to train their own models, may allow for improved data analysis not only in the cryoET workflow, but also the cryoEM workflow. In cryoET, researchers are often exploring densely-packed, unique 3D structures that are not repetitive enough to allow for sub-volume alignment to increase the SNR. The 3D denoising model shown here and included in the software increases the SNR of tomograms, which as a consequence may make manual and automated tomogram segmentation28 easier and more reliable. In single particle cryoEM, we anticipate that the 3D denoising model and models trained on half-maps may be used to denoise maps during iterative alignment, as has previously been shown to be useful after alignment29. In our experience, training models on half-maps performs a form of local b-factor correction on the full map, which may allow for more reliable and accurate iterative mask generation during single particle alignment.

Models generated using Topaz-Denoise, including the provided general models, may be susceptible to the hallucination problem in neural networks30. Details in denoised micrographs or tomograms may exhibit imprints of encodings from the datasets used for training. Practically, this means that denoised particles should not be relied on for reconstruction as demonstrated in Supplementary Fig. 12. We suspect that the issue here is two-fold: (1) cryoEM/ET refinement and reconstruction software assume noise distributions typical of raw data, not denoised data, and (2) denoised particles may present hallucinated information from the denoising model that is not detectable by visual inspection. For these reasons, we recommend that Topaz-Denoise models be used to assist with visualization and object identification, then the objects of interest be extracted and processed from raw micrographs/tomograms. Misuse of Topaz-Denoise and other opaque augmentations of raw data may result in subtle and difficult-to-detect forms of hallucinated signal31,32.

As cryoEM and cryoET continue to expand into adjacent fields, researchers new to micrograph and tomogram data analysis will benefit from improved methods for visualization and interpretation of these low SNR data. Topaz-Denoise provides a bridge to these researchers, in addition to assisting those experienced in cryoEM and cryoET. We expect Topaz-Denoise to become a standard component of the micrograph analysis pipeline due to its performance, modularity, and integration into CryoSPARC, Relion, Appion, and Scipion.

### Training dataset preparation for 2D denoising models

To train the denoising models, we collected a large dataset of micrograph frames from public repositories33 and internal datasets at the New York Structural Biology Center (NYSBC), as described in Supplementary Table 3. These micrograph frames were collected under a large variety of imaging conditions and contain data collected on FEI Krios, FEI Talos Arctica, and JEOL CRYOARM300 microscopes with Gatan K2, FEI Falcon II, and FEI Falcon III DDD cameras at both super-resolution (K2) and counting modes and at many defocus levels. Including several microscopes, cameras, and datasets allows for robust denoising parameters to be modelled across common microscope setups.

We form two general aggregated datasets, one we call “Large” and one called “Small”. The “Large” dataset contains micrographs from all individual datasets. To roughly balance the contribution of the individual datasets in these aggregate datasets, we randomly select up to 200 micrographs from each individual dataset for inclusion rather than all micrographs. The Small dataset contains micrographs from individual datasets selected by eye based on the denoising performance of individually-trained U-net denoising models.

The Noise2Noise framework requires paired noisy observations of the same underlying signal. We generate these pairs by splitting the micrograph frames into even/odd frames which represent independent observations. These even/odd micrograph frames are then summed directly to form the paired observations. Because micrographs are typically motion corrected before summing and this motion correction procedure can change the noise distribution of the micrographs, we also form aligned, summed micrograph pairs by aligning the even/odd micrograph frames with MotionCor234 using 5 by 5 patches and a b-factor of 100. This resulted in 1929 paired micrographs for the Small dataset and 3439 paired micrographs for the Large dataset.

### Model architectures

We adopt a U-Net model architecture35 similar to that used by Lehtinen et al.9 except that the input and output feature maps are one-dimensional (n = 1 to match monochrome micrographs) and we replace the first two width 3 convolutional layers of Lehtinen et al. with a single width 11 convolutional layer (Supplementary Fig. 19) similar to other convolutional neural networks used in cryoEM16. This model contains five max pooling downsampling blocks and five nearest-neighbor upsampling blocks with skip connections between down- and up-sampling blocks at each spatial resolution. We refer to this as the U-net model. For comparison, we also consider a smaller U-net model with only 3 downsampling and upsampling blocks which we refer to as the U-net (small) model. We also compare with a fully convolutional neural network consisting of three convolutional layers of width 11 × 11 with 64 filters each and leaky rectified linear unit activations, termed FCNN, and an affine model with a single convolutional filter of width 31 × 31.

### Loss functions and the Noise2Noise framework

The Noise2Noise framework takes advantage of the observation that we can learn models that recover statistics of the noise distribution given paired noisy observations of the same underlying signal. Given a ground truth signal, y, we observe images of this signal that have been corrupted by some probabilistic noise process, x ~ Noise(y). Given paired noisy observations for matched signals, xa ~ Noise(y) and xb ~ Noise(y), we can learn a function that recovers statistics of this distribution. This is accomplished by finding parameters of the denoising function, f with parameters θ, such that the error between the denoised sample f(xa) and raw xb are minimized. The form of this error function determines what statistics of the noise distribution we learn to recover. Given a dataset, X, containing many such image pairs, minimizing the L2 error over paired samples,

{\mathrm{argmin}}_\theta \,E_{x_z,x_b \sim X}[

The Adobe transition to a subscription-based business model has been successful by many measures, although it doesn’t meet everyone’s needs. If you want Adobe software but you don’t want to pay a regular subscription fee, do you still have options? Depending on what you need, the answer is “maybe”…although as of 2017, the non-subscription options from Adobe are fewer than ever. (Update: As of 2019, nearly all Adobe professional software is now available only through a Creative Cloud subscription.)

First let’s make sure we understand the two common types of software licenses for consumer single-user software. The older way to pay for software is called a perpetual license, because you buy the license once and it doesn’t expire. With Adobe Creative Cloud and some other newer applications, you maintain your license to use Adobe software and services by paying a subscription fee every year or every month, as you might with Netflix or Spotify.

### How to get Photoshop and other Creative Cloud applications today

Between 2012 and 2017, some Adobe professional applications were available by both subscription and perpetual licenses. This led to confusion about which version to get, especially as Adobe began to hide the perpetual license options. After CS6 went off the retail market in 2017, the choice became clear only because almost all Adobe pro applications became available exclusively by subscription. Still, I’ve included information on how to get current versions, how to know the difference between the two versions of Lightroom, some non-subscription alternatives, and whether you should consider the second-hand market.

The king of Adobe software is, of course, Adobe Photoshop. Now that Adobe no longer sells CS6 applications, you can get Photoshop only through a paid Creative Cloud membership. The most affordable membership is the Photography Plan, which for USD $9.99 a month, includes Photoshop, Lightroom Classic, and Lightroom as well as a range of online services, including Lightroom cloud storage and syncing across devices as well as an Adobe Portfolio website (All of that may change, so read over the current offers carefully.) If you use Photoshop for business reasons this is probably going to be one of the smallest business expenses you have. The relatively low cost of the Photography Plan subscriptions means that many of the objections to it are not economic. (The full Creative Cloud plan, which includes nearly all Adobe pro applications, is much more costly.) The only non-subscription version of Photoshop currently for sale is Photoshop Elements, or you can use a non-Adobe Photoshop alternative. See below for more information about those options. ### Lightroom On October 18, 2017, Adobe announced the 2018 releases of Lightroom CC and Lightroom Classic CC under a choice of Creative Cloud plans; it was also announced that Lightroom 6 is the last version available through a perpetual license. If you’re not sure about the difference between the subscription and perpetual license versions of Lightroom, it’s this: • Lightroom and Lightroom Classic are available as part of an Adobe Creative Cloud subscription, including the inexpensive Photography Plan. Lightroom is the newer form that stores all of your images in the cloud; Lightroom Classic is the current version of the original Lightroom that stores all of your original images on your own local storage. These versions have Creative Cloud-specific features, such as the ability to sync with Lightroom in the cloud and on other devices. They are eligible for all Lightroom updates, which can contain new features or bug fixes. (These applications were formerly called Lightroom CC and Lightroom Classic CC, but Adobe dropped the CC after it was no longer necessary to distinguish the subscription and perpetual license versions.) • Lightroom 6 was sold as a perpetual license. The last perpetual license version of Lightroom was Lightroom 6. Introduced in 2015, Adobe stopped selling it in 2019. In terms of features, the main difference is that Lightroom 6 didn’t connect or sync to any Creative Cloud services such as Lightroom Photos. Lightroom 6 received bug fixes as they become available, but new features added to the subscription version of Lightroom were not added to the perpetual license version. Lightroom 6 will not receive any further major upgrades; the equivalent of Lightroom 7 was Lightroom Classic CC (version 7) which is subscription-only. For several years you could buy Lightroom 6 (perpetual license, no subscription) from Amazon.com, B&H, and Adorama. But when I checked on March 31, 2019, the only one of those three links that still worked was for B&H. Finally, some time around October 10, 2019, B&H withdrew Lightroom 6 from sale and listed it as Discontinued. Again, Adobe has stopped selling new or upgrade licenses for Lightroom 6 directly from their website. If you find a copy of Lightroom 6 and are thinking about buying it, keep the following in mind: • Lightroom 6 is no longer supported or receiving updates, so raw files of newer cameras may not be supported. • The Lightroom 6 feature set is falling further behind Lightroom Classic. For example, it lacks features such as Dehaze and Texture, and does not include the performance enhancements and improved GPU support in Lightroom Classic. • After November 30, 2018, the live map view in Lightroom Classic 7.5 and earlier no longer works because the connection to the map server has changed (The rest of the Map module still works). The live map view has been updated and continues to function in the current versions of Lightroom Classic (version 8 or later) and Lightroom (version 2 or later). • On macOS, some Lightroom 6 components won’t run on macOS 10.15 Catalina, preventing it from being installed or uninstalled. Lightroom 6 may work if it was already installed before upgrading to macOS 10.15 Catalina. ### Acrobat As of January 2021, Acrobat 2020 Standard and Pro are still available as a one-time Full License purchase, but it isn’t easy to find. Go to https://www.adobe.com/products/catalog.html, expand the PDF & E-Signatures category, and select PDF. Or go to this direct link: https://www.adobe.com/products/catalog.html#category=Pdf-esignatures After you click Buy Now, the Full License version is available from the Type menu as shown below. ### Buying a used copy There may be copies of Creative Suite software available for sale through the used market, but if you are interested in buying it that way you should exercise extreme caution to avoid scams, pirated copies hacked with malware, and serial numbers that Adobe has deactivated. If you’re buying software that has been previously opened and installed, it’s a good idea to make sure the seller is willing to do an official transfer of license to ensure that you become the new legal owner of the software. Also, CS6 applications were released in 2012, so they were not written for the latest operating systems and hardware. They are no longer being updated, so if you upgrade your hardware or system and a CS6 application now has a problem running on it, a fix is probably not available. If you’re thinking about buying a used copy, confirm that its version is supported on the computer and operating system version you have. This is especially true if you use a Mac, because changes Apple made to macOS and Mac hardware over the last few years mean that only the current subscription versions of most Adobe software will install and run on the latest Macs. ### Non-subscription alternatives from Adobe: Photoshop Elements and Premiere Elements Years ago, hobbyists and non-professionals used to buy the full version of Photoshop because it was one of the few applications that could do a good job of editing images. Today many of those users may be satisfied with recent versions of Photoshop Elements. It’s sold from many retailers as a perpetual license for under USD$100, no subscription needed or available.

Over time many advanced features in recent versions of Photoshop (such as healing, hair selection, camera shake reduction, and panorama merge) have been handed down to Photoshop Elements, so some areas of Photoshop Elements are more powerful than older versions of Photoshop.

Here’s an intriguing option: A non-Adobe plug-in called Elements+ unlocks a long list of Photoshop features that are present but hidden in the Elements version. Elements+ is not free, but using Elements+ with Photoshop Elements gets you a lot closer to the full version of Photoshop, and the combined non-subscription price of both is still reasonably low.

For video editing, Premiere Elements serves a similar consumer audience, and is also sold as perpetual license software.

Photo editing software has matured greatly since the days when Photoshop was the clear standout. On the Mac, hobbyists and others needing something more advanced than Apple Photos can turn to Acorn, Pixelmator, Polarr, and others. However, photo editors at that level tend to be missing features that advanced and professional users rely on in Photoshop. If you do need more advanced features such as support for true camera raw editing and non-RGB color modes (such as CMYK and Lab) and ICC profile conversions, take a look at Affinity Photo. That affordable application seems much closer to Photoshop than most other alternatives. GIMP is also a frequently mentioned Photoshop alternative; it’s mature and powerful but can be challenging to learn.

Affinity is the developer to watch here. Before Affinity Photo they released Affinity Designer, a legitimate alternative to Adobe Illustrator. In June 2019, Affinity released Publisher, a potential alternative to Adobe InDesign. This means Affinity now has a trio of perpetual license desktop applications that covers much of the same ground as the old Adobe Creative Suite. Serif (the parent company of Affinity) certainly has the background to build it, as they are the developer of the long-established PhotoPlus, DrawPlus, and PagePlus applications for Windows. Affinity has also said they are working on a digital asset manager, which could compete with Adobe Lightroom or Bridge.

For pure raw processing, alternatives to Lightroom and Camera Raw include Capture One, DxO PhotoLab, ON1 Photo Raw, Skylum Luminar, and the free/open source Darktable, Lightzone, and RawTherapee. These are generally very capable raw processors. If you value the organizational features in Lightroom you should evaluate the alternatives carefully, because in general their photo organization features are not as strong as their raw development features.

Some enjoy using Apple Photos enhanced with editing extensions made by Skylum, DxO and others. These extensions bring the image-editing capabilities of Photos closer to Lightroom. But because these extensions are created by multiple developers, the editing experience is less integrated and consistent than in Lightroom. Another problem is that the organizational abilities of Apple Photos fall well short of what Lightroom can do, and so far, it looks like extensions are not able to improve that area of Photos.

### Some history: The transition to subscriptions

After the launch of Creative Cloud in 2012, Adobe originally stated that CS6 applications would remain on sale “indefinitely” (A word that does not mean “forever,” although many read it that way). Through most of 2015 Adobe provided a web link where you could still pay once to buy a perpetual license of CS6 applications. But in late 2015, Adobe redirected the link to a web page, shown below, where ordering by phone was the only option:

Then, on January 9, 2017, the content of that web page changed to this:

Note the text that my arrow points to, which says:

As of January 9, 2017 Creative Suite is no longer available for purchase.

### The big picture

From the Adobe point of view, there’s no question that Adobe Creative Cloud has been successful for Adobe. Since switching to a subscription model, Adobe has reported many quarters of record revenue growth partially driven by Creative Cloud subscription rates that exceeded their projections, year after year. When people ask “Why doesn’t Adobe offer a perpetual license option for their professional applications?” the short answer is that Adobe doesn’t have any motivation to. Subscriptions bring in more revenue than perpetual license software did, and by an extremely wide margin.

From the customer point of view, Adobe Creative Cloud isn’t just about subscriptions. It includes features that perpetual license software usually doesn’t offer such as online storage and sharing, a portfolio website, fonts for desktop and mobile devices, and other online services that work together as a single integrated workflow across your desktop and mobile devices. These benefits tend to have the most appeal for highly mobile creatives who work and collaborate daily with the latest workflows and need features that support them. For example, if you frequently prepare graphics for websites and devices that are Retina/HiDPI enabled, you’d probably want the Adobe Generator, Export As, and Artboards features that are in the current version of Photoshop, and were not in Photoshop CS6.

But all of that still does not mean subscriptions work for everyone. If you have a more modest or occasional workflow, like weekly processing of a few images for prints or a simple website, one of the non-subscription alternatives in this article might be all you need.

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