Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

/pdf/classical-mathematical-models-for-description-and-prediction-3ugueumekg.pdf

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

Several state-of-the-art video deblurring methods are based on a strong assumption that the captured scenes are static. These methods fail to deblur blurry videos in dynamic scenes. We propose a video deblurring method to deal with general blurs inherent in dynamic scenes, contrary to other methods. To handle locally varying and general blurs caused by various sources, such as camera shake, moving objects, and depth variation in a scene, we approximate pixel-wise kernel with bidirectional optical flows. Therefore, we propose a single energy model that simultaneously estimates optical flows and latent frames to solve our deblurring problem. We also provide a framework and efficient solvers to optimize the energy model. By minimizing the proposed energy function, we achieve significant improvements in removing blurs and estimating accurate optical flows in blurry frames. Extensive experimental results demonstrate the superiority of the proposed method in real and challenging videos that state-of-the-art methods fail in either deblurring or optical flow estimation.

/pdf/generalized-video-deblurring-for-dynamic-scenes-3czs5697qo.pdf

Generalized video deblurring for dynamic scenes

Capturing high-dimensional (HD) data is a long-term challenge in signal processing and related fields. Snapshot compressive imaging (SCI) uses a two-dimensional (2D) detector to capture HD ($\ge3$D) data in a {\em snapshot} measurement. Via novel optical designs, the 2D detector samples the HD data in a {\em compressive} manner; following this, algorithms are employed to reconstruct the desired HD data-cube. SCI has been used in hyperspectral imaging, video, holography, tomography, focal depth imaging, polarization imaging, microscopy, \etc.~Though the hardware has been investigated for more than a decade, the theoretical guarantees have only recently been derived. Inspired by deep learning, various deep neural networks have also been developed to reconstruct the HD data-cube in spectral SCI and video SCI. This article reviews recent advances in SCI hardware, theory and algorithms, including both optimization-based and deep-learning-based algorithms. Diverse applications and the outlook of SCI are also discussed.

Snapshot Compressive Imaging: Principle, Implementation, Theory, Algorithms and Applications.

Dense motion estimations obtained from optical flow techniques play a significant role in many image processing and computer vision tasks. Remarkable progress has been made in both theory and its application in practice. In this paper, we provide a systematic review of recent optical flow techniques with a focus on the variational method and approaches based on Convolutional Neural Networks (CNNs). These two categories have led to state-of-the-art performance. We discuss recent modifications and extensions of the original model, and highlight remaining challenges. For the first time, we provide an overview of recent CNN-based optical flow methods and discuss their potential and current limitations.

A survey of variational and CNN-based optical flow techniques

Capturing high-dimensional (HD) data is a long-term challenge in signal processing and related fields. Snapshot compressive imaging (SCI) uses a 2D detector to capture HD (g3D) data in a snapshot measurement. Via novel optical designs, the 2D detector samples the HD data in a compressive manner; following this, algorithms are employed to reconstruct the desired HD data cube. SCI has been used in hyperspectral imaging, video, holography, tomography, focal depth imaging, polarization imaging, microscopy, and so on. Although the hardware has been investigated for more than a decade, the theoretical guarantees have only recently been derived. Inspired by deep learning, various deep neural networks have also been developed to reconstruct the HD data cube in spectral SCI and video SCI. This article reviews recent advances in SCI hardware, theory, and algorithms, including both optimizationbased and deep learning-based algorithms. Diverse applications and the outlook for SCI are also discussed.

Snapshot Compressive Imaging: Theory, Algorithms, and Applications

Prostate cancer is commonly treated by a form of hormone therapy called androgen suppression. This form of treatment, while successful at reducing the cancercell population, adversely affects quality of life and typically leads to a recurrence of the cancer in an androgen-independent form. Intermittent androgen suppression aims to alleviate some of these adverse affects by cycling the patient on and off treatment. Clinical studies have suggested that intermittent therapy is capable of maintaining androgen dependence over multiple treatment cycles while increasing quality of life during off-treatment periods. This paper presents a mathematical model of prostate cancer to study the dynamics of androgen suppression therapy and the production of prostate-specific antigen (PSA), a clinical marker for prostate cancer. Preliminary models were based on the assumption of an androgen-independent (AI) cell population with constant net growth rate. These models gave poor accuracy when fitting clinical data during simulation. The final model presented hypothesizes an AI population with increased sensitivity to low levels of androgen. It also hypothesizes that PSA production is heavily dependent on androgen. The high level of accuracy in fitting clinical data with this model appears to confirm these hypotheses, which are also consistent with biological evidence.

/pdf/a-clinical-data-validated-mathematical-model-of-prostate-1xujherzra.pdf

A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy

This paper extends the classical warping-based optical flow method to achieve accurate flow in the presence of spatially-varying motion blur. Our idea is to parameterize the appearance of each frame as a function of both the pixel motion and the motion-induced blur. We search for the flows that best match two consecutive frames, which amounts to finding the derivative of a blurred frame with respect to both the motion and the blur, where the blur itself is a function of the motion. We propose an efficient technique to calculate the derivatives using prefiltering. Our technique avoids performing spatially-varying filtering (which can be computationally expensive) during the optimization iterations. In the end, our derivative calculation technique can be easily incorporated with classical flow code to handle video with non-uniform motion blur with little performance penalty. Our method is evaluated on both synthetic and real videos and outperforms conventional flow methods in the presence of motion blur.

http://pages.cs.wisc.edu/~lizhang/projects/blurflow/portz-cvpr2012.pdf

Optical flow in the presence of spatially-varying motion blur

We propose a novel method for capturing high-speed, high dynamic range video with a single low-speed camera using a coded sampling technique. Traditional video cameras use a constant full-frame exposure time, which makes temporal super-resolution difficult due to the ill-posed nature of inverting the sampling operation. Our method samples at the same rate as the traditional low-speed camera but uses random per-pixel exposure times and offsets. By exploiting temporal and spatial redundancy in the video, we can reconstruct a high-speed video from the coded input. Furthermore, the different exposure times used in our sampling scheme enable us to obtain a higher dynamic range than a traditional camera or other temporal superresolution methods. We validate our approach using simulation and provide a detailed discussion on how to make a hardware implementation. In particular, we believe that our approach can maintain a 100% light throughput similarly to existing cameras and can be implemented on a single chip, making it suitable for small form factors.

/pdf/random-coded-sampling-for-high-speed-hdr-video-249cybqbtq.pdf

Random coded sampling for high-speed HDR video

A mathematical model of advanced prostate cancer treatment is developed to examine the combined effects of androgen deprivation therapy and immunotherapy. Androgen deprivation therapy has been the primary form of treatment for advanced prostate cancer for the past 50 years. While initially successful, this therapy eventually results in a relapse after two to three years in the form of androgen-independent prostate cancer. Intermittent androgen deprivation therapy attempts to prevent relapse by cycling the patient on and off treatment. Over the past decade, dendritic cell vaccines have been used in clinical studies for the immunotherapy of prostate cancer with some success. The model presented in this paper examines the efficacy of dendritic cell vaccines when used with continuous or intermittent androgen deprivation therapy schedules. Numerical simulations of the model suggest that immunotherapy can successfully stabilize the disease using both continuous and intermittent androgen deprivation.

A mathematical model for the immunotherapy of advanced prostate cancer

New digital cameras, such as Canon SD1100 and Nikon COOLPIX S8100, have an Auto Exposure (AE) function that is based on motion estimation. The motion estimation helps to set short exposure and high ISO for frames with fast motion, thereby minimizing most motion blur in recorded videos. This AE function largely turns video enhancement into a denoising problem. This paper studies the problem of how to achieve high-quality video denoising in the context of motion-based exposure control. Unlike previous denoising works which either avoid using motion estimation, such as BM3D [7], or assume reliable motion estimation as input, such as [13], our method evaluates the reliability of flow at each pixel and uses that reliability as a weight to integrate spatial denoising and temporal denoising. This weighted combination scheme makes our method robust to optical flow failure over regions with repetitive texture or uniform color and combines the advantages of both spatial and temporal denoising. Our method also exploits high quality frames in a sequence to effectively enhance noisier frames. In experiments using both synthetic and real videos, our method outperforms the state of the art [7, 13].

Travis Portz

Papers

A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy

Optical flow in the presence of spatially-varying motion blur

Random coded sampling for high-speed HDR video

A mathematical model for the immunotherapy of advanced prostate cancer

High-Quality Video Denoising for Motion-Based Exposure Control.