abstract: The depth richness of a scene translates into a spatially variable defocus blur in the acquired image. Blurring can mislead computational image understanding; therefore, blur detection can be used for selective image enhancement of blurred regions and the application of image understanding algorithms to sharp regions. This work focuses on blur detection and its application to image enhancement. This work proposes a spatially-varying defocus blur detection based on the quotient of spectral bands; additionally, to avoid the use of computationally intensive algorithms for the segmentation of foreground and background regions, a global threshold defined using weak textured regions on the input image is proposed. Quantitative results expressed in the precision-recall space as well as qualitative results overperform current state-of-the-art algorithms while keeping the computational requirements at competitive levels. Imperfections in the curvature of lenses can lead to image radial distortion (IRD). Computer vision applications can be drastically affected by IRD. This work proposes a novel robust radial distortion correction algorithm based on alternate optimization using two cost functions tailored for the estimation of the center of distortion and radial distortion coefficients. Qualitative and quantitative results show the competitiveness of the proposed algorithm. Blur is one of the causes of visual discomfort in stereopsis. Sharpening applying traditional algorithms can produce an interdifference which causes eyestrain and visual fatigue for the viewer. A sharpness enhancement method for stereo images that incorporates binocular vision cues and depth information is presented. Perceptual evaluation and quantitative results based on the metric of interdifference deviation are reported; results of the proposed algorithm are competitive with state-of-the-art stereo algorithms. Digital images and videos are produced every day in astonishing amounts. Consequently, the market-driven demand for higher quality content is constantly increasing which leads to the need of image quality assessment (IQA) methods. A training-free, no-reference image sharpness assessment method based on the singular value decomposition of perceptually-weighted normalized-gradients of relevant pixels in the input image is proposed. Results over six subject-rated publicly available databases show competitive performance when compared with state-of-the-art algorithms. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2019

No description available.

Esta tese apresenta dois métodos diferentes de estimativa de desfocagem usando uma única imagem. Ambos os métodos assumem uma função de espalhamento de ponto (Point Spread Function - PSF) Gaussiana e exploram a razão de magnitudes de gradientes de versões re-borradas da imagem original com escalas diferentes nas bordas da imagem, o que fornece uma expressão matemática fechada para borramento local. A primeira abordagem calcula perfis 1D ao longo de pontos de borda ortogonais ao contorno local, e avalia a localização da borda (máximo da derivada primeira) para selecionar adaptativamente o número de escalas no re-borramento. Considerando o consumo de tempo de explorar perfis de aresta orientados 1D, um segundo método foi proposto com base em gradientes de imagem diretamente no domínio 2D, e os parâmetros de re-borramento locais foram selecionados com base na concordância de um detector de bordas calculado em várias escalas. Dada uma estimativa inicial da escala de desfocagem nas posições de borda proporcionada por qualquer um destes dois métodos, é também proposto um passo de correção que atenua os erros introduzidos pela discretização da formulação contínua. Um novo método de filtragem local que suaviza as estimativas refinadas ao longo dos contornos de imagem também é proposto, e um filtro de domínio conjunto (jointdomain filter) rápido é explorado para propagar informações de desfocagem para toda a imagem, gerando o mapa de desfocagem completo. Os resultados experimentais em imagens sintéticas e reais mostram que os métodos propostos apresentam resultados promissores para a estimativa de borramento por desfoco, com um bom compromisso entre qualidade e tempo de execução quando comparados a técnicas estado-da-arte. Para lidar com sequências de vídeo desfocadas, a consistência temporal também foi incluída no modelo proposto. Mais precisamente, Filtros de Kalman foram aplicados para gerar estimativas temporais suaves para cada pixel quando a aparência local da sequência de vídeo não varia muito, permitindo transições durante mudanças drásticas da aparência local, que podem se relacionar com oclusões/desoclusões. Finalmente, esta tese também mostra aplicações dos métodos propostos para a estimativa de desfocagem de imagem e vídeo. Um novo método de redimensionamento (retargeting) de imagens é proposto para fotos tiradas por câmera com baixa profundidade de campo. O método inclui informação de desfocamento local no contexto do método seam carving, visando preservar objetos em foco com melhor qualidade visual. Assumindo que os pixels em foco estejam relacionados às regiões de interesse de uma imagem com desfocamento, o método de redimensionamento proposto começa com um método de corte (cropping), o qual remove as partes sem importância (borradas) da imagem, e então o método seam carving é aplicado com uma nova função de energia que prioriza as regiões em foco. Os resultados experimentais mostram que o método proposto funciona melhor na preservação de objetos em foco do que outras técnicas de redimensionamento de imagens. A tese também explora o método de estimação de desfocagem proposto no contexto de des-borramento de imagens e sequências de vídeo, e os resultados foram comparados com vários outros métodos de estimação de desfocagem. Os resultados obtidos mostram que as métricas tipicamente usadas para avaliar métodos de estimação de desfocagem (por exemplo, erro absoluto médio) podem não estar correlacionadas com a qualidade das métricas de imagem desfocada, como a Relação Sinal-Ruído de Pico. / This dissertation presents two different defocus blur estimation methods for still images. Both methods assume a Gaussian Point Spread Function (PSF) and explore the ratio of gradient magnitudes of reblurred images computed at edge location with different scales, which provides a closed form mathematical formulation for the local blur assuming continuous-time signals. The first approach computes 1D profiles along edge points orthogonal to the local contour, and evaluate the location of the edge (maximum of the derivative) to adaptively select the number of reblurring scales. Considering the time consumption of exploring 1D oriented edge profiles, a second method was proposed based on 2D multiscale image gradients, and local reblurring parameters were selected based on the agreement of an edge detector computed at several scales. Given an initial estimate of the blur scale at edge locations provided by either of these two methods, a correction step that accounts for the discretization of the continuous formulation is also proposed. A novel local filtering method that smooths the refined estimates along the image contours is also proposed, and a fast joint domain filter is explored to propagate blur information to the whole image to generate the full blur map. Experimental results on synthetic and real images show that the proposed methods have promising results for defocus blur estimation, with a good trade off between running time and accuracy when compared to state-of-the art defocus blur estimation methods. To deal with blurry video sequences, temporal consistency was also included in the proposed model. More precisely, Kalman Filters were applied to generate smooth temporal estimates for each pixel when the local appearance of the video sequence does not vary much, and allowing sharp transitions during drastic local appearance changes, which might relate to occlusions/disocclusions. Finally, this dissertation also shows applications of the proposed methods for image and video blur estimation. A new image retargeting method is proposed for photos taken by a shallow Depth of Field (DoF) camera. The method includes defocus blur information with the seam carving framework aiming to preserve in-focus objects with better visual quality. Assuming the in-focus pixels related to regions of interest of a blurry image, the proposed retargeting method starts with a cropping method, which removes the unimportant parts (blurry) of the image, then the seam carving method is applied with a novel energy function that prioritizes in-focus regions. Experimental results show that the proposed blur aware retargeting method works better at preserving in-focus objects than other well known competitive retargeting methods. The dissertation also explores the proposed blur estimation method in the context of image and video deblurring, and results were compared with several other blur estimation methods. The obtained results show that metrics typically used to evaluate blur estimation methods (e.g. Mean Absolute Error) might not be correlated with the quality of deblurred image metrics, such as Peak Signal to Noise Ratio.

No description available.

Esta tese apresenta dois métodos diferentes de estimativa de desfocagem usando uma única imagem. Ambos os métodos assumem uma função de espalhamento de ponto (Point Spread Function - PSF) Gaussiana e exploram a razão de magnitudes de gradientes de versões re-borradas da imagem original com escalas diferentes nas bordas da imagem, o que fornece uma expressão matemática fechada para borramento local. A primeira abordagem calcula perfis 1D ao longo de pontos de borda ortogonais ao contorno local, e avalia a localização da borda (máximo da derivada primeira) para selecionar adaptativamente o número de escalas no re-borramento. Considerando o consumo de tempo de explorar perfis de aresta orientados 1D, um segundo método foi proposto com base em gradientes de imagem diretamente no domínio 2D, e os parâmetros de re-borramento locais foram selecionados com base na concordância de um detector de bordas calculado em várias escalas. Dada uma estimativa inicial da escala de desfocagem nas posições de borda proporcionada por qualquer um destes dois métodos, é também proposto um passo de correção que atenua os erros introduzidos pela discretização da formulação contínua. Um novo método de filtragem local que suaviza as estimativas refinadas ao longo dos contornos de imagem também é proposto, e um filtro de domínio conjunto (jointdomain filter) rápido é explorado para propagar informações de desfocagem para toda a imagem, gerando o mapa de desfocagem completo. Os resultados experimentais em imagens sintéticas e reais mostram que os métodos propostos apresentam resultados promissores para a estimativa de borramento por desfoco, com um bom compromisso entre qualidade e tempo de execução quando comparados a técnicas estado-da-arte. Para lidar com sequências de vídeo desfocadas, a consistência temporal também foi incluída no modelo proposto. Mais precisamente, Filtros de Kalman foram aplicados para gerar estimativas temporais suaves para cada pixel quando a aparência local da sequência de vídeo não varia muito, permitindo transições durante mudanças drásticas da aparência local, que podem se relacionar com oclusões/desoclusões. Finalmente, esta tese também mostra aplicações dos métodos propostos para a estimativa de desfocagem de imagem e vídeo. Um novo método de redimensionamento (retargeting) de imagens é proposto para fotos tiradas por câmera com baixa profundidade de campo. O método inclui informação de desfocamento local no contexto do método seam carving, visando preservar objetos em foco com melhor qualidade visual. Assumindo que os pixels em foco estejam relacionados às regiões de interesse de uma imagem com desfocamento, o método de redimensionamento proposto começa com um método de corte (cropping), o qual remove as partes sem importância (borradas) da imagem, e então o método seam carving é aplicado com uma nova função de energia que prioriza as regiões em foco. Os resultados experimentais mostram que o método proposto funciona melhor na preservação de objetos em foco do que outras técnicas de redimensionamento de imagens. A tese também explora o método de estimação de desfocagem proposto no contexto de des-borramento de imagens e sequências de vídeo, e os resultados foram comparados com vários outros métodos de estimação de desfocagem. Os resultados obtidos mostram que as métricas tipicamente usadas para avaliar métodos de estimação de desfocagem (por exemplo, erro absoluto médio) podem não estar correlacionadas com a qualidade das métricas de imagem desfocada, como a Relação Sinal-Ruído de Pico. / This dissertation presents two different defocus blur estimation methods for still images. Both methods assume a Gaussian Point Spread Function (PSF) and explore the ratio of gradient magnitudes of reblurred images computed at edge location with different scales, which provides a closed form mathematical formulation for the local blur assuming continuous-time signals. The first approach computes 1D profiles along edge points orthogonal to the local contour, and evaluate the location of the edge (maximum of the derivative) to adaptively select the number of reblurring scales. Considering the time consumption of exploring 1D oriented edge profiles, a second method was proposed based on 2D multiscale image gradients, and local reblurring parameters were selected based on the agreement of an edge detector computed at several scales. Given an initial estimate of the blur scale at edge locations provided by either of these two methods, a correction step that accounts for the discretization of the continuous formulation is also proposed. A novel local filtering method that smooths the refined estimates along the image contours is also proposed, and a fast joint domain filter is explored to propagate blur information to the whole image to generate the full blur map. Experimental results on synthetic and real images show that the proposed methods have promising results for defocus blur estimation, with a good trade off between running time and accuracy when compared to state-of-the art defocus blur estimation methods. To deal with blurry video sequences, temporal consistency was also included in the proposed model. More precisely, Kalman Filters were applied to generate smooth temporal estimates for each pixel when the local appearance of the video sequence does not vary much, and allowing sharp transitions during drastic local appearance changes, which might relate to occlusions/disocclusions. Finally, this dissertation also shows applications of the proposed methods for image and video blur estimation. A new image retargeting method is proposed for photos taken by a shallow Depth of Field (DoF) camera. The method includes defocus blur information with the seam carving framework aiming to preserve in-focus objects with better visual quality. Assuming the in-focus pixels related to regions of interest of a blurry image, the proposed retargeting method starts with a cropping method, which removes the unimportant parts (blurry) of the image, then the seam carving method is applied with a novel energy function that prioritizes in-focus regions. Experimental results show that the proposed blur aware retargeting method works better at preserving in-focus objects than other well known competitive retargeting methods. The dissertation also explores the proposed blur estimation method in the context of image and video deblurring, and results were compared with several other blur estimation methods. The obtained results show that metrics typically used to evaluate blur estimation methods (e.g. Mean Absolute Error) might not be correlated with the quality of deblurred image metrics, such as Peak Signal to Noise Ratio.

Esta tese apresenta dois métodos diferentes de estimativa de desfocagem usando uma única imagem. Ambos os métodos assumem uma função de espalhamento de ponto (Point Spread Function - PSF) Gaussiana e exploram a razão de magnitudes de gradientes de versões re-borradas da imagem original com escalas diferentes nas bordas da imagem, o que fornece uma expressão matemática fechada para borramento local. A primeira abordagem calcula perfis 1D ao longo de pontos de borda ortogonais ao contorno local, e avalia a localização da borda (máximo da derivada primeira) para selecionar adaptativamente o número de escalas no re-borramento. Considerando o consumo de tempo de explorar perfis de aresta orientados 1D, um segundo método foi proposto com base em gradientes de imagem diretamente no domínio 2D, e os parâmetros de re-borramento locais foram selecionados com base na concordância de um detector de bordas calculado em várias escalas. Dada uma estimativa inicial da escala de desfocagem nas posições de borda proporcionada por qualquer um destes dois métodos, é também proposto um passo de correção que atenua os erros introduzidos pela discretização da formulação contínua. Um novo método de filtragem local que suaviza as estimativas refinadas ao longo dos contornos de imagem também é proposto, e um filtro de domínio conjunto (jointdomain filter) rápido é explorado para propagar informações de desfocagem para toda a imagem, gerando o mapa de desfocagem completo. Os resultados experimentais em imagens sintéticas e reais mostram que os métodos propostos apresentam resultados promissores para a estimativa de borramento por desfoco, com um bom compromisso entre qualidade e tempo de execução quando comparados a técnicas estado-da-arte. Para lidar com sequências de vídeo desfocadas, a consistência temporal também foi incluída no modelo proposto. Mais precisamente, Filtros de Kalman foram aplicados para gerar estimativas temporais suaves para cada pixel quando a aparência local da sequência de vídeo não varia muito, permitindo transições durante mudanças drásticas da aparência local, que podem se relacionar com oclusões/desoclusões. Finalmente, esta tese também mostra aplicações dos métodos propostos para a estimativa de desfocagem de imagem e vídeo. Um novo método de redimensionamento (retargeting) de imagens é proposto para fotos tiradas por câmera com baixa profundidade de campo. O método inclui informação de desfocamento local no contexto do método seam carving, visando preservar objetos em foco com melhor qualidade visual. Assumindo que os pixels em foco estejam relacionados às regiões de interesse de uma imagem com desfocamento, o método de redimensionamento proposto começa com um método de corte (cropping), o qual remove as partes sem importância (borradas) da imagem, e então o método seam carving é aplicado com uma nova função de energia que prioriza as regiões em foco. Os resultados experimentais mostram que o método proposto funciona melhor na preservação de objetos em foco do que outras técnicas de redimensionamento de imagens. A tese também explora o método de estimação de desfocagem proposto no contexto de des-borramento de imagens e sequências de vídeo, e os resultados foram comparados com vários outros métodos de estimação de desfocagem. Os resultados obtidos mostram que as métricas tipicamente usadas para avaliar métodos de estimação de desfocagem (por exemplo, erro absoluto médio) podem não estar correlacionadas com a qualidade das métricas de imagem desfocada, como a Relação Sinal-Ruído de Pico. / This dissertation presents two different defocus blur estimation methods for still images. Both methods assume a Gaussian Point Spread Function (PSF) and explore the ratio of gradient magnitudes of reblurred images computed at edge location with different scales, which provides a closed form mathematical formulation for the local blur assuming continuous-time signals. The first approach computes 1D profiles along edge points orthogonal to the local contour, and evaluate the location of the edge (maximum of the derivative) to adaptively select the number of reblurring scales. Considering the time consumption of exploring 1D oriented edge profiles, a second method was proposed based on 2D multiscale image gradients, and local reblurring parameters were selected based on the agreement of an edge detector computed at several scales. Given an initial estimate of the blur scale at edge locations provided by either of these two methods, a correction step that accounts for the discretization of the continuous formulation is also proposed. A novel local filtering method that smooths the refined estimates along the image contours is also proposed, and a fast joint domain filter is explored to propagate blur information to the whole image to generate the full blur map. Experimental results on synthetic and real images show that the proposed methods have promising results for defocus blur estimation, with a good trade off between running time and accuracy when compared to state-of-the art defocus blur estimation methods. To deal with blurry video sequences, temporal consistency was also included in the proposed model. More precisely, Kalman Filters were applied to generate smooth temporal estimates for each pixel when the local appearance of the video sequence does not vary much, and allowing sharp transitions during drastic local appearance changes, which might relate to occlusions/disocclusions. Finally, this dissertation also shows applications of the proposed methods for image and video blur estimation. A new image retargeting method is proposed for photos taken by a shallow Depth of Field (DoF) camera. The method includes defocus blur information with the seam carving framework aiming to preserve in-focus objects with better visual quality. Assuming the in-focus pixels related to regions of interest of a blurry image, the proposed retargeting method starts with a cropping method, which removes the unimportant parts (blurry) of the image, then the seam carving method is applied with a novel energy function that prioritizes in-focus regions. Experimental results show that the proposed blur aware retargeting method works better at preserving in-focus objects than other well known competitive retargeting methods. The dissertation also explores the proposed blur estimation method in the context of image and video deblurring, and results were compared with several other blur estimation methods. The obtained results show that metrics typically used to evaluate blur estimation methods (e.g. Mean Absolute Error) might not be correlated with the quality of deblurred image metrics, such as Peak Signal to Noise Ratio.

A new methodology is proposed to perform nonlinear time domain analysis on three-dimensional reinforced concrete bridge structures subjected to spatially varying seismic ground motions. A stochastic algorithm is implemented to generate unique and correlated time history records under each bridge support to model the spatial variability effects of seismic wave components traveling in the longitudinal and transverse direction of the bridge. Three-dimensional finite element models of highway bridges with variable geometry are considered where the nonlinear response is concentrated at bidirectional plastic hinges located at the pier end zones. The ductility demand at each pier is determined from the bidirectional rotations occurring at the plastic hinges during the seismic response evaluation of the bridge models. Variability of the soil characteristics along the length of the bridge is addressed by enforcing soil response spectrum compatibility of the generated time history records and of the dynamic stiffness properties of the spring sets modeling soil rigidity at the soil-foundation interface at each support location. The results on pier ductility demand values show that their magnitude depends on the type of soil under the pier supports, the pier location and the overall length and geometry of the bridge structure. Maximum ductility demand values were found to occur in piers supported on soft soils and located around the mid span of long multi-span bridges. The results also show that pier ductility demand values in the transverse direction of the bridge can be significantly different than the values in the longitudinal direction and in some instances, the maximum value occurs in the transverse direction. Moreover, results also show that ignoring the effects of spatial variability of the seismic excitation, the pier ductility demand can be severely underestimated. Finally, results show that increasing the vertical acceleration component in the seismic wave will generate an increase in the pier axial loads, which will reduce the ductility range of the pier plastic zones. As result, even though the increase in pier ductility demand associated with the increase in the vertical acceleration component was found to be relatively small, the number piers exhibiting significant structural damage increased.

Earlier ecological studies on the relation between H. pylori infection and stomach cancer have considered that the relation between these two variables, as estimated by the exposure coefficient, is constant. However, there is evidence to suggest that this relation changes geographically due to differences in strains of H. pylori. Since the prevalence of H. pylori varies with socio-economic status, the association between the latter and stomach cancer mortality may also vary geographically. This thesis studies stomach cancer by taking into account the geographical variability of the exposure coefficients. The study proposes the use of regression mixtures, clustering models and spatially varying regressions for the study of varying exposure coefficients. The effect of transformations of variables in these models appears to have been little considered. We provide new necessary conditions for invariance under transformations of variables for mixed effect models in general, and for the proposed models in particular. In addition, we show that varying exposure coefficients may induce a varying baseline risk. The regression mixtures and the clustering model are applied to a data set on stomach cancer incidence and H. pylori prevalence in 57 countries worldwide. We extend the clustering model to reflect any distance measure between the geographical units, including the Euclidean distance, in the formation of clusters. We also show that the clustering model performs better than the regression mixture model when the aim is to identify connected clusters and the observations present large variance. The results obtained with the clustering model supported the existence of three clusters where the interaction between the human and H. pylori populations have similar characteristics. Spatially varying regressions are applied to a data set of areal death counts of stomach cancer and spending power in 275 counties in continental Portugal. We provide an original strategy for implementing multivectorial intrinsic autoregressions as the distribution for the random effects. The results obtained with the application of this methodology were consistent with a varying exposure coefficient of spending power.

Earthquake is undoubtedly one of the greatest natural disasters that can induce serious structural damage and huge losses of properties and lives. The resulting destructive consequences not only have made structural seismic analysis and design much more important but have impelled the necessity of more realistic representation of ground motions, such as inclusion of ground motion spatial variations in earthquake modelling and seismic analysis and design of structures. Recorded seismic ground motions exhibit spatial variations in their amplitudes and phases, and the spatial variabilities have an important effect on the responses of structures extended in space, such as long span bridges. Because of the multi-parametric nature and the complexity of the problems, the development of specific design provisions on spatial variabilities of ground motions in modern seismic codes has been impeded. Eurocode 8 is currently the only seismic standard worldwide that gives a set of detailed guidelines to explicitly tackle spatial variabilities of ground motions in bridge design, providing both a simplified design scheme and an analytical approach. However, there is gap between the code-specified provisions in Eurocode 8 and the realistic representation of spatially varying ground motions (SVGM) and the corresponding stochastic vibration analysis (SVA) approaches. This study is devoted to bridge this gap on modelling of SVGM and development of SVA approaches for structures extended in space under SVGM. A complete and realistic SVGM representation approach is developed by accounting for the incoherence effect, wave-passage effect, site-response effect, ground motion nonstationarity, tridirectionality, and spectra-compatibility. This effort brings together various aspects regarding rational seismic scenarios determination, comprehensive methods of accounting for varying site effects, conditional modelling of SVGM nonstationarity, and code-specified ground motion spectra-compatibility. A comprehensive, systematic, and efficient SVA methodology is derived for long span structures under tridirectional nonstationary SVGM. An absolute-response-oriented scheme of pseudo-excitation method and an improved high precision direct integration method are proposed to reduce the enormous computational effort of conventional nonstationary SVA. A scheme accounting for tridirectional varying site-response effect is incorporated in the nonstationary SVA scheme systematically. The proposed highly efficient and accurate SVA approach is implemented and verified in a general finite element analysis platform to make it readily applicable in SVA of complex structures. Based on the proposed SVA approach, parametric studies of two practical long span bridges under SVGM are conducted. To account for spatial randomness and variability of soil properties in soil-structure interaction analysis of structures under SVGM, a meshfree-Galerkin approach is proposed within the Karhunen-Loeve expansion scheme for representation of spatial soil properties modelled as a random field. The meshfree shape functions are proposed as a set of basis functions in the Galerkin scheme to solve integral equation of Karhunen-Loeve expansion, with a proposed optimization scheme in treating the compatibility between the target and analytical covariance models. The accuracy and validity of the meshfree-Galerkin scheme are assessed and demonstrated by representation of covariance models for various homogeneous and nonhomogeneous spatial fields. The developed modelling approaches of SVGM and the derived analytical SVA approaches can be applied to provide more refined solutions for quantitatively assessing code-specified design provisions and developing new design provisions. The proposed meshfree-Galerkin approach can be used to account for spatial randomness and variability of soil properties in soil-structure interaction analysis.

Gas chromatography (GC) is an analytical chemistry tool used to determine the chemical composition of a gas sample by separating sample analytes as they travel through a GC column. Recent efforts have been made to understand and control gas chromatography separations with a negative thermal gradient on the column. The present work presents results from thermal gradient GC separations on two GC columns in different configurations (serpentine and radial) in a stainless-steel plate. Methods to fabricate the GC systems capable of isothermal, temperature programmed and thermal gradient separations are presented. Isothermal experimental data from the serpentine column were used to fit retention and dispersion parameters in a transport model that simulates GC separation for hydrocarbons C12-C14. Transport model simulated retention times and peak widths matched experimental values well for isothermal, temperature programmed and thermal gradient separations. The validated transport model was used to study the effect of static (not varying temporally) thermal gradients on GC separations with varying injection widths, injection band shapes and stationary phase thickness. Resolution results from different heating conditions were considered comparable if retention times for each analyte were within 5%. An optimal, static thermal gradient is shown to reduce analyte band spreading from axially-varying velocity gradients with resolution improvements over isothermal separations of up to 8% for analytes with similar retention factors. Static thermal gradients have a larger effect on fronting peak shape than tailing peak shape. Stationary phase distribution acts similar to a velocity gradient and can be corrected by a thermal gradient. Another transport model was created from isothermal experimental data on a commercial column for hydrocarbons C12-C20. An optimal, static thermal gradient does not improve resolution for all analyte pairs. An optimal, dynamic (varying tempo-rally) thermal gradient is created by uniformly increasing the temperature on an optimal, static thermal gradient. Improvements in resolution of up to 20% are achievable over temperature programmed GC separation. A dynamic thermal gradient can also correct for a poor sample injection by creating a temperature trap at the beginning of the column.