Automatic Registration of Phalanges Regions in CR Images Based on Scale-Invariant Salient Region Features

As two common orthopedic diseases, there are rheumatoid arthritis (RA) and osteoporosis. And early detection and early treatment are important for these diseases. However, some problem such as mass screening on data sets, mis-diagnosis are still remained in visual screening. In order to solve these problems and reduce the burden to physicians, needs of an automatic diagnosis system capable of performing quantitative analysis is anticipated. In this paper, we carry out the development of a registration method of phalanges regions from CR images of the hand to detect temporal changes of phalanges regions by alignment between previous image and current one. The proposed method is carried out registration of phalanges regions using salient region features (SRF) in image. Specifically, SRF are detected from phalanges regions. Then, rigid registration technique is performed using deformation amount based on SRF. We applied our method on 84 pairs of CR temporal images of phalanges regions.


Introduction
Rheumatoid arthritis (RA) and osteoporosis are two common diseases.Dysfunction caused by joint destruction occurs when the symptom progress over a long period of time.Therefore, early detection of these diseases are important, to drug therapy, surgical treatment, rehabilitation, and basic treatment.Frequency of the disease called osteoporosis increases bone if bone is degraded with aging.Incidences caused by these orthopedic diseases have increased dramatically in the context of the aging society of Japan.Due to the decrease of trabecular bone, fracture becomes more easily to happen.When a people decreased his trabecula it is difficult to recover.Therefore, discovery of the bone loss as early as possible is very important.Diagnostic imaging such as X-ray is mainly used in the diagnosis of osteoporosis and moreover diagnostic of imaging is the most important in the visual screening for the RA (1)(2)(3)(4)(5) .However, experience of the physician is frequently required for visual screening.Evaluation of the structure of trabecular bone and measurement of bone mineral density is mainly used in the diagnosis of osteoporosis.However, visual assessment of trabecular bone structure by x-ray image is important because it cannot be diagnosed with osteoporosis.Diagnostic imaging is important for both osteoporosis and RA, but current diagnostic imaging is performed in the subjective assessment by the physician.Therefore, diagnostic results are different because of the experience of the physician interpreting the images.In addition, the burden to the doctors on account of the handling of the huge number of images manually also forms a problem (6,7) .In this paper, by motivation for a quantitative evaluation of RA and osteoporosis, we develop an automatic method for registration of phalanges regions to detect temporal changes by alignment between previous image and current one.The advantage of proposed method is that efficient registration is performed by using salient region features(SRF) in two images respectively to determine the optimal deformation.We performed our methods on 84 pairs of CR temporal images of phalanges regions.

Overview of the proposed method
We proposed a registration method using scale-invariant SRF (7,8) .As general flow of processing, the proposed method consists of three main steps.At the first step, the salient region features is detected (SRFD) from the phalanges region which is automatic segmented from the CR images (9)(10)(11) .As the second step, the region component matching (RCPM) is performed from the result of the SRFD step.In RCPM step, high correlation pairs are determined.And amount of deformation is determined for each pair.Finally, region configural matching (RCFM) is performed.In RCFM step, optimum amount of deformation is obtained by the binding of multiple pairs.The entire image is deformed by using the resulting amount of deformation (See Fig. 1).

Salient Region Features Detection (SRFD)
We believe that every point regardless of their local characteristics (edgeness, cornerness, medialness, curvature, etc.) in the image can be made unique if a proper scale and its neighborhood is selected to calculate the feature.Therefore, we seek to use scale-invariant region features as the basis for our proposed registration method.In (12), a salient region feature detector is proposed.The salient regions are found using an entropy-based detector, which aims to select regions with highest local saliency.For each pixel x on an image, a probability density function (PDF) (, x) is computed from the intensities in a circular region of certain scale described by a radius  centered at x.The local differential entropy of the region is defined by: (, x) = − ∫   (, x) log 2   (, x)    (1)   where  takes on values in the set of possible intensity values.The best scale  x for the region centered at x is selected as the one that maximize the local entropy: x = argmax  (, x).Then the saliency value, ( x , x), for the region with the best scale is defined by the extrema entropy value, weighted by the best scale and a differential self-similarity measure in the scale space: As the flow of SRFD step, firstly, for each pixel location x, the best scale  x of the region centered and saliency value ( x , x) are computed.Then, among the salient regions, the N most salient ones are picked as region features for the image.One of the main advantages of SRF is that they are theoretically invariant to rotation, translation.

Region Component Matching (RCPM)
Once we have extracted the salient region features from both the fixed and moving images, the alignment of the two images is achieved by finding a robust joint correspondence between multiple pairs of region features.This joint correspondence is then used to estimate the parameters of a desires transformation model.This translation can be described by three parameters : (  ,   , ), where   ,   are the translation along  and  directions respectively, and  is the rotation angle.Also   is the fixed image,   is the moving image, and   is the transformed moving image.We aim to recover the parameters of a similarity transformation that geometrically transforms the moving image to be aligned with the fixed image.  and   are number of detected salient region features on   and   , respectively. , is denoted the hypothesized correspondence between the  th region feature on   and the  th feature on   .And furthermore,   1 , 1 ∩   2 , 2 ∩ ⋯ ∩    ,  is denoted that a hypothesized joint correspondence between multiple region feature pairs.In the RCPM step, we measure the likelihood of each hypothesized correspondence between a region feature from   and a region feature from   .That is to say, we want to measure the likelihood   ( , ) for each individual feature correspondence hypothesis  , .We can then acquire a total ordering of these hypotheses according to their likelihoods.We define the likelihood to be proportional to the similarity between the interior intensities Fig. 1.Overview of the proposed processing flow. of the two salient regions involved.Let us denote the  th region on   as  and the  th region on   as .The translation invariance is intrinsic by aligning the two region centers.To further achieve rotation invariance, we sample the parameter space for rotation sparsely and use the largest similarity value over all possible angles as the similarity between the two regions.The similarity measure we use is a normalized form mutual information, the Entropy Correlation Coefficient (ECC) (13,14) .The likelihood of a correspondence hypothesis  , is defined as: where   is the region  rotated angle ,  indicates the joint or marginal differential entropy of the intensity value random variables of the two regions.We are able to sort these hypotheses in the order of descending likelihood.
We then choose the top M such hypotheses to be used in the RCFM step to extract a globally consistent joint correspondence.The RCPM step also generates useful information regarding the transformation to align the two images, based on the purely local region-based matching.
For instance, given a high likelihood correspondence between a region  on   and a region  on   , the rotation angle can be estimated as :  = argmax  (,   ).And the translation can also be estimated by the displacement between the center of the region  and the center of the region .These estimates are associated with the related feature correspondence hypothesis, to provide the initial estimate for the transformation in the next RCFM step.

Region Configural Matching (RCFM)
In the RCFM step, we aim to detect a joint correspondence   1 , 1 ∩   2 , 2 ∩ ⋯ ∩    ,  ⋯ between multiple pairs of region features, which results in the maximum likelihood in terms of global images "alignedness".We measure the likelihood of a hypothesized joint correspondence with  feature pairs using the ECC measure between the overlapping portions of the fixed image   and the transformed moving image   (  ) .
Here the transformation   =   is estimated from all feature pairs contained by current hypothesis.This can be written as: In the end, we want to find a joint correspondence that has the maximum likelihood, while containing adequate number of feature pairs to recover the parameters of a similarity transformation.To address the combinatorial complexity in detecting the joint correspondence, we first compute a minimal correspondence and get an initial estimation of transformation.To choose this first correspondence, we measure   ( To allow converging to a globally optimal solution, we further use a generalized Expectation-Maximization (EM) algorithm to incrementally add in new feature pairs to the joint correspondence base, while refining the center locations of the corresponding features.Let current joint correspondence be  = (  1 , 1 ∩ ⋯ ∩    ,  ) .For each feature pair  , that is in the top M individual matches, but not in the current joint correspondence , we estimate the likelihood of this feature pair being a valid correspondence in terms of global consistency as   ( ∩  , ),  , ∉ .Then, we choose the new feature correspondence  ,̂ that has the maximum likelihood.We also require the addition of  ,̂ increasing the global image "alignedness".If   ( ∩  ,̂) is larger than   , let the new joint correspondence be  = ( ∩  ,̂) , and we re-compute the transformation  using the new joint correspondence.And furthermore we repeat EM step.If   ( ∩  ,̂) is smaller than   , we output current transformation  as the converged transformation to align the fixed image   and the moving image   .Having at most M iterations, our RCFM step is very efficient.Two key points contribute to this efficiency: First, pick a minimal correspondence base with only one feature pair; Second, use the EM algorithm to add in new feature pairs incrementally, thus enabling the converged joint correspondence to include as many good feature pairs as possible, while keeping a minimal complexity.

Conversion by GA
Proposed Method Fig. 2. Registration result.
, ) for each individual feature match among the top M hypothesized correspondences resulted from the RCPM step.Using Equation4, the parameters of   are (  ,   , ) , when measuring the likelihood of  , .Then the first feature pair in the minimal correspondence base is the correspondence yielding the maximum likelihood, i.e.,