Wind-vector estimation for RADARSAT-1 SAR images: Validation of wind-direction estimates based upon geometry diversity

In this letter, a new wind-vector algorithm is presented that uses radar backscatter sigma(0) measurements at two adjacent subscenes of RADARSAT-1 synthetic aperture radar (SAR) images, with each subscene having slightly different geometry. Resultant wind vectors are validated using in situ buoy measurements and compared with wind vectors determined from a hybrid wind-retrieval model using wind directions determined by spectral analysis of wind-induced image streaks and observed by colocated QuikSCAT measurements. The hybrid wind-retrieval model consists of CMOD-IFR2 [applicable to C-band vertical-vertical (W) polarization] and a C-band copolarization ratio according to Kirchhoff scattering. The new algorithm displays improved skill in wind-vector estimation for RADARSAT-1 SAR data when compared to conventional wind-retrieval methodology. In addition, unlike conventional methods, the present method is applicable to RADARSAT-1 images both with and without visible streaks. However, this method requires ancillary data such as buoy measurements to resolve the ambiguity in retrieved wind direction.

Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications

We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call "relative affine structure". Via a number of corollaries of our main results we show that our framework unifies previous work --- including Euclidean, projective and affine --- in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.

The Three-Dimensional Interpretation of a Class of Simple Line-Drawings

We provide a theory of the three-dimensional interpretation of a class of line-drawings called p-images, which are interpreted by the human vision system as parallelepipeds ("boxes"). Despite their simplicity, p-images raise a number of interesting vision questions: *Why are p-images seen as three-dimensional objects? Why not just as flatimages? *What are the dimensions and pose of the perceived objects? *Why are some p-images interpreted as rectangular boxes, while others are seen as skewed, even though there is no obvious distinction between the images? *When p-images are rotated in three dimensions, why are the image-sequences perceived as distorting objects---even though structure-from-motion would predict that rigid objects would be seen? *Why are some three-dimensional parallelepipeds seen as radically different when viewed from different viewpoints? We show that these and related questions can be answered with the help of a single mathematical result and an associated perceptual principle. An interesting special case arises when there are right angles in the p-image. This case represents a singularity in the equations and is mystifying from the vision point of view. It would seem that (at least in this case) the vision system does not follow the ordinary rules of geometry but operates in accordance with other (and as yet unknown) principles.

Automatically Recovering Geometry and Texture from Large Sets of Calibrated Images

Three-dimensional models which contain both geometry and texture have numerous applications such as urban planning, physical simulation, and virtual environments. A major focus of computer vision (and recently graphics) research is the automatic recovery of three-dimensional models from two-dimensional images. After many years of research this goal is yet to be achieved. Most practical modeling systems require substantial human input and unlike automatic systems are not scalable. This thesis presents a novel method for automatically recovering dense surface patches using large sets (1000's) of calibrated images taken from arbitrary positions within the scene. Physical instruments, such as Global Positioning System (GPS), inertial sensors, and inclinometers, are used to estimate the position and orientation of each image. Essentially, the problem is to find corresponding points in each of the images. Once a correspondence has been established, calculating its three-dimensional position is simply a matter of geometry. Long baseline images improve the accuracy. Short baseline images and the large number of images greatly simplifies the correspondence problem. The initial stage of the algorithm is completely local and scales linearly with the number of images. Subsequent stages are global in nature, exploit geometric constraints, and scale quadratically with the complexity of the underlying scene. We describe techniques for: 1) detecting and localizing surface patches; 2) refining camera calibration estimates and rejecting false positive surfels; and 3) grouping surface patches into surfaces and growing the surface along a two-dimensional manifold. We also discuss a method for producing high quality, textured three-dimensional models from these surfaces. Some of the most important characteristics of this approach are that it: 1) uses and refines noisy calibration estimates; 2) compensates for large variations in illumination; 3) tolerates significant soft occlusion (e.g. tree branches); and 4) associates, at a fundamental level, an estimated normal (i.e. no frontal-planar assumption) and texture with each surface patch.

Discrimination between low atomic number materials from their characteristic scattering of X-ray radiation

C.R. Bull and R. Zwiggelaar, 'Discrimination between low atomic number materials from their characteristic scattering of X-ray radiation', Journal of Agricultural Engineering Research 68 (2), 77-87 (1997)

The Geometry of Frequency Squares

Mavron, Vassili; Jungnickel, D.; McDonough, T.P., (2001) 'The Geometry of Frequency Squares', Journal of Combinatorial Theory, Series A 96, pp.376-387 RAE2008

Genome-wide association with bone mass and geometry in the Framingham Heart Study

BACKGROUND:Osteoporosis is characterized by low bone mass and compromised bone structure, heritable traits that contribute to fracture risk. There have been no genome-wide association and linkage studies for these traits using high-density genotyping platforms.METHODS:We used the Affymetrix 100K SNP GeneChip marker set in the Framingham Heart Study (FHS) to examine genetic associations with ten primary quantitative traits: bone mineral density (BMD), calcaneal ultrasound, and geometric indices of the hip. To test associations with multivariable-adjusted residual trait values, we used additive generalized estimating equation (GEE) and family-based association tests (FBAT) models within each sex as well as sexes combined. We evaluated 70,987 autosomal SNPs with genotypic call rates [greater than or equal to]80%, HWE p [greater than or equal to] 0.001, and MAF [greater than or equal to]10% in up to 1141 phenotyped individuals (495 men and 646 women, mean age 62.5 yrs). Variance component linkage analysis was performed using 11,200 markers.RESULTS:Heritability estimates for all bone phenotypes were 30-66%. LOD scores [greater than or equal to]3.0 were found on chromosomes 15 (1.5 LOD confidence interval: 51,336,679-58,934,236 bp) and 22 (35,890,398-48,603,847 bp) for femoral shaft section modulus. The ten primary phenotypes had 12 associations with 100K SNPs in GEE models at p < 0.000001 and 2 associations in FBAT models at p < 0.000001. The 25 most significant p-values for GEE and FBAT were all less than 3.5 x 10-6 and 2.5 x 10-5, respectively. Of the 40 top SNPs with the greatest numbers of significantly associated BMD traits (including femoral neck, trochanter, and lumbar spine), one half to two-thirds were in or near genes that have not previously been studied for osteoporosis. Notably, pleiotropic associations between BMD and bone geometric traits were uncommon. Evidence for association (FBAT or GEE p < 0.05) was observed for several SNPs in candidate genes for osteoporosis, such as rs1801133 in MTHFR; rs1884052 and rs3778099 in ESR1; rs4988300 in LRP5; rs2189480 in VDR; rs2075555 in COLIA1; rs10519297 and rs2008691 in CYP19, as well as SNPs in PPARG (rs10510418 and rs2938392) and ANKH (rs2454873 and rs379016). All GEE, FBAT and linkage results are provided as an open-access results resource at http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?id=phs000007.CONCLUSION:The FHS 100K SNP project offers an unbiased genome-wide strategy to identify new candidate loci and to replicate previously suggested candidate genes for osteoporosis.

Searching the Sky with CONFIGR-STARS

SyNAPSE program of the Defense Advanced Projects Research Agency (HRL Laboratories LLC, subcontract #801881-BS under DARPA prime contract HR0011-09-C-0001); CELEST, a National Science Foundation Science of Learning Center (SBE-0354378)

On-board Robotic Multi-pinhole SPECT System for Region-of-interest (ROI) Imaging

On-board image guidance, such as cone-beam CT (CBCT) and kV/MV 2D imaging, is essential in many radiation therapy procedures, such as intensity modulated radiotherapy (IMRT) and stereotactic body radiation therapy (SBRT). These imaging techniques provide predominantly anatomical information for treatment planning and target localization. Recently, studies have shown that treatment planning based on functional and molecular information about the tumor and surrounding tissue could potentially improve the effectiveness of radiation therapy. However, current on-board imaging systems are limited in their functional and molecular imaging capability. Single Photon Emission Computed Tomography (SPECT) is a candidate to achieve on-board functional and molecular imaging. Traditional SPECT systems typically take 20 minutes or more for a scan, which is too long for on-board imaging. A robotic multi-pinhole SPECT system was proposed in this dissertation to provide shorter imaging time by using a robotic arm to maneuver the multi-pinhole SPECT system around the patient in position for radiation therapy.

A 49-pinhole collimated SPECT detector and its shielding were designed and simulated in this work using the computer-aided design (CAD) software. The trajectories of robotic arm about the patient, treatment table and gantry in the radiation therapy room and several detector assemblies such as parallel holes, single pinhole and 49 pinholes collimated detector were investigated. The rail mounted system was designed to enable a full range of detector positions and orientations to various crucial treatment sites including head and torso, while avoiding collision with linear accelerator (LINAC), patient table and patient.

An alignment method was developed in this work to calibrate the on-board robotic SPECT to the LINAC coordinate frame and to the coordinate frames of other on-board imaging systems such as CBCT. This alignment method utilizes line sources and one pinhole projection of these line sources. The model consists of multiple alignment parameters which maps line sources in 3-dimensional (3D) space to their 2-dimensional (2D) projections on the SPECT detector. Computer-simulation studies and experimental evaluations were performed as a function of number of line sources, Radon transform accuracy, finite line-source width, intrinsic camera resolution, Poisson noise and acquisition geometry. In computer-simulation studies, when there was no error in determining angles (α) and offsets (ρ) of the measured projections, the six alignment parameters (3 translational and 3 rotational) were estimated perfectly using three line sources. When angles (α) and offsets (ρ) were provided by Radon transform, the estimation accuracy was reduced. The estimation error was associated with rounding errors of Radon transform, finite line-source width, Poisson noise, number of line sources, intrinsic camera resolution and detector acquisition geometry. The estimation accuracy was significantly improved by using 4 line sources rather than 3 and also by using thinner line-source projections (obtained by better intrinsic detector resolution). With 5 line sources, median errors were 0.2 mm for the detector translations, 0.7 mm for the detector radius of rotation, and less than 0.5° for detector rotation, tilt and twist. In experimental evaluations, average errors relative to a different, independent registration technique were about 1.8 mm for detector translations, 1.1 mm for the detector radius of rotation (ROR), 0.5° and 0.4° for detector rotation and tilt, respectively, and 1.2° for detector twist.

Simulation studies were performed to investigate the improvement of imaging sensitivity and accuracy of hot sphere localization for breast imaging of patients in prone position. A 3D XCAT phantom was simulated in the prone position with nine hot spheres of 10 mm diameter added in the left breast. A no-treatment-table case and two commercial prone breast boards, 7 and 24 cm thick, were simulated. Different pinhole focal lengths were assessed for root-mean-square-error (RMSE). The pinhole focal lengths resulting in the lowest RMSE values were 12 cm, 18 cm and 21 cm for no table, thin board, and thick board, respectively. In both no table and thin board cases, all 9 hot spheres were easily visualized above background with 4-minute scans utilizing the 49-pinhole SPECT system while seven of nine hot spheres were visible with the thick board. In comparison with parallel-hole system, our 49-pinhole system shows reduction in noise and bias under these simulation cases. These results correspond to smaller radii of rotation for no-table case and thinner prone board. Similarly, localization accuracy with the 49-pinhole system was significantly better than with the parallel-hole system for both the thin and thick prone boards. Median localization errors for the 49-pinhole system with the thin board were less than 3 mm for 5 of 9 hot spheres, and less than 6 mm for the other 4 hot spheres. Median localization errors of 49-pinhole system with the thick board were less than 4 mm for 5 of 9 hot spheres, and less than 8 mm for the other 4 hot spheres.

Besides prone breast imaging, respiratory-gated region-of-interest (ROI) imaging of lung tumor was also investigated. A simulation study was conducted on the potential of multi-pinhole, region-of-interest (ROI) SPECT to alleviate noise effects associated with respiratory-gated SPECT imaging of the thorax. Two 4D XCAT digital phantoms were constructed, with either a 10 mm or 20 mm diameter tumor added in the right lung. The maximum diaphragm motion was 2 cm (for 10 mm tumor) or 4 cm (for 20 mm tumor) in superior-inferior direction and 1.2 cm in anterior-posterior direction. Projections were simulated with a 4-minute acquisition time (40 seconds per each of 6 gates) using either the ROI SPECT system (49-pinhole) or reference single and dual conventional broad cross-section, parallel-hole collimated SPECT. The SPECT images were reconstructed using OSEM with up to 6 iterations. Images were evaluated as a function of gate by profiles, noise versus bias curves, and a numerical observer performing a forced-choice localization task. Even for the 20 mm tumor, the 49-pinhole imaging ROI was found sufficient to encompass fully usual clinical ranges of diaphragm motion. Averaged over the 6 gates, noise at iteration 6 of 49-pinhole ROI imaging (10.9 µCi/ml) was approximately comparable to noise at iteration 2 of the two dual and single parallel-hole, broad cross-section systems (12.4 µCi/ml and 13.8 µCi/ml, respectively). Corresponding biases were much lower for the 49-pinhole ROI system (3.8 µCi/ml), versus 6.2 µCi/ml and 6.5 µCi/ml for the dual and single parallel-hole systems, respectively. Median localization errors averaged over 6 gates, for the 10 mm and 20 mm tumors respectively, were 1.6 mm and 0.5 mm using the ROI imaging system and 6.6 mm and 2.3 mm using the dual parallel-hole, broad cross-section system. The results demonstrate substantially improved imaging via ROI methods. One important application may be gated imaging of patients in position for radiation therapy.

A robotic SPECT imaging system was constructed utilizing a gamma camera detector (Digirad 2020tc) and a robot (KUKA KR150-L110 robot). An imaging study was performed with a phantom (PET CT PhantomTM), which includes 5 spheres of 10, 13, 17, 22 and 28 mm in diameter. The phantom was placed on a flat-top couch. SPECT projections were acquired with a parallel-hole collimator and a single-pinhole collimator both without background in the phantom, and with background at 1/10th the sphere activity concentration. The imaging trajectories of parallel-hole and pinhole collimated detectors spanned 180 degrees and 228 degrees respectively. The pinhole detector viewed a 14.7 cm-diameter common volume which encompassed the 28 mm and 22 mm spheres. The common volume for parallel-hole was a 20.8-cm-diameter cylinder which encompassed all five spheres in the phantom. The maneuverability of the robotic system was tested by navigating the detector to trace the flat-top table while avoiding collision with the table and maintaining the closest possible proximity to the common volume. For image reconstruction, detector trajectories were described by radius-of-rotation and detector rotation angle θ. These reconstruction parameters were obtained from the robot base and tool coordinates. The robotic SPECT system was able to maneuver the parallel-hole and pinhole collimated SPECT detectors in close proximity to the phantom, minimizing impact of the flat-top couch on detector to center-of-rotation (COR) distance. In no background case, all five spheres were visible in the reconstructed parallel-hole and pinhole images. In with background case, three spheres of 17, 22 and 28 mm diameter were readily observed with the parallel-hole imaging, and the targeted spheres (22 and 28 mm diameter) were readily observed in the pinhole ROI imaging.

In conclusion, the proposed on-board robotic SPECT can be aligned to LINAC/CBCT with a single pinhole projection of the line-source phantom. Alignment parameters can be estimated using one pinhole projection of line sources. This alignment method may be important for multi-pinhole SPECT, where relative pinhole alignment may vary during rotation. For single pinhole and multi-pinhole SPECT imaging onboard radiation therapy machines, the method could provide alignment of SPECT coordinates with those of CBCT and the LINAC. In simulation studies of prone breast imaging and respiratory-gated lung imaging, the 49-pinhole detector showed better tumor contrast recovery and localization in a 4-minute scan compared to parallel-hole detector. On-board SPECT could be achieved by a robot maneuvering a SPECT detector about patients in position for radiation therapy on a flat-top couch. The robot inherent coordinate frames could be an effective means to estimate detector pose for use in SPECT image reconstruction.

Monte Carlo Analysis and Physics Characterization of a Novel Nanoparticle Detector for Medical and Micro-dosimetry Applications

The outcomes for both (i) radiation therapy and (ii) preclinical small animal radio- biology studies are dependent on the delivery of a known quantity of radiation to a specific and intentional location. Adverse effects can result from these procedures if the dose to the target is too high or low, and can also result from an incorrect spatial distribution in which nearby normal healthy tissue can be undesirably damaged by poor radiation delivery techniques. Thus, in mice and humans alike, the spatial dose distributions from radiation sources should be well characterized in terms of the absolute dose quantity, and with pin-point accuracy. When dealing with the steep spatial dose gradients consequential to either (i) high dose rate (HDR) brachytherapy or (ii) within the small organs and tissue inhomogeneities of mice, obtaining accurate and highly precise dose results can be very challenging, considering commercially available radiation detection tools, such as ion chambers, are often too large for in-vivo use.

In this dissertation two tools are developed and applied for both clinical and preclinical radiation measurement. The first tool is a novel radiation detector for acquiring physical measurements, fabricated from an inorganic nano-crystalline scintillator that has been fixed on an optical fiber terminus. This dosimeter allows for the measurement of point doses to sub-millimeter resolution, and has the ability to be placed in-vivo in humans and small animals. Real-time data is displayed to the user to provide instant quality assurance and dose-rate information. The second tool utilizes an open source Monte Carlo particle transport code, and was applied for small animal dosimetry studies to calculate organ doses and recommend new techniques of dose prescription in mice, as well as to characterize dose to the murine bone marrow compartment with micron-scale resolution.

Hardware design changes were implemented to reduce the overall fiber diameter to <0.9 mm for the nano-crystalline scintillator based fiber optic detector (NanoFOD) system. Lower limits of device sensitivity were found to be approximately 0.05 cGy/s. Herein, this detector was demonstrated to perform quality assurance of clinical 192Ir HDR brachytherapy procedures, providing comparable dose measurements as thermo-luminescent dosimeters and accuracy within 20% of the treatment planning software (TPS) for 27 treatments conducted, with an inter-quartile range ratio to the TPS dose value of (1.02-0.94=0.08). After removing contaminant signals (Cerenkov and diode background), calibration of the detector enabled accurate dose measurements for vaginal applicator brachytherapy procedures. For 192Ir use, energy response changed by a factor of 2.25 over the SDD values of 3 to 9 cm; however a cap made of 0.2 mm thickness silver reduced energy dependence to a factor of 1.25 over the same SDD range, but had the consequence of reducing overall sensitivity by 33%.

For preclinical measurements, dose accuracy of the NanoFOD was within 1.3% of MOSFET measured dose values in a cylindrical mouse phantom at 225 kV for x-ray irradiation at angles of 0, 90, 180, and 270˝. The NanoFOD exhibited small changes in angular sensitivity, with a coefficient of variation (COV) of 3.6% at 120 kV and 1% at 225 kV. When the NanoFOD was placed alongside a MOSFET in the liver of a sacrificed mouse and treatment was delivered at 225 kV with 0.3 mm Cu filter, the dose difference was only 1.09% with use of the 4x4 cm collimator, and -0.03% with no collimation. Additionally, the NanoFOD utilized a scintillator of 11 µm thickness to measure small x-ray fields for microbeam radiation therapy (MRT) applications, and achieved 2.7% dose accuracy of the microbeam peak in comparison to radiochromic film. Modest differences between the full-width at half maximum measured lateral dimension of the MRT system were observed between the NanoFOD (420 µm) and radiochromic film (320 µm), but these differences have been explained mostly as an artifact due to the geometry used and volumetric effects in the scintillator material. Characterization of the energy dependence for the yttrium-oxide based scintillator material was performed in the range of 40-320 kV (2 mm Al filtration), and the maximum device sensitivity was achieved at 100 kV. Tissue maximum ratio data measurements were carried out on a small animal x-ray irradiator system at 320 kV and demonstrated an average difference of 0.9% as compared to a MOSFET dosimeter in the range of 2.5 to 33 cm depth in tissue equivalent plastic blocks. Irradiation of the NanoFOD fiber and scintillator material on a 137Cs gamma irradiator to 1600 Gy did not produce any measurable change in light output, suggesting that the NanoFOD system may be re-used without the need for replacement or recalibration over its lifetime.

For small animal irradiator systems, researchers can deliver a given dose to a target organ by controlling exposure time. Currently, researchers calculate this exposure time by dividing the total dose that they wish to deliver by a single provided dose rate value. This method is independent of the target organ. Studies conducted here used Monte Carlo particle transport codes to justify a new method of dose prescription in mice, that considers organ specific doses. Monte Carlo simulations were performed in the Geant4 Application for Tomographic Emission (GATE) toolkit using a MOBY mouse whole-body phantom. The non-homogeneous phantom was comprised of 256x256x800 voxels of size 0.145x0.145x0.145 mm3. Differences of up to 20-30% in dose to soft-tissue target organs was demonstrated, and methods for alleviating these errors were suggested during whole body radiation of mice by utilizing organ specific and x-ray tube filter specific dose rates for all irradiations.

Monte Carlo analysis was used on 1 µm resolution CT images of a mouse femur and a mouse vertebra to calculate the dose gradients within the bone marrow (BM) compartment of mice based on different radiation beam qualities relevant to x-ray and isotope type irradiators. Results and findings indicated that soft x-ray beams (160 kV at 0.62 mm Cu HVL and 320 kV at 1 mm Cu HVL) lead to substantially higher dose to BM within close proximity to mineral bone (within about 60 µm) as compared to hard x-ray beams (320 kV at 4 mm Cu HVL) and isotope based gamma irradiators (137Cs). The average dose increases to the BM in the vertebra for these four aforementioned radiation beam qualities were found to be 31%, 17%, 8%, and 1%, respectively. Both in-vitro and in-vivo experimental studies confirmed these simulation results, demonstrating that the 320 kV, 1 mm Cu HVL beam caused statistically significant increased killing to the BM cells at 6 Gy dose levels in comparison to both the 320 kV, 4 mm Cu HVL and the 662 keV, 137Cs beams.

Let´s teach geometry

In this work we present an activity for High School students in which various mathematical concepts of plane and spatial geometry are involved. The final objective of the proposed tasks is constructing a particular polyhedron, the cube, by using a modality of origami called modular origami.

Conceptualización de área del rectángulo con la mediación del programa Cabri Geometry

En esta charla se presentará el trabajo realizado durante el año 2010 por el grupo Nuevas Tecnologías de EDUMAT-UIS coordinado por el Dr. Martín Eduardo Acosta Gempeler. El grupo viene realizando un trabajo de capacitación a profesores de varios colegios del área metropolitana de Bucaramanga en cuanto a la implementación de software de geometría dinámica en la enseñanza de diferentes conceptos geométricos en secundaria.

Ethnomathematical research and drama in education techniques: developing a dialogue in a geometry class of 10th grade students

Ethnomathematical research, together with digital technologies (WebQuest) and Drama-in- Education (DiE) techniques, can create a fruitful learning environment in a mathematics classroom—a hybrid/third space—enabling increased student participation and higher levels of cognitive engagement. This article examines how ethnomathematical ideas processed within the experiential environment established by the Drama-in-Education techniques challenged students‘ conceptions of the nature of mathematics, the ways in which students engaged with mathematics learning using mind and body, and the ̳dialogue‘ that was developed between the Discourse situated in a particular practice and the classroom Discourse of mathematics teaching. The analysis focuses on an interdisciplinary project based on an ethnomathematical study of a designing tradition carried out by the researchers themselves, involving a search for informal mathematics and the connections with context and culture; 10th grade students in a public school in Athens were introduced to the mathematics content via an original WebQuest based on this previous ethnomathematical study; Geometry content was further introduced and mediated using the Drama-in-Education (DiE) techniques. Students contributed in an unfolding dialogue between formal and informal knowledge, renegotiating both mathematical concepts and their perception of mathematics as a discipline.

Material properties, geometry and their effect on the fatigue life of two flip-chip models

This paper describes how modeling technology has been used in providing fatigue life time data of two flip-chip models. Full-scale three-dimensional modeling of flip-chips under cyclic thermal loading has been combined with solder joint stand-off height prediction to analyze the stress and strain conditions in the two models. The Coffin-Manson empirical relationship is employed to predict the fatigue life times of the solder interconnects. In order to help designers in selecting the underfill material and the printed circuit board, the Young's modulus and the coefficient of thermal expansion of the underfill, as well as the thickness of the printed circuit boards are treated as variable parameters. Fatigue life times are therefore calculated over a range of these material and geometry parameters. In this paper we will also describe how the use of micro-via technology may affect fatigue life

Low temperature crystal structures of two rhodanine derivatives, 3-amino rhodanine and 3-methyl rhodanine: geometry of the rhodanine ring

Rhodanines (2-thio-4-oxothiazolidines) are synthetic small molecular weight organic molecules with diverse applications in biochemistry, medicinal chemistry, photochemistry, coordination chemistry and industry. The X-ray crystal structure determination of two rhodanine derivatives, namely (I), 3-aminorhodanine [3-amino-2-thio-4-oxothiazolidine], C3H4N2OS2, and (II) 3-methylrhodanine [3-methyl-2-thio-4-oxothiazolidine], C4H5NOS2, have been conducted at 100 K. I crystallizes in the monoclinic space group P2(1)/n with unit cell parameters a = 9.662(2), b = 9.234(2), c = 13.384(2) angstrom, beta = 105.425(3)degrees, V = 1151.1(3) angstrom(3), Z = 8 (2 independent molecules per asymmetric unit), density (calculated) = 1.710 mg/m(3), absorption coefficient = 0.815 mm(-1). II crystallizes in the orthorhombic space group Iba2 with unit cell a = 20.117(4), b = 23.449(5), c = 7.852(2) angstrom, V = 3703.9(12) angstrom(3), Z = 24 (three independent molecules per asymmetric unit), density (calculated) = 1.584 mg/m(3), absorption coefficient 0.755 mm(-1). For I in the final refinement cycle the data/restraints/parameter ratios were 2639/0/161, goodness-of-fit on F-2 = 0.934, final R indices [I > 2sigma(I)] were R1 = 0.0299, wR2 = 0.0545 and R indices (all data) R1 = 0.0399, wR2 = 0.0568. The largest difference peak and hole were 0.402 and -0.259 e angstrom(-3). For II in the final refinement cycle the data/restraints/parameter ratios were 3372/1/221, goodness-of-fit on F(2) = 0.950, final R indices [I > 2sigma(I)] were R1 = 0.0407, wR2 = 0.1048 and R indices (all data) R1 = 0.0450, wR2 = 0.1088. The absolute structure parameter = 0.19(9) and largest difference peak and hole 0.934 and -0.301 e angstrom(-3). Details of the geometry of the five molecules (two for I and three for II) and the crystal structures are fully discussed. Corresponding features of the molecular geometry are highly consistent and firmly establish the geometry of the rhodanine