Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Curvatures are fast to compute but easily affected by noise and incomplete surfaces.

“Curvatures are fast to compute, but easily affected by noise and incomplete surfaces.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Recent intrinsic techniques enforce isometric consistency.

“From a high level viewpoint, recent intrinsic techniques enforce isometric consistency.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Integral invariants are robust to noise and give similar information to curvature.

“Integral invariants are robust to noise and give similar information to curvature.”

May combine two claims.

No rigid registration methods use templates, while many non-rigid methods do.

“A significant difference is that while no rigid registration methods use templates, many non-rigid methods do.”

May combine two claims.

Some constraints have been adopted by non-rigid registration; for example, an isometry constraint based on Euclidean distance in [46] is replaced by geodesic distance in [2].

“Some constraints have been adopted by non-rigid registration, e.g., [46] defines an isometry constraint based on Euclidean distance, which is replaced by geodesic distance in [2].”

• cites [46] sourceNot checked yet

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• cites [2] sourceNot checked yet

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Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

Choice of features for feature matching is not well discussed in the literature.

“Choice of features for feature matching is not well discussed in the literature.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Registration cast as global optimization does a complete search with bounds or approximates/relaxes the problem into continuous settings to find a near global solution.

“Registration, when cast as global optimization, does a complete search with bounds (exact global solution), or approximates / relaxes the problem into continuous settings so that a near global solution can be found.”

May combine two claims.

Space-time registration techniques usually target sequences, require denser temporal sampling, assume small deformation, and require large overlap of regions for feature correspondences between consecutive frames.

“These techniques usually target sequences, require denser temporal sampling, assume small deformation and large overlap of regions for feature correspondences between consecutive frames.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Many registration techniques optimize both transformations and correspondences, while some optimize transformations or find correspondences only.

“Many techniques optimize both transformations and correspondences whilst some optimize transformations or find correspondences only.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Most methods based on CPC formulate an energy functional with data and regularization terms.

“Most methods based on CPC formulate an energy functional with data and regularization terms.”

May combine two claims.

The distance root mean squared error used by [48] as a bound on CPC error is both tight and fast to compute.

“as a bound on CPC error (Eqn 5); it is both tight and fast to compute.”

• cites [48] Gelfand, Robust Global RegistrationNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

Many techniques model registration and correspondence determination with statistics and probabilistic approaches to handle noise, outliers and missing data.

“Many techniques model registration and the correspondence determination problem with statistics and probabilistic approaches in order to handle datasets with noise, outliers and missing data.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Both registration and data fitting are formulated as optimization problems which can be solved in a similar fashion.

“Both registration and data fitting are formulated as optimization problems which can be solved in a similar fashion.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

One of the major concerns in data-fitting is to avoid overfitting, when χ fits noise rather than the data. The same applies to registration where the models f of extrinsic techniques usually have high degrees of freedom. This potentially leads to over-fitting problems.

“One of the major concerns in data-fitting is to avoid overfitting, when χ fits noise rather than the data.The same applies to registration where the models f of extrinsic techniques usually have high degrees of freedom.This potentially leads to over-fitting problems (in which there are too many parameters to describe the transformation).”

• AssumptionRests on an assumption: Using too many degrees of freedom can overfit noise.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

A general observation made by all extrinsic models of non-rigid techniques is that the more high frequency information on the surface, the more DoF required.

“A general observation made by all extrinsic models of non-rigid techniques is that the more high frequency information on the surface, the more DoF required.”

May combine two claims.

[3] can handle up to 35% noise and the part-in-whole problem.

“These include [3] which can handle up to 35% noise, and part-in-whole problem”

• cites [3] sourceNot checked yet

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May combine two claims.

[5] can handle large gaps in 4D sequences and reduce high dimensionality of deformations through automatic construction of consensus skeletons.

“[5] that can handle large gaps in 4D sequences, reduce high dimensionality of deformations through automatic construction of consensus skeletons”

• cites [5] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

In the extreme case, non-rigid registration methods that handle large deformation involving articulation or fine detail preservation use 12 DoF (an affine transformation) per point or node.

“In the extreme case, non-rigid registration methods that handle large deformation involving articulation or fine detail preservation, use 12 DoF (an affine transformation) per point or node.”

May combine two claims.

In extrinsic techniques, regularization becomes highly essential, not only to obtain a smooth surface, but also to constrain arbitrary transformation to obtain a reasonable solution.

“In these techniques, regularization becomes highly essential, not only to obtain a smooth surface, but also to constrain arbitrary transformation to obtain a reasonable solution.”

Probably not a substantial claim: may not pass S3 (load-bearing).

E_reg is a regularization term that provides additional information to constrain an arbitrary transformation so that the solution a is a reasonable one.

“E reg is a regularization term that provides additional information to constrain an arbitrary transformation so that the solution a is a reasonable one.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Registration can be further classified into extrinsic and intrinsic techniques.

“Registration can be further classified into extrinsic and intrinsic techniques (Figure 1).”

Probably not a substantial claim: may not pass S3 (load-bearing).

Four main types of transformation models are common: rigid transformation, piecewise rigid deformation, general deformation and (nearly) isometric deformation.

“Four main types are common: rigid transformation, piecewise rigid deformation, general deformation and (nearly) isometric deformation.”

Probably not a substantial claim: may not pass S3 (load-bearing).

When non-rigid registrations assume high DoFs, overfitting can become a problem (though not frequently discussed).

“When non-rigid registrations assume high DoFs, overfitting can become a problem (though not frequently discussed).”

• AssumptionRests on an assumption: Using too many degrees of freedom can overfit noise.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Rigid alignment with non-rigid correction is a transitional case between the rigid and non-rigid models.

“Rigid alignment with non-rigid correction is a transitional case between the rigid and non-rigid models.”

Probably not a substantial claim: may not pass S3 (load-bearing).

[7] supports facial capture and animation of avatar heads in real-time.

“[7] that supports facial capture and animation of avatar heads in real-time”

• cites [7] sourceNot checked yet

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Classified as probably not a substantial claim. May combine two claims.

Study of these components shows how over-fitting arises in non-rigid registration and the reasons for increasing interest in intrinsic techniques.

“Study of these components (i) provides a basis for comparison of the novelties of different techniques, (ii) reveals the similarity of rigid and non-rigid registration in terms of problem representations, and (iii) shows how over-fitting arises in non-rigid registration and the reasons for increasing interest in intrinsic techniques.”

May combine two claims.

To alleviate overfitting, [2], [6], [32] reduce the DoF explicitly by computing local transformations with respect to clusters or nodes, and most non-rigid registration methods use regularization to further constrain the solutions.

“To alleviate it, [2], [6], [32] reduce the DoF explicitly by computing local transformations with respect to clusters or nodes, and most non-rigid registration methods use regularization to further constrain the solutions.”

• cites [2] sourceNot checked yet

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• cites [6] sourceNot checked yet

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• cites [32] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

In rigid registration, correspondences assist in further pruning the transformation search space, whilst in the non-rigid case, establishing correspondences is the essential step that drives alignment.

“In rigid registration, correspondences assist in further pruning the transformation search space, whilst in the non-rigid case, establishing correspondences is the essential step that drives alignment.”

Probably not a substantial claim: may not pass S4 (based).

Registration is closely related to data fitting in that it comprises three core interwoven components: model selection, correspondences & constraints, and optimization.

“Registration is closely related to data fitting in that it comprises three core interwoven components: model selection, correspondences & constraints and optimization.”

Classified as probably not a substantial claim. May combine two claims.

The rigid transformation is global, can be uniquely defined by three non-collinear pairs of correspondences, and has low dimension (6 DoF).

“This transformation (i) is global-the same for every point p i , (ii) can be uniquely defined by three non-collinear pairs of correspondences, and (iii) has low dimension (6 DoF).”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

Comparatively, non-rigid registration techniques are still in their infancy.

“Comparatively, non-rigid registration techniques are still in their infancy.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In rigid registration, the overfitting problem is generally ignored because there are 6 DoF only.

“In rigid registration, the overfitting problem is generally ignored because there are 6 DoF only.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

[6] can register 4D surfaces and produce an urshape template.

“[6] that can register 4D surfaces and produce an urshape template”

• cites [6] sourceNot checked yet

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May combine two claims.

[4] can handle up to 40% outliers and down to 40% overlap as demonstrated in their experiments.

“[4] which can handle up to 40% outliers, and down to 40% overlap as demonstrated in their experiments.”

• cites [4] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

While not every registration technique fits well into this framework derived from data fitting, these components and constraints do exist in most surveyed methods.

“While not every registration technique fits well into this framework derived from data fitting, these components and constraints do exist in most surveyed methods.”

Probably not a substantial claim: may not pass S3 (load-bearing).

[8], [9] can handle near-to approximate isometric deformation.

“[8], [9] that can handle near-to approximateisometric deformation.”

• cites [8] sourceNot checked yet

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• cites [9] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

Using the first two properties, if both point sets contain at least one pair of triplets that match exactly and provide the correct transformation, it takes O(N^6) time to test all possible transformations for sets of N points.

“Using the first two properties, if both point sets contain at least one pair of triplets that match exactly and provide the correct transformation, it takes O(N 6 ) time to test all possible transformations for sets of N points.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

All these have changed the landscape of digital geometry processing, migrating the focuses to dynamic scenes and motions.

“All these have changed the landscape of digital geometry processing, migrating the focuses to dynamic scenes and motions.”

May combine two claims.

In intrinsic techniques, both P and Q are transformed into a canonical form and the mapping function h is usually low-dimensional. The intrinsic transformation g provides the most important constraint to avoid arbitrary transformation. This is one reason why these techniques have become the recent research focus.

“In intrinsic techniques, both P and Q are transformed into a canonical form and the mapping function h is usually low-dimensional.The intrinsic transformation g provides the most important constraint to avoid arbitrary transformation.This is one reason why these techniques have become the recent research focus.”

May combine two claims.

Non-rigid registration is more difficult than rigid registration because it must account for deformation, making the solution space much larger.

“Non-rigid registration is even more difficult, as it not only faces the above challenges but also needs to account for deformation, so the solution space is much larger.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

[62] gives a fast ICP algorithm based on localization. They restrict the search for a new CPC at each iteration to the local neighborhood of the correspondence in the previous iteration, avoiding a global exhaustive search.

“Localization: [62] gives a fast ICP algorithm (Section 4.1.1)based on localization.They restrict the search for a new CPC at each iteration to the local neighborhood of the correspondence in the previous iteration, avoiding a global exhaustive search.”

• cites [62] sourceNot checked yet

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May combine two claims.

Features and saliency used in nonrigid registration are usually defined on local surface geometry and are at least assumed to be invariant under transformation.

“They are usually defined on local surface geometry and are (at least, assumed to be) invariant under transformation.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Regularization involves adding penalty terms to the objective function. It incorporates a priori information, improves search, and avoids local minima during optimization.

“Regularization involves adding penalty terms to the objective function.It incorporates a priori information, improves search, and avoids local minima during optimization.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Intrinsic models assume (nearly) isometric deformation.

“Intrinsic models assume (nearly) isometric deformation.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Given two surfaces P and Q in arbitrary initial poses, [4] randomly selects a 4-point tuple from P and another 4-point tuple from Q, and compares the affine ratios. If they form a correspondence, their affine ratio will match.

“Given two surfaces P and Q in arbitrary initial poses, [4] randomly selects a 4-point tuple from P and another 4-point tuple from Q, and compares the affine ratios.If they form a correspondence, their affine ratio will match.”

• cites [4] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

[65] uses the term to maximize correspondences and bias the objective function towards more matches. This maximizes the overlapping area.

“Maximizing Correspondences: [65] uses the term i j M ij to maximize correspondences and bias the objective function towards more matches (i.e. it favors M ij = 1 over M ij = 0).This maximizes the overlapping area.”

• cites [65] sourceNot checked yet

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May combine two claims.

Templates simplify the part-to-part alignment problem to part-to-whole alignment, by providing strong structural information including priors for shape, constraints on arbitrary deformation, and connectivity. These greatly help to handle topological noise and missing data.

“Templates simplify the part-to-part alignment problem to part-to-whole alignment, by providing strong structural information including priors for shape, constraints on arbitrary deformation, and connectivity.These greatly help to handle topological noise and missing data.”

May combine two claims.

Extrinsic non-rigid registration allows fairly arbitrary deformation due to high dimensionality (an over-fitting problem) but encourages isometry through heavy regularization.

“Extrinsic non-rigid registration allows fairly arbitrary deformation (due to the high dimensionality of the models (an over-fitting problem)) but encourages isometry through the heavy use of regularization.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

PCA methods are most useful for whole object registration.

“PCA methods are most useful for whole object registration.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Slippage analysis is unsuited to smooth surfaces due to its definition.

“Slippage analysis is unsuited to smooth surfaces due to its definition.”

May combine two claims.

Point-to-plane ICP minimizes the shortest distance between a point and the tangent plane of the closest point on another surface. This allows faster tangential movement of the surfaces.

“The first of these was point-to-plane ICP.[51] minimizes the shortest distance between a point and the tangent plane of the closest point on another surface.This allows faster tangential movement of the surfaces.”

• cites [51] sourceNot checked yet

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May combine two claims.

[6], [28], [79] constructs a template, an urshape, by accumulating and filling in missing data from other scans in the same sequence. They have been used extensively in non-rigid registration to constrain dense correspondences. This works for objects with well defined forms, such as the human face and body.

“[6], [28], [79] constructs a template, an urshape, by accumulating and filling in missing data from other scans in the same sequence.They have been used extensively in non-rigid registration to constrain dense correspondences [23], [29], [32], [34], [80].This works for objects with well defined forms, such as the human face and body.”

• cites [6] sourceNot checked yet

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• cites [28] sourceNot checked yet

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• cites [79] Wand, Reconstruction of Deforming Geometry from Time-Varying Point CloudsNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

[67] proposed a similar method based on a generalized Gauss-Markov model which uses a statistical framework to model noise.

“Independently, [67] proposed a similar method based on a generalized Gauss-Markov model which uses a statistical framework to model noise.”

• cites [67] sourceNot checked yet

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May combine two claims.

Higher-dimensional features offer greater pruning power because of the low probability of matching all components of the feature, but often take longer to compute.

“Higher-dimensional features offer greater pruning power because of the low probability of matching all components of the feature, but often take longer to compute.”

May combine two claims.

Rigid registration is often applied to unknown or much more general objects and scenes, and templates are less useful for it.

“Rigid registration is often applied to unknown or much more general objects and scenes, and templates are less useful.”

• AssumptionRests on an assumption: Rigid registration is often applied to unknown or much more general objects and scenes.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Isometry is a very powerful constraint sufficient to define a class of intrinsic transformation models and is used in optimization in various ways.

“Isometry is a very powerful constraint which is sufficient to define a class of intrinsic transformation models (Section 3.5), and is used in optimization in various ways.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Markers and templates are explicit prior knowledge provided by users.

“Markers and templates are explicit prior knowledge provided by users.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Fine surface details are usually ignored when establishing correspondences in intrinsic models, due to their intrinsic nature.

“Fine surface details are usually ignored when establishing correspondences, due to their intrinsic nature.”

Probably not a substantial claim: may not pass S3 (load-bearing).

RANSAC-based DARCES [47] uses distance-preserving constraint to enumerate and test three pairs of correspondences in a sphere to limit the transformation search space.

“RANSAC-based DARCES [47] uses distance-preserving constraint to enumerate and test three pairs of correspondences in a sphere to limit the transformation search space.”

• cites [47] sourceNot checked yet

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Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

The appropriate model to use depends on the data itself.

“The appropriate model to use depends on the data itself.”

May combine two claims.

Most non-rigid constraints, both extrinsic and intrinsic, focus on modelling the relationship between correspondences, whereas in rigid registration this relationship is implicitly captured by the rigid transformation.

“In general, most non-rigid constraints (both extrinsic and intrinsic) focus on modelling the relationship between correspondences, whilst this relationship is implicitly captured by the rigid transformation in rigid registration.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Saliency is a measure of local significance in a surface: salient points/regions are those whose properties are unlike most of their neighbours. They are used for key point/region detection, often in conjunction with features. They reduce the size of correspondence space, potential mismatches and obtain more reliable coarse correspondences.

“Saliency is a measure of local significance in a surface: salient points/regions are those whose properties are unlike most of their neighbours.They are used for key point/region detection, often in conjunction with features (Section 4.1.2).They reduce the size of correspondence space, potential mismatches and obtain more reliable coarse correspondences.”

Probably not a substantial claim: may not pass S3 (load-bearing).

[46] assumes that the Euclidean distance between the centers of a pair of features on a surface, and the angles between their principal directions and their connecting line, are preserved under a rigid transformation.

“[46] assumes that the Euclidean distance between the centers of a pair of features on a surface, and the angles between their principal directions and their connecting line, are preserved under a rigid transformation.”

• cites [46] sourceNot checked yet

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May combine two claims.

Many intrinsic methods require mesh data with consistent topology, and may not work on point cloud data.

“Many methods of this kind require mesh data with consistent topology, and may not work on point cloud data.”

Probably not a substantial claim: may not pass S3 (load-bearing).

[48] uses (Euclidean) distance-based lower-bounding and the branch-and-bound to reduce the correspondence search space.

“[48] uses (Euclidean) distancebased lower-bounding and the branch-and-bound to reduce the correspondence search space (Section 5.2.1).”

• cites [48] Gelfand, Robust Global RegistrationNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

3D markers provide sparse correspondences.

“3D markers provide sparse correspondences.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The iterative closest point algorithm must be carefully initialized.

“This iterative algorithm must be carefully initialized.”

May combine two claims.

[65] casts registration as a continuous optimization problem that handles both rigid transformation and correspondence determination simultaneously. It uses CPC, and formulates a regularization term based on entropy. This term can be interpreted as equalizing the importances of point matches, forcing them to the same distance and thus causing the surfaces to run parallel, rather than intersecting.

“Equalization: [65] casts registration as a continuous optimization problem that handles both rigid transformation and correspondence determination simultaneously.It uses CPC, and formulates a regularization term based on entropy:i j M ij log M ij where M is the matching probability matrix of all correspondences.When all point matches are equally likely, the entropy reaches a maximum.This term can”

• cites [65] sourceNot checked yet

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• cites [59] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

Search constraints are for efficiency.

“Search constraints are for efficiency.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Principal axes, computed through PCA, are three orthogonal directions where the greatest variance of the datapoints lie.

“Principal axes, computed through principal component analysis (PCA), are three orthogonal directions (eigenvectors correspond to the largest eigenvalues) where the greatest variance of the datapoints lie.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

[56] uses a hierarchy of surface features in the form of points, curves and finally surfaces. They estimate a Euclidean transformation using a few salient points. The transformation is then refined using curves, and surfaces.

“[56] uses a hierarchy of surface features in the form of points, curves and finally surfaces.They estimate a Euclidean transformation using a few salient points.The transformation is then refined using curves, and surfaces.”

• cites [56] Krsek, Range Image Registration Driven by a Hierarchy of Surface Differential FeaturesNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

[13] uses a similar argument involving equalization of confidence weightings based on mean field variables.

“[13] uses a similar argument involving equalization of confidence weightings based on mean field variables.”

• cites [13] sourceNot checked yet

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May combine two claims.

In nonrigid registration, most deformation models allow arbitrary local transformation, and the results may not adequately respect the material properties of the underlying surfaces.

“In nonrigid registration, most deformation models allow arbitrary local transformation, and the results may not adequately respect the material properties of the underlying surfaces.”

• AssumptionRests on an assumption: Non-rigid registration results should adequately respect the material properties of the underlying surfaces.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Low-dimensional features are quick to compute and are usually used in conjunction with other constraints like saliency.

“Low-dimensional features are quick to compute and is usually used in conjunction with other constraints like saliency (Section 4.1.3).”

Probably not a substantial claim: may not pass S3 (load-bearing).

A recent advance [49] combines PCA with the least median of squares, providing resistance to noise and outliers.

“A recent advance [49] combines PCA with the least median of squares, providing resistance to noise and outliers.”

• cites [49] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

[62] further combines the above with a coarse-to-fine hierarchical search technique. Use of down-sampled data speeds up the first few iterations of ICP; the resolution is gradually increased to obtain more reliable alignment.

“Hierarchical Approaches: [62] further combines the above with a coarse-to-fine hierarchical search technique.Use of down-sampled data speeds up the first few iterations of ICP; the resolution is gradually increased to obtain more reliable alignment.”

• cites [62] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Features are quantities that describe a point. Multiple features can be concatenated to form a feature vector. When features of two points match, a meaningful correspondence may exist.

“Features are quantities (e.g.principal curvatures) that describe a point.Multiple features can be concatenated to form a feature vector.When features of two points (or clusters) match, a meaningful correspondence may exist.”

Probably not a substantial claim: may not pass S3 (load-bearing).

[115] discusses how to evaluate registration without ground truth.

“In the computer vision literature, [115] discusses how to evaluate registration without ground truth.”

• cites [115] Schestowitz, 2006, Non-Rigid Registration Assessment Without Ground Truth, Medical Image Understanding and AnalysisNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Local deterministic optimization methods are efficient but depend heavily on initialization and often converge to local minima.

“These techniques are efficient but also depend heavily on initialization and often converge to local minimum.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

More temporal data helps constrain an arbitrary deformation.

“The idea is that more temporal data helps constrain an arbitrary deformation.”

• AssumptionRests on an assumption: More temporal data helps constrain an arbitrary deformation.

Probably not a substantial claim: may not pass S4 (based).

Two general surfaces can always be brought into alignment with arbitrarily small error.

“Ultimately, two general surfaces can always be brought into alignment with arbitrarily small error.”

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

A surface comprises different materials and may undergo different kinds of deformation.

“However, a surface comprises different materials and may undergo different kinds of deformation.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The efficiency of branch-and-bound depends on how tight the bound is and how quickly it can be computed.

“Its efficiency depends on how tight the bound is, and how quickly it can be computed.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Isometric distortion is meaningful only if the datasets are undergoing a (near-)isometric deformation.

“Note that isometric distortion is meaningful only if the datasets are undergoing a (near-)isometric deformation.”

May combine two claims.

Transformation-induced constraints allow registration on highly sparse data, single-view data, and often in a pairwise manner.

“These constraints allow registration to be carried out on highly sparse data, or data from a single view, and often in a pairwise manner.”

Probably not a substantial claim: may not pass S3 (load-bearing).

One idea to evaluate registration without ground truth is to use image-based techniques [116] and compare the results with non-rigid registrations.

“One idea is to use image-based techniques [116] and compare the results with non-rigid registrations.”

• cites [116] sourceNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

After a few steps, more emphasis is put on the data term because the original shape has been deformed close enough to the aligning shape.

“After a few steps, more emphasis is put on the data term because the original shape has been deformed to lie close enough to the aligning shape [29], [30].”

• cites [29] sourceNot checked yet

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• cites [30] sourceNot checked yet

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Probably not a substantial claim: may not pass S4 (based).

It is well-known theoretically that high dimensionality can lead to over-fitting.

“It is well-known theoretically that such high dimensionality can lead to over-fitting.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Global optimization tries to find a global solution and avoid local minima.

“Global optimization tries to find a global solution and to avoid local minima.”

May combine two claims.

In rigid transformation estimation, a closed-form least-squares solution exists if three or more distinct non-collinear pairs of correspondences are given, and can be solved by SVD, quaternions, orthonormal matrices or dual quaternions.

“In rigid transformation estimation, a closed-form least-squares solution (preferable for efficiency and robustness) exists if three or more distinct non-collinear pairs of correspondences are given [100], which can be solved by SVD, quaternions, orthonormal matrices or dual quaternions.”

• cites [100] sourceNot checked yet

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May combine two claims.

Low-dimensional representations enable registration techniques to handle sparser data and multiple or all frames at a time, and generate more accurate results.

“These enable registration techniques to handle sparser data and multiple or all frames at a time, and generate more accurate results.”

Probably not a substantial claim: may not pass S3 (load-bearing).

[8] recruited a volunteer to label 10-35 semantically meaningful and consistent feature points for each class of objects in the watertight meshes dataset [114].

“[8] also recruited a volunteer to label 10-35 semantically meaningful and consistent feature points for each class of objects in the watertight meshes dataset [114].”

• cites [8] sourceNot checked yet

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• cites [114] Giorgi, 2013, SHREC: Shape Retrieval Contest: Watertight Models TrackNot checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

A benchmark database [91] based on TOSCA allows evaluations on isometry, topology, holes, scale, sampling, and noise of features and saliency.

“A benchmark database [91] based on TOSCA further allows evaluations on isometry, topology, holes, scale, sampling, and noise of features and saliency.”

• cites [91] Boyer, SHREC 2011: Robust Feature Detection and Description BenchmarkNot checked yet

  Not checked in the free run.

May combine two claims.

Transformation-induced constraints and reliable features and saliency measures are important priors.

“Transformation (deformation)-induced constraints and reliable features & saliency measures are important priors.”

May combine two claims.

Existing extrinsic techniques encourage smoothness through (i) formulating a priori knowledge or assumptions as regularization, (ii) introducing additional equations by some linear constraints on neighborhoods or (iii) uses a reduced representation (e.g. embedded graph nodes, meshless element models).

“To alleviate the over-fitting problem, existing extrinsic techniques encourage smoothness through (i) formulating a priori knowledge or assumptions as regularization, (ii) introducing additional equations by some linear constraints on neighborhoods or (iii) uses a reduced representation (e.g.embedded graph nodes, meshless element models).”

Probably not a substantial claim: may not pass S3 (load-bearing).

[8] uses the sum of isometric distortion-difference of geodesic distances between the end-points of one correspondence with respect to all the other correspondences.

“[8] uses sum of isometric distortion-difference of geodesic distances between the end-points of one correspondence with respect to all the other correspondences.”

• cites [8] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

Related techniques [118] are emerging.

“Related techniques [118] are emerging.”

• cites [118] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

The area of using physical models relating tissues, bones and muscles in 3D face registration is yet to explore, possibly due to the complexity of facial physiology.

“This area is yet to explore, possibly due to the complexity of facial physiology.”

Probably not a substantial claim: may not pass S3 (load-bearing).

[9] sums isometric distortions all over the surface to obtain one single number.

“[9] sums these isometric distortions all over the surface to obtain one single number.”

• cites [9] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

Branch-and-bound is a complete search technique based on a lower bound on the cost function.

“Branch-and-bound is a complete search technique, which is based on a lower bound on the cost function.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

In general, obtaining ground truth data is difficult.

“In general, obtaining ground truth data is difficult.”

May combine two claims.

The main difficulties of using multiple deformation models are the need for surface segmentation, constraints between adjacent models, and approaches to merge registration and deformation results.

“The main difficulties of doing so are the need for surface segmentation, constraints between adjacent models, and approaches to merge registration and deformation results.”

Probably not a substantial claim: may not pass S4 (based).

Local optimization can become stuck in local minima if the initial solution is not close to a global solution.

“Local optimization can become stuck in local minima if the initial solution is not close to a global solution.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The evaluation of new techniques on dataset type 3 may actually compare their performance against the techniques that create the dataset.

“Note also that the evaluation of new techniques on dataset type 3 may actually compare their performance against the techniques that create the dataset.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Assuming a single model for the two surfaces being aligned is practical, enabling optimization to simultaneously find the best transformations for all points.

“This is practical, enabling optimization to simultaneously find the best transformations for all points.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The envelope of motion is perhaps the weakest prior and requires both dense spatial and temporal sampling.

“Perhaps the weakest prior is the envelop of motion which requires both dense spatial and temporal sampling.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Search constraints are mostly for efficiency.

“(Search constraints are mostly for efficiency.)”

Probably not a substantial claim: may not pass S3 (load-bearing).

Given ground truth data, receiver operating characteristic (ROC) curves may be used to evaluate registration.

“Given ground truth data, receiver operating characteristic (ROC) curves, which are plots of true positive rate against false positive rate, may be used.”

Probably not a substantial claim: may not pass S3 (load-bearing).

One way to evaluate registration without ground truth is to evaluate the results by generalizing them to unseen data.

“One way is to evaluate the results by generalizing them to unseen data (a well known method in datafitting).”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

In general, non-rigid registration is problem- and data-dependent.

“In general, non-rigid registration is problem-and data-dependent.”

May combine two claims.

For non-rigid shapes, many deformations are only near/approximate isometric, which may lead to matching ambiguities [8].

“For non-rigid shapes, many deformations are only near/approximateisometric, which may lead to matching ambiguities [8].”

• cites [8] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

These transformations are similar to the domain theory in analytical learning-a global rule, one reason why these techniques can be cast as optimization problems and solved using the Hough transform [17], [39] or RANSAC technique [4], [71] efficiently.

“These transformations are similar to the domain theory in analytical learning-a global rule, one reason why these techniques can be cast as optimization problems and solved using the Hough transform [17], [39] or RANSAC technique [4], [71] efficiently.”

• cites [17] Li, Multi-Scale Features for Approximate Alignment of Point-Based SurfacesNot checked yet

  Not checked in the free run.

• cites [39] sourceNot checked yet

  Not checked in the free run.

• cites [4] sourceNot checked yet

  Not checked in the free run.

May combine two claims.

In cases with large topological changes, the isometry assumption may fail [38]; handling such issues is a challenging task.

“In cases with large topological changes, the isometry assumption may fail [38]; handling such issues is a challenging task.”

• cites [38] sourceNot checked yet

  Not checked in the free run.

May combine two claims.

Groupwise registration techniques have been developed [33], [123] which are typically more reliable, and reduce the accumulated errors that arise in pairwise registration.

“Groupwise registration techniques have been developed [33], [123] which are typically more reliable, and reduce the accumulated errors that arise in pairwise registration.”

• cites [33] sourceNot checked yet

  Not checked in the free run.

• cites [123] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

As has been found in medical imaging, registration utilizing heterogeneous information (e.g. geometry and texture [41], [120]) may give higher accuracy.

“As has been found in medical imaging, registration utilizing heterogeneous information (e.g.geometry and texture [41], [120]) may give higher accuracy.”

• cites [41] sourceNot checked yet

  Not checked in the free run.

• cites [120] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

One way of providing more training data is to look into the temporal domain.

“One way of providing more training data is to look into the temporal domain.”

Probably not a substantial claim: may not pass S3 (load-bearing).

[98] answers how many correspondences are required to constrain deformations of non-rigid shapes.

“[98] further answers how many correspondences are required to constrain deformations of non-rigid shapes.”

• cites [98] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

This is similar to inductive learning with limited prior knowledge.

“This is similar to inductive learning with limited prior knowledge.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Analytical learning uses domain theory (e.g. rules) and deductive inference to derive hypothesis.

“Analytical learning uses domain theory (e.g.rules) and deductive inference to derive hypothesis.”

• cites [122] Mitchell, 1997Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

Computation efficiency is another issue.

“Computation efficiency is another issue.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

There are no precise definitions and methods for evaluating quality of correspondences.

“As we have noted, there are no precise definitions and methods for evaluating quality of correspondences.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Recent research in intrinsic geometry and isometric consistency has led to important advances for isometric deformation, especially for face and body modeling.

“Recent research in intrinsic geometry and isometric consistency has led to important advances for isometric deformation, especially for face and body modeling.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

Many challenges posed by rigid registration have been addressed [2].

“Many challenges posed by rigid registration have been addressed [2].”

• cites [2] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Intrinsic transformations require the two surfaces (and all points on them) to satisfy isometric consistency.

“Intrinsic transformations require the two surfaces (and all points on them) to satisfy isometric consistency.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Evaluation of correspondences and transformations are two important areas.

“Evaluation of correspondences and transformations are two important areas.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Further challenges lie in (i) avoiding the need for markers or templates, and (ii) capturing and processing fine scale details [32].

“Further challenges lie in (i) avoiding the need for markers or templates, and (ii) capturing and processing fine scale details [32].”

• cites [32] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

The pitfall of analytical learning is that it depends on a perfect domain theory.

“The pitfall of analytical learning is that it depends on a perfect domain theory.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Analytical learning does not require lots of training data but is seriously affected if the domain theory is incorrect.

“It does not require lots of training data but is seriously affected if the domain theory is incorrect.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Stochastic approaches are promising methods that are not sensitive to initialization.

“Stochastic approaches are promising methods that are not sensitive to initialization.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Recent research has focused on analyzing sequences of 3D scans: (i) hardware for capturing such sequences at a high frame rate is now readily available, and (ii) sequences assist registration by providing intermediate information, and thereby constraints.

“Recent research has focused on analyzing sequences of 3D scans: (i) hardware for capturing such sequences at a high frame rate is now readily available, and (ii) sequences assist registration by providing intermediate information, and thereby constraints.”

Classified as probably not a substantial claim.

If one wants to register surfaces from heterogeneous sources (e.g., two totally different human faces and their expressions), these techniques do not work.

“If one wants to register surfaces from heterogeneous sources (e.g., two totally different human faces and their expressions), these techniques do not work.”

Probably not a substantial claim: may not pass S3 (load-bearing).

[8] has started in this direction using blended conformal maps.

“[8] has started in this direction using blended conformal maps.”

• cites [8] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

By transforming non-rigid shapes into the intrinsic domain, many stochastic methods have found applications in establishing correspondences, and often near globally optimal solutions are obtained.

“By transforming non-rigid shapes into the intrinsic domain, many stochastic methods have found applications in establishing correspondences, and often near globally optimal solutions are obtained.”

Probably not a substantial claim: may not pass S3 (load-bearing).

These approaches may be considered a combination of inductive and analytical learning techniques [122].

“These approaches may be considered a combination of inductive and analytical learning techniques [122].”

• cites [122] Mitchell, 1997Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

[40] suggests that fixing one correspondence, all other correspondences can be inferred for non-rigid shapes.

“[40] suggests that fixing one correspondence, all other correspondences can be inferred for non-rigid shapes.”

• cites [40] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Optimization is an important issue in registration as it affects accuracy, robustness and convergence.

“Optimization is an important issue in registration as it affects accuracy, robustness and convergence.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The justification of inductive learning is based on statistical inference.

“The justification is based on statistical inference.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Non-rigid registration is similar to data fitting, where there are many well-established techniques for model selection: cross-validation, early stopping and model comparison (e.g. information-based criteria).

“However, non-rigid registration is similar to data fitting, where there are many well-established techniques for model selection: cross-validation, early stopping and model comparison (e.g.information-based criteria).”

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

Existing techniques focus mostly on modelling near-isometric deformation and obtaining a global consistent set of correspondences.

“Existing techniques focus mostly on modelling near-isometric deformation and obtaining a global consistent set of correspondences.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Inductive learning (e.g. neural network) generalizes hypotheses, in terms of a function, from training examples to unseen data.

“Inductive learning (e.g.neural network) generalizes hypotheses, in terms of a function, from training examples to unseen data.”

• cites [122] Mitchell, 1997Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Most techniques focus on registering surfaces of similar sources.

“Most techniques focus on registering surfaces of similar sources.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Rigid Registration is becoming more robust and reliable over the past two decades of researches.

“Rigid Registration is becoming more robust and reliable over the past two decades of researches.”

Probably not a substantial claim: may not pass S3 (load-bearing).

This type of technique assumes the deformation (hypotheses) can be learnt from sufficient training data.

“This type of technique assumes the deformation (hypotheses) can be learnt from sufficient training data.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Defining the semantic meaning of correspondences is a hard problem in itself, and currently no work considers the evaluation of transformations.

“Defining the semantic meaning of correspondences is a hard problem in itself, and currently no work considers the evaluation of transformations.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Having a rigid transformation requires all points to transform rigidly.

“Having a rigid transformation requires all points to transform rigidly.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Many optimization techniques used in rigid registration have yet to be applied to non-rigid cases.

“Many optimization techniques used in rigid registration have yet to be applied to non-rigid cases.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The advantage of inductive learning is that it requires little prior knowledge, but the hypothesis may be incorrect if there is not sufficient training data-overfitting.

“The advantage is that it requires little prior knowledge, but the hypothesis may be incorrect if there is not sufficient training data-overfitting.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Although many techniques and constraints have been proposed to facilitate correspondence search, human assistance and visual inspection are sometimes required to provide semantic input.

“Although many techniques and constraints have been proposed to facilitate correspondence search, human assistance and visual inspection are sometimes required to provide semantic input.”

Classified as probably not a substantial claim.

Many existing non-rigid techniques are still in the stage of proof-of-concept-showing what can be done.

“Many existing non-rigid techniques are still in the stage of proof-of-concept-showing what can be done.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Recent efforts of the community is to model and study these factors (e.g. Section 4.1.4).

“Recent efforts of the community is to model and study these factors (e.g.Section 4.1.4).”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The minimum description length criterion is well-known for determining the best model from data; it has been used in image registration [119], face (texture and depth) registration [120] and medical data registration [121] in computer vision, but is relatively little used in computer graphics and shape analysis.

“In information theory, the minimum description length criterion is well-known for determining the best model from data; it has been used in image registration [119], face (texture and depth) registration [120] and medical data registration [121] in computer vision, but is relatively little used in computer graphics and shape analysis.”

• cites [119] sourceNot checked yet

  Not checked in the free run.

• cites [120] sourceNot checked yet

  Not checked in the free run.

• cites [121] sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

There are two kinds of learning methods in ML [122]: inductive and analytical learning.

“There are two kinds of learning methods in ML [122]: inductive and analytical learning.”

• cites [122] Mitchell, 1997Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Adapting these techniques to large scale data, deriving specific objective functions, handling various levels of geometric and topological noise, and extending them to non-isometric and elastic deformation are some of the challenges.

“Adapting these techniques to large scale data, deriving specific objective functions, handling various levels of geometric and topological noise, and extending them to non-isometric and elastic deformation are some of the challenges.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

A hypothesis in inductive learning is assumed to be found/fitted empirically from a large amount of training data.

“A hypothesis is assumed to be found/fitted empirically from a large amount of training data.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

Meaningful correspondences should relate homologous sections of the shapes, i.e., sections that are semantically related.

“Meaningful correspondences should relate homologous sections of the shapes, i.e., sections that are semantically related.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing). May combine two claims.

Non-Rigid Registration, in general, is still at its infant stage, largely because of the large varieties of transformations in the real world and the shortage of our knowledge of these transformations.

“Non-Rigid Registration, in general, is still at its infant stage, largely because of the large varieties of transformations in the real world and the shortage of our knowledge of these transformations.”