Space Curve Representation Research Articles

Efficient bending and lifting patterns in snake locomotion

We optimize three-dimensional snake kinematics for locomotor efficiency. We assume a general space-curve representation of the snake backbone with small-to-moderate lifting off the ground and negligible body inertia. The cost of locomotion includes work against friction and internal viscous dissipation. When restricted to planar kinematics, our population-based optimization method finds the same types of optima as a previous Newton-based method. With lifting, a few types of optimal motions prevail. We have an s-shaped body with alternating lifting of the middle and ends at small-to-moderate transverse friction. With large transverse friction, curling and sliding motions are typical at small viscous dissipation, replaced by large-amplitude bending at large viscous dissipation. With small viscous dissipation, we find local optima that resemble sidewinding motions across friction coefficient space. They are always suboptimal to alternating lifting motions, with average input power 10–100% higher.

Frenet Frame-Based Generalized Space Curve Representation for Pose-Invariant Classification and Recognition of 3-D Face

The state-of-the-art methods in classifying 3-D representation of the face involve challenges in extracting representative features directly from the large volume of facial data. These methods mostly ignore the effect of pose distortions on 3-D facial data and entail heavy computations as well as manual processing steps. This work proposes a novel Frenet frame-based generalized space curve representation method for 3-D pose-invariant face and facial expression recognition and classification. Three-dimensional facial curves are extracted from either frontal or synthetically posed 3-D facial data to derive the proposed Frenet frame-based features. A mathematical framework shows the proof of pose invariance property for the features. The effectiveness of the proposed method is evaluated in two recognition tasks: 3-D face recognition (3D-FR) and 3-D facial expression recognition (3D-FER) using benchmarked 3-D datasets. The proposed framework yields 96% rank-I recognition rate for 3D-FR and 91.4% area under ROC curves for six basic 3D-FER. The performance evaluation also shows that the proposed mathematical framework yields pose-invariant 3D-FR and 3D-FER for a wide range of pose angles. This pose invariance property of the Frenet frame-based features alleviates the need for an expensive 3-D face registration in the preprocessing step, which, in turn, enables a faster processing time. The evaluation results further suggest that the proposed method is not only computationally efficient and versatile, but also offers competitive performance when compared with the existing state-of-the-art methods reported for either 3D-FR or 3D-FER.

A graphic representation of protein sequence and predicting the subcellular locations of prokaryotic proteins

Zp curve, a three-dimensional space curve representation of protein primary sequence based on the hydrophobicity and charged properties of amino acid residues along the primary sequence is suggested. Relying on the Zp parameters extracted from the three components of the Zp curve and the Bayes discriminant algorithm, the subcellular locations of prokaryotic proteins were predicted. Consequently, an accuracy of 81.5% in the cross-validation test has been achieved using 13 parameters extracted from the curve for the database of 997 prokaryotic proteins. The result is slightly better than that of using the neural network method (80.9%) based on the amino acid composition for the same database. By jointing the amino acid composition and the Zp parameters, the overall predictive accuracy 89.6% can be achieved. It is about 3% higher than that of the Bayes discriminant algorithm based merely on the amino acid composition for the same database. The prediction is also performed with a larger dataset derived from the version 39 SWISS-PROT databank and two datasets with different sequence similarity. Even for the dataset of non-sequence similarity, the improvement can be of 4.4% in the cross-validation test. The results indicate that the Zp parameters are effective in representing the information within a protein primary sequence. The method of extracting information from the primary structure may be useful for other areas of protein studies.

Space Curve Representation and Recognition Based on Wavelet Transform Zero-Crossings

A method to construct a representation of space curves based on the zero-crossings of the dyadic wavelet transform is introduced. The principal axes of inertia of these space curves, referred to as objects, are considered as the reference system. The representation is translation, rotation and size invariant. Instances of objects in images are recognised by matching their representations with those of the models. A string-matching technique is adapted and used for this purpose. Experimental results show that the representation is robust and efficient in extracting and matching object information.

3‐D model of vascular network in rat skin obtained by stereo vision techniques

The quantitative analysis of the depth of injury, penetration of therapeutic agents in tissues, and the regeneration of vascular patency after a graded degree of thermal injury requires a knowledge of the shape and spatial configuration of the vascular networks in the tissue. We have applied computational stereo vision techniques to describe the 3-D configuration of microvessels in full thickness rat skin vascular casts produced by perfusion of Yellow Microfil latex solution through the aorta. The principal concern is to describe the 3-D structure of vascular networks using a set of 3-D space curves. This representation is computed by integrating monocular and binocular processing; the 2-D curve representation of blood vessels computed through monocular analysis is integrated with disparity data to yield a space curve representation for each vessel. A connection diagram is also computed to indicate the connections existing among the computed space curve representations.