Image processing apparatus, image processing method, and computer program product

Abstract

An image processing apparatus includes an operating unit that calculates a tangent-line direction of an edge and a normal-line direction of the edge by using a vertical-direction derivative value and a horizontal-direction derivative value of a pixel value of a pixel in an input image; a converting unit that converts local coordinates positioned within a predetermined area with respect to a target pixel in the input image into rotated coordinates, by rotating the local coordinates according to an angle formed by the horizontal direction and the tangent-line direction of the edge; and a fitting unit that performs, at the rotated coordinates, a fitting process that employs a least-squares method by using a curved-plane model expressed with the pixel value of the target pixel in the input image.

1 . An image processing apparatus comprising:
 a calculating unit that calculates at least one of a tangent-line direction and a normal-line direction of an edge around a target pixel in an input image by using a direction and a magnitude of a gradient of pixel values of pixels that neighbor the target pixel in the input image;   a converting unit that converts coordinates of pixels around the target pixel into a rotated coordinate system by rotating the axes according to an angle between a horizontal direction of the input image and the tangent-line direction of the edge or the normal-line direction of the edge; and   a fitting unit that performs a fitting process to fit a local gradient around the target pixel, on the rotated coordinate system, into a curved-plane model by the method of least-squares, and an outputting process to obtain a reconstructed pixel value of the target pixel by using the curved-plane model.   
   
   
       2 . The apparatus according to  claim 1 , further comprising:
 a selecting unit that classifies the target pixel as one of a plurality of predetermined classes by using the direction and the magnitude of the gradient, and selects one of curved-plane models that respectively correspond, in a one-to-one correspondence, to the classes as a curved-plane model for the target pixel, wherein   the fitting unit performs the fitting process by using the curved-plane model selected by the selecting unit.   
   
   
       3 . The apparatus according to  claim 1 , wherein the fitting unit configures the curved-plane model so that a degree of freedom in a normal-line direction of the edge is higher than a degree of freedom in a tangent-line direction of the edge. 
   
   
       4 . The apparatus according to  claim 1 , further comprising a weight calculator that applies a weight to a pixel value of a pixel in the input image according a distance from the target pixel to the pixel. 
   
   
       5 . The apparatus according to  claim 4 , wherein the weight calculator calculates the weight in such a manner that the larger a difference between the pixel value of the pixel in the input image and the pixel value of the target pixel is, the smaller is the weight applied to the pixel value of the pixel in the input image. 
   
   
       6 . The apparatus according to  claim 1 , further comprising:
 a storage unit that stores a normal equation based on the least-squares method for each of mutually-different tangent-line directions of the edge, wherein   the fitting unit performs the fitting process using the curved-plane model by selecting a normal equation corresponding to a tangent-line direction of the edge from the normal equations stored in the storage unit and performing a convolution operation on the selected normal equation and the pixel value of the target pixel at the rotated coordinates.   
   
   
       7 . The apparatus according to  claim 1 , further comprising:
 a difference calculator that calculates a difference between the pixel value of the pixel in the input image and a pixel value in the curved-plane model, wherein   the fitting unit performs the fitting process that employs the least-squares method by using a texture curved-plane model that is formed according to the pixel value of the target pixel, based on the calculated difference.   
   
   
       8 . An image processing method comprising:
 calculating at least one of a tangent-line direction and a normal-line direction of an edge around a target pixel in an input image by using a direction and a magnitude of a gradient of pixel values of pixels that neighbor the target pixel in the input image;   converting coordinates of pixels around the target pixel into a rotated coordinate system by rotating the axes according to an angle between a horizontal direction of the input image and the tangent-line direction of the edge or the normal-line direction of the edge; and   performing a fitting process to fit a local gradient around the target pixel, on the rotated coordinate system, into a curved-plane model by the method of least squares, and an outputting process to obtain a reconstructed pixel value of the target pixel by using the curved-plane model.   
   
   
       9 . A computer program product having a computer readable medium including programmed instructions for performing image processing, wherein the instructions, when executed by a computer, cause the computer to perform:
 calculating at least one of a tangent-line direction and a normal-line direction of an edge around a target pixel in an input image by using a direction and a magnitude of a gradient of pixel values of pixels that neighbor the target pixel in the input image;   converting coordinates of pixels around the target pixel into a rotated coordinate system by rotating the axes according to an angle between a horizontal direction of the input image and the tangent-line direction of the edge or the normal-line direction of the edge; and   performing a fitting process to fit a local gradient around the target pixel, on the rotated coordinate system, into a curved-plane model by the method of least squares, and an outputting process to obtain a reconstructed pixel value of the target pixel by using the curved-plane model.