Local Spatial Correlation Research Articles

A Physics-Assisted Convolutional Neural Network for Bathymetric Mapping Using ICESat-2 and Sentinel-2 Data

Machine learning methods for water depth estimation using remote sensing require accurate prior depth measurements. The successful operation of the ICESat-2 mission provides depth in shallow water directly; however, its spatial coverage is limited. Machine learning has been used to link optical remote sensing images and ICESat-2 data for bathymetric mapping. Compared with other machine learning models, convolutional neural network (CNN) models utilize the local spatial correlation between adjacent pixels and can thus reduce the effect of environmental noise. However, existing CNN and other machine learning models rely on data mining to build a general relationship between water depth and spectral information, and they ignore the known physical law. In this paper, we propose a physics-assisted convolutional neural network (PACNN) model. This model incorporates knowledge from radiative transfer theory into a normal CNN model by building a series of spectral feature input layers. In the PACNN model, the spectral information, which is directly related to water depth, is emphasized. Multitemporal ICESat-2 data and Sentinel-2 images were used to validate the model. In experiments with data from three study areas, the PACNN model outperformed the existing CNN model, achieving an accuracy of over 98%. The proposed method can effectively solve the underestimation in deeper water (20–30 m) and reduce the variance of estimates. The superiority of the PACNN model demonstrates how a machine learning model can be assisted by physics theory.

Reducing Local Correlations Among Causal Factor Classifications as a Strategy to Improve Landslide Susceptibility Mapping

A landslide susceptibility map (LSM) is the basis of hazard and risk assessment, guiding land planning and utilization, early warning of disaster, etc. Researchers are often overly keen on hybridizing state-of-the-art models or exploring new mathematical susceptibility models to improve the accuracy of the susceptibility map in terms of a receiver operator characteristic curve. Correlation analysis of the causal factors is a necessary routine process before susceptibility modeling to ensure that the overall correlation among all factors is low. However, this overall correlation analysis is insufficient to detect a high local correlation among the causal factor classes. The objective of this study is to answer three questions: 1) Is there a high correlation between causal factors in some parts locally? 2) Does it affect the accuracy of landslide susceptibility assessment? and 3) How can this influence be eliminated? To this aim, Wanzhou County was taken as the test site, where landslide susceptibility assessment based on 12 causal factors has been previously performed using the frequency ratio (FR) model and random forest (RF) model. In this work, we conducted a local spatial correlation analysis of the “altitude” and “rivers” factors and found a sizeable spatial overlap between altitude-class-1 and rivers-class-1. The “altitude” and “rivers” factors were reclassified, and then the FR model and RF model were used to reevaluate the susceptibility and analyze the accuracy loss caused by the local spatial correlation of the two factors. The results demonstrated that the accuracy of LSMs was markedly enhanced after reclassification of “altitude” and “rivers,” especially for the RF model–based LSM. This research shed new light on the local correlation of causal factors arising from a particular geomorphology and their impact on susceptibility.

Manifold Discriminative Learning Inspired Hybrid Beamforming for Millimeter-Wave Massive MIMO Systems

Millimeter-wave (mmWave) massive MIMO (multiple-input multiple-output) is a promising technology as it provides significant beamforming gains and interference reduction capabilities due to the large number of antennas. However, mmWave massive MIMO is computationally demanding, as the high antenna count results in high-dimensional matrix operations when conventional MIMO processing is applied. Hybrid precoding is an effective solution for the mmWave massive MIMO systems to significantly decrease the number of radio frequency (RF) chains without an apparent sum-rate loss. In this paper, we propose user clustering hybrid precoding to enable efficient and low-complexity operation in high-dimensional mmWave massive MIMO, where a large number of antennas are used in low-dimensional manifolds. By modeling each user set as a manifold, we formulate the problem as clustering-oriented multi-manifolds learning. The manifold discriminative learning seek to learn the embedding low-dimensional manifolds, where manifolds with different user cluster labels are better separated, and the local spatial correlation of the high-dimensional channels within each manifold is enhanced. Most of the high-dimensional channels are embedded in the low-dimensional manifolds by manifold discriminative learning, while retaining the potential spatial correlation of the high-dimensional channels. The nonlinearity of high-dimensional channel is transformed into global and local nonlinearity to achieve dimensionality reduction. Through proper user clustering, the hybrid precoding is investigated for the sum-rate maximization problem by manifold quasi conjugate gradient methods. The high signal to interference plus noise ratio (SINR) is achieved and the computational complexity is reduced by avoiding the conventional schemes to deal with high-dimensional channel parameters. Performance evaluations show that the proposed scheme can obtain near-optimal sum-rate and considerably higher spectral efficiency than some existing solutions

A geographic identification of sustainable development obstacles and countermeasures in drylands: A case study in Inner Mongolia, China

Drylands cover about 41% of the Earth’s land surface and are inhabited by more than two billion people, who rely on the diversified ecosystem services provided by drylands for their livelihoods. Achieving sustainable livelihoods (SLs) is a key component of achieving the sustainable development goals set by the agenda in 2030. Although it has aroused extensive interest, research on SLs in drylands at a regional scale is still limited. This paper aims to address this research gap by evaluating SLs through a geographic gradient of aridity in Inner Mongolia. A sustainable livelihood index (SLI) was developed using a wide range of indicators in a sustainable livelihood framework (SLF). The weight of the indicators was determined by the entropy weight method, and the characteristics of the spatial distribution of the SLI were analyzed. The results showed that the SLI varies greatly across aridity zones. In terms of livelihood assets, the SLI in the dry sub-humid zone was 15% higher than in the arid zones, while, surprisingly, semi-arid zones were found to have the most vulnerable livelihoods (rather than the arid zones). The reason for this is that land management and planning approaches are necessary in drylands. In further detail, Moran’s I index illustrated that the overall performance of the SLI of each league or city has a positive spatial correlation, while through local spatial correlation it was found that Hinggan and Chifeng are hot spot areas and Hohhot is a cold spot area. The lack of physical and social capital is an important obstacle for SLs. Based on the analysis of SLs in Inner Mongolia, the characteristics of the sustainable development of local residents were revealed. In this paper, we call for an integrated (i.e., focusing on natural and human capital) land management and planning approach for drylands to reflect the nature of the tightly coupled socio-ecological systems.

Spatiotemporal Difference Characteristics and Influencing Factors of Tourism Urbanization in China's Major Tourist Cities.

Tourism is crucial for promoting industrial development and is an important driver of China’s new type of urbanization. A tourism urbanization index system was constructed in three dimensions: the tourism industry, urbanization, and the ecological environment. The spatial–temporal differentiation characteristics and influencing factors of tourism urbanization in 35 major tourist cities in China from 2009 to 2018 were analyzed using the state space method, standard deviation ellipse, and spatial autocorrelation analysis. The results show the following. (1) Over time, the tourism industry index displays an upward trend, the urbanization index exhibits a more obvious upward trend, and the ecological environment index fluctuates strongly. Under the influence of all three factors, the tourism urbanization index shows a fluctuating rising trend. (2) Regarding the spatial distribution pattern, the development center of tourism urbanization shifts to the southeast, and the distribution direction is northeast-southwest. There is a significant agglomeration in global spatial autocorrelation. The local spatial correlation pattern is dominated by correlation characteristics and supplemented by different characteristics. (3) In terms of influencing factors, policy and regional development strategy, tourism resource endowment, economic development level, and traffic conditions are listed in descending order of influencing degree. Finally, we put forward some suggestions.

Evaluating Sustainable Development of Land Resources in the Yangtze River Economic Belt of China

The Yangtze River Economic Belt (YREB) is one of the most economically active regions in China, where an imbalance between the demand for land and the non-renewable is increasingly prominent. We present the patterns of land use in the YREB, then construct an evaluation index based on the Pressure-State-Response model. The TOPSIS model is used to evaluate sustainable land development in the YREB, and the spatial deductive characteristics of sustainable development levels are analyzed using three aspects: global spatial correlation, local spatial correlation, and regional difference. The results about the YREB show that: (1) The comprehensive sustainable land development score is average, indicating moderate sustainability with a fluctuating upward trend and good prospects. (2) The sustainable development levels of land have strong positive spatial correlation and agglomeration; the agglomeration characteristics follow a pattern similar to that of the status of economic development. (3) Sustainable development levels of land in the provinces and cities show great spatial differences.

Spatiotemporal characteristics and impact mechanism of high-quality development of cultural tourism in the Yangtze River Delta urban agglomeration.

The Yangtze River Delta urban agglomeration is the leading and demonstration area for the high-quality development of culture tourism (HDCT) in China. It is of great significance to study the spatiotemporal characteristics and impact mechanism of the HDCT for revealing the internal law of HDCT and promoting the collaborative innovation of culture tourism among cities. Based on the scientific construction of the evaluation system of HDCT, this paper made a quantitative analysis of 26 cities’ HDCT by using coupling coordination degree model, Lisa spatiotemporal transition and spatial Durbin model (SDM). The results show that: The overall level of 26 cities’ HDCT shows a fluctuating upward trend, and presents a "Z" pattern in space. More than 80% of the cities are at the medium and high level. Shanghai has obvious advantages in the primacy degree. There is a significant positive spatial autocorrelation among cities with high-quality of culture tourism development. The spatial clustering and proximity of the same kind are increasing, and the radiation effect is gradually obvious. The local spatial association patterns are mainly HH and LL agglomeration, and the characteristics of polarization are gradually prominent. The local spatial correlation structure of HDCT has strong stability, the transfer inertia between types is prominent, and the overall spatial evolution is lack of integration with obvious path dependence and lock-in effect. The spatiotemporal evolution of the HDCT is a complex process under the interaction of multiple factors, and there is a significant spatial spillover effect (0.256). The level of economic development, technological innovation, professional talent allocation are the three main factors. According to the dominant factor, it can be divided into economy stabilizing type, industry optimizing type, innovation driving type and traffic impacting type. These findings have implications for local governments and tourism management departments to achieve high-quality innovative development of cultural tourism.

Nutrient supply, cell spatial correlation and Gompertzian tumor growth.

Gompertzian tumor growth can be reproduced by mitosis, related to nutrient supply, with local spatial cell correlations. The global energy constraint alone does not reproduce in vivo data by the observed values of the nutrient expenditure for the cell activities. The depletion of the exponential growth, described by the Gompertz law, is obtained by mean field spatial correlations or by a small word network among cells. The well-known interdependence between the two parameters of the Gompertz growth naturally emerges and depends on the cell volume and on the tumor density.

Spatial Analysis of Industrial Green Development and Sustainable Cities in the Yellow River Basin

The Yellow River Basin (YRB) is an important ecological defense and economic zone in China and occupies a very important position in the economy and society of China. Premise condition of ecological protection and development of high quality in YRB is the greening of the industry. Based on the data of 35 cities in YRB in 2012, 2015, and 2018, this paper constructs an evaluation index system for the industrial green development (IGD) and explores spatial differentiation characteristics of the IGD by the exploratory spatial data analysis (ESDA) method. On this basis, this paper uses the geographical weighted regression (GWR) model to analyze the influencing factors. The results indicate the following: (1) in general, IGD in YRB shows an upward trend. (2) The Global Moran’s I index of IGD shows a small increase; the distribution of local spatial correlation is basically unchanged. (3) There are obvious regional differences in the influencing factors of IGD. The degree of influence of each factor on IGD is openness > industrial upgrading index > urbanization rate > science and technology expenditures > reduction rate of energy consumption.

Global to Local: Clip-LSTM-Based Object Detection From Remote Sensing Images

Object detection from remote sensing images (RSIs) is a basic topic in the area of aviation and satellite image processing, which has great effects on geological disaster detection, agricultural planning, and land utilization. However, it is always faced with several severe difficulties. For instance, the scale of the target spans over a very wide range, and the difference between the target size and the image size is huge, as some targets only account for a dozen pixels compared with the RSI of the megapixel level. In this work, an innovative object detection network (GLNet) is proposed for remote sensing imagery. Our approach integrates global context clues extracted by the multiscale perception (MSP) module and local spatial contextual correlations encoded by Clip long short-term memory (Clip-LSTM). These rich semantic features are further exploited to design a self-adapted anchor (SA) module to alleviate the scale variations in RSIs. Extensive experiments are executed on several public easily accessed benchmarks, including DOTA, NWPU VHR-10, and DIOR. Experimental results have demonstrated that our GLNet outperforms numerous latest methods.

Hyperspectral image sparse reconstruction model based on collaborative multidimensional correlation

In recent years, the sparse reconstruction of hyperspectral images based on compressed sensing theory has attracted great attention of the research community. How to better explore the sparsity priori that conforms to the statistical properties and structural properties of the original hyperspectral images is one of the key problems. To address this, in this paper, a novel hyperspectral image sparse reconstruction model based on collaborative multidimensional correlations is proposed. First, considering the high-dimensional and high-redundancy properties of hyperspectral data, the correlations of hyperspectral images are studied from multiple dimensions, except the “spectral correlation” between hyperspectral bands and the “local spatial correlation” within a single band, the “overall nonlocal correlation” is novel defined in band groups with highly correlated spectral features, where the “nonlocal correlation” of the key band in the band group can be used to guide the “nonlocal correlation” of other bands within the group. Then, the sparse measurement models are provided corresponding to the above correlations in different dimensions, at the same time, a band group collaborative sparse model which integrates the multidimensional correlations has been proposed. Finally, the proposed band group collaborative sparse model is used as the sparse constraint to construct the hyperspectral sparse reconstruction framework. Experimental results demonstrate that, the newly defined “global non-local correlation” can effectively enhance the detail information in the reconstruction process of hyperspectral images, which provides the possibility for better analyzing land-cover objects in the subsequent applications.

Spatiotemporal Heterogeneity and Driving Force Analysis of Innovation Output in the Yangtze River Economic Zone: The Perspective of Innovation Ecosystem

The Yangtze River Economic Zone (YREZ) is a major corridor of national science and innovation culture, an innovation-driven region that fosters new drivers of growth and leads transformation and development, and plays an important strategic support and exemplary leading role in the overall pattern of regional development. This paper analyzes the spatiotemporal differentiation characteristics of innovation output of 110 cities of YREZ from 2008 to 2018 by using Gini coefficient, coefficient of variation (CV), geographical weighted regression, and other methods. The factors affecting innovation output are selected from the perspective of innovation ecosystem. The results show the following. (1) Innovation output showed an increasing trend, and the high-value concentration cities in downstream areas gradually became prominent, the geographical concentration degree fluctuated and declined, and the distribution of innovation output gradually became balanced. (2) The global Moran’s I index of innovation output shows a fluctuation pattern of “M” shape and an overall upward trend. The analysis of local spatial correlation indicates that spatial distribution pattern of innovation output has not changed significantly. (3) There is obvious regional heterogeneity under different impacts of factors of innovation ecosystem on innovation output. Enterprises have the greatest impact, followed by financial resources and infrastructure environment.

Spatial pattern matching analysis of grain production and rainfall in the Ziya River Basin.

The exploratory spatial data analysis (ESDA) method, which includes global spatial autocorrelation and local spatial autocorrelation, is used to analyze the spatial pattern of the annual grain production and annual grain production increment in the Ziya River Basin from 2007 to 2017. Then, the spatial mismatch index is used to analyze the spatial mismatch relationship between the annual grain output and annual precipitation in the Ziya River Basin in 2015. The results showed that (1) the spatial pattern of the annual grain production in the Ziya River Basin is stable, with Low-Low clusters and High-High clusters concentrated on the left and right sides of the Ziya River Basin, respectively. The overall difference in the annual grain production of each district and county increased gradually from 2013 to 2017. (2) The local spatial correlation structure of the annual grain production of adjacent districts and counties in the Ziya River Basin had strong stability, and its space-time transition had a certain path dependence or spatial-locking characteristics. The reason why the High-High clusters are concentrated on the right side of the Ziya River is that there are large cultivated areas, such as the Shijin irrigation district, on the right side of the Ziya River Basin. (3) A spatial change rule "the proportion of grain production is low and the proportion of rainfall is high" changed to "the proportion of grain production and rainfall is balanced" and then to "the proportion of grain production is high and the proportion of rainfall is low" in the Ziya River Basin in 2015. The Shijin irrigation district is mainly located in the area where the spatial mismatch between the annual grain output and the average annual rainfall in the Ziya River Basin in 2015 is assessed as grade V, which indicates that the spatial mismatch between the annual grain output and the annual average rainfall is serious. In summary, grain production in the Shijin irrigation district has been increasing annually, while the supply of water for irrigation has not increased as much. There is a serious deficit between the irrigation water supply and the water demand for grain production in the Shijin irrigation district. Therefore, it is necessary to plan for the development and utilization of surface water and groundwater resources and to adjust the planting structure in the Shijin irrigation district for the purpose of saving water.

Multiscale Fusion Signal Extraction for Spaceborne Photon-Counting Laser Altimeter in Complex and Low Signal-to-Noise Ratio Scenarios

Extracting signal photons from noisy raw data is one of the critical processes for the new generation of spaceborne photon-counting laser altimeter. Affected by vast noise photon-counting events, the extraction of weak signal events still faces challenges in complex scenarios with low signal-to-noise ratio (SNR). Aiming to improve the extraction ability of signal photon events in these scenarios, a multiscale fusion signal extraction method was proposed, characterized by combining global spatial correlation constraint with optimized local spatial correlation constraint. The local constraint is implemented based on a density-based spatial clustering of applications with noise (DBSCAN) clustering method with adaptive parameter estimation, which is used to extract possible signal photons. A subsequent global constraint based on the spatial correlation of the terrain profiles is designed to remove the pseudo-signal photons clustered in the local constraints’ step. The global constraint is implemented based on a cost function, which is used to quantify different candidate paths. Our method was verified based on the actual Ice, Cloud, and land Elevation satellite-(ICESat2) data containing vegetation, mountains, and residential areas. The experimental results show that compared with the ICESat-2 extraction method, our method can significantly improve the precision and recall rate of signal photon events from the low SNR photon-counting data.

Brain tissue segmentation via non-local fuzzy c-means clustering combined with Markov random field.

The segmentation and extraction of brain tissue in magnetic resonance imaging (MRI) is a meaningful task because it provides a diagnosis and treatment basis for observing brain tissue development, delineating lesions, and planning surgery. However, MRI images are often damaged by factors such as noise, low contrast and intensity brightness, which seriously affect the accuracy of segmentation. A non-local fuzzy c-means clustering framework incorporating the Markov random field for brain tissue segmentation is proposed in this paper. Firstly, according to the statistical characteristics that MRF can effectively describe the local spatial correlation of an image, a new distance metric with neighborhood constraints is constructed by combining probabilistic statistical information. Secondly, a non-local regularization term is integrated into the objective function to utilize the global structure feature of the image, so that both the local and global information of the image can be taken into account. In addition, a linear model of inhomogeneous intensity is also built to estimate the bias field in brain MRI, which has achieved the goal of overcoming the intensity inhomogeneity. The proposed model fully considers the randomness and fuzziness in the image segmentation problem, and obtains the prior knowledge of the image reasonably, which reduces the influence of low contrast in the MRI images. Then the experimental results demonstrate that the proposed method can eliminate the noise and intensity inhomogeneity of the MRI image and effectively improve the image segmentation accuracy.

ANÁLISE DA CORRELAÇÃO ESPACIAL ENTRE OS USUÁRIOS DE SISTEMAS DE TRANSPORTE PÚBLICO E OS CASOS DE COVID-19: UM ESTUDO DE CASO PARA RECIFE (PE)

Using public transport systems has been reported to be a possible vector of virus transmission during epidemics. In this context, this article aims to analyze the spatial correlation between public transportation users and COVID-19 cases, using Recife (PE) as a case study. Using spatial analysis, the Moran I Global and Local index were calculated, and global and geographically weighted regression models were estimated for the months of March to June 2020, considering neighborhoods in Recife as a spatial unit of analysis. The results indicated global and local spatial correlation between the variables considered. Nevertheless, the number of public transport users is a variable that influenced the number of COVID-19 cases, especially in April, May, and June. Finally, the public transport system may not have been the only factor that contributed to the spread of COVID-19 in Recife, given the high number of neighborhoods without an indicator of local spatial association with statistical significance. As the public transport system contributes to the mobility of people who work in essential activities to the urban life, strategies that contribute to social distance within the vehicles of the system are necessary.

How competitive intransitivity and niche overlap affect spatial coexistence

Competitive intransitivity is mostly considered outside the main body of coexistence theories that rely primarily on the role of niche overlap and differentiation. How the interplay of competitive intransitivity and niche overlap jointly affects species coexistence has received little attention. Here, we consider a rock–paper–scissors competition system where interactions between species can represent the full spectra of transitive–intransitive continuum and niche overlap/differentiation under different levels of competition asymmetry. By comparing results from pair approximation that only considers interference competition between neighbouring cells in spatial lattices, with those under the mean‐field assumption, we show that 1) species coexistence under transitive competition is only possible at high niche differentiation; 2) in communities with partial or pure intransitive interactions, high levels of niche overlap are not necessary to beget species extinction; and 3) strong spatial clustering can widen the condition for intransitive loops to facilitate species coexistence. The two mechanisms, competitive intransitivity and niche differentiation, can support species persistence and coexistence, either separately or in combination. Finally, the contribution of intransitive loops to species coexistence can be enhanced by strong local spatial correlations, modulated and maximised by moderate competition asymmetry. Our study, therefore, provides a bridge to link intransitive competition to other generic ecological theories of species coexistence.

Systematically addressing the heterogeneity in the response of ecosystem services to agricultural modernization, industrialization and urbanization in the Qinghai-Tibetan Plateau from 2000 to 2018

Ecosystem services (ESS) change and its response to human activities is critical for enhancing ecosystem management and regional sustainability. This study constructs a theoretical framework of coupled ESS and three modernization (agricultural modernization (AM), industrialization and urbanization) systems, depicts the dynamic changes of ESS and three modernizations in the Qinghai-Tibetan Plateau (QTP) from 2000 to 2018, and further analyses the heterogeneity in the response of multiple ESS to different human activities using the Pearson correlation method and bivariate spatial autocorrelation model. (1) AM showed a significant negative impact on ESS and other single ESS except for food production and waste treatment services, and there was also an increasingly significant negative correlation between them in space, indicating that AM did not coordinate the local ecological protection and exerted the strongest destruction and an expanding scope of spatially negative effects on ESS. (2) Industrialization was negatively correlated with ESS as well as all of their associated single ESS to a different extent and was only significantly correlated with regulation services, while it interacted spatially with ESS, changing from presenting a weak negative correlation to presenting a weak positive correlation during 2000–2018, which reveals that industrialization had relatively less pressure on ESS and developed in a more eco-friendly mode. (3) Urbanization exerted a weak negative influence on ESS and most single ESS, whereas urbanization was positively correlated with waste treatment, landscape culture provision and biodiversity maintenance services in 2018, and it showed a significant positive impact of a growing tendency to effect ESS in space, which reveals that urbanization was conducive to reducing the overall disturbance of human activities on ESS. (4) The heterogeneity characteristics of the local spatial correlation patterns between the three modernization levels and ESS as well as their changes during 2000–2018 were investigated and presented obvious differences, and the low-high/high-low areas of the levels and changes for these two constructs should be given enough attention and take corresponding adaptive management measures. This study indicates that there are remarkable heterogeneous effects of different intensities and types of human activities on ESS, which should be understood systematically to coordinate the development pathways and patterns of three modernizations and the restoration and sustainable utilization of ecosystems.

Spatial and Temporal Evaluation of Ecological Footprint Intensity of Jiangsu Province at the County-Level Scale.

Due to the high ecological pressure that exists in the process of rapid economic development in Jiangsu Province, it is necessary to evaluate its ecological footprint intensity (EFI). This article focuses on ecological footprint intensity analysis at the county scale. We used county-level data to evaluate the spatial distributions and temporal trends of the ecological footprint intensity in Jiangsu’s counties from 1995 to 2015. The temporal trends of counties are divided into five types: linear declining type, N-shape type, inverted-N type, U-shape type and inverted-U shape type. It was discovered that the proportions of the carbon footprint intensity were maintained or increased in most counties. Exploratory spatial data analysis shows that there was a certain regularity of the EFI spatial distributions, i.e., a gradient decrease from north to south, and there was a decline in the spatial heterogeneity of EFI in Jiangsu’s counties over time. The global Moran’s index (Moran’s I) and local spatial association index (LISA) are used to analyze both the global and local spatial correlation of EFIs among counties of Jiangsu Province. The high-high and low-low agglomeration effects were the most common, and there were assimilation impacts of counties with strong agglomeration on adjacent units over time. The results implied the utility of differentiated EFI reduction control measures and promotion of low-low agglomeration and suppression of high-high agglomeration in EFI-related ecology policy.

An Image-Based Approach to Variational Path Synthesis of Linkages

Abstract This paper brings together computer vision, mechanism synthesis, and machine learning to create an image-based variational path synthesis approach for linkage mechanisms. An image-based approach is particularly amenable to mechanism synthesis when the input from mechanism designers is deliberately imprecise or inherently uncertain due to the nature of the problem. In addition, it also lends itself naturally to the creation of a unified approach to mechanism synthesis for different types of mechanisms, since for example, images are formed from a collection of pixels, which themselves could be generated from a four-bar or six-bar. Path synthesis problems have generally been solved for a set of precision points on the intended path such that the designed mechanism passes through those points. This approach usually leads to a small set of over-fitted solutions to particular precision points. However, most kinematic synthesis problems are concept generation problems, where a designer cares more about generating a large number of plausible solutions, which could reach given precision points only approximately. This paper models the input curve as a probability distribution of image pixels and employs a probabilistic generative model to capture the inherent uncertainty in the input. In addition, it gives feedback on the input quality and provides corrections for a more conducive input. The image representation allows for capturing local spatial correlations, which plays an important role in finding a variety of solutions with similar semantics as the input curve. This approach is also conducive to implementation for pressure-sensitive touch-based design interfaces, where the input is not a zero-thickness curve, but the sweep of a small patch on the finger.