Jacobi-Fourier matrice series describing image

• Main Authors: ZILIANG PING, WURIHENG BO, HAIPING REN
• Format: Patent
• Language: Chinese; English
• Published: 08.12.2004
• Edition: 7
• Subjects: CALCULATING; COMPUTING; COUNTING; ELECTRIC DIGITAL DATA PROCESSING; PHYSICS

In the present invention, Jacobian-Fourier function series is set up in polar coordinates as function is formed by Jn(p, q, r) Jacobian polymerization in radial deformation and exp(jm theta) complex index function; Jacobian-Fourier function is quadrature, completeness function series which is ued to carry out quadrature discomposition to image for obtaining Jacobian-Fourier image matrix, original image can be completely restored by using above image matrix to multiply with the same order above function and overlying for sum; by using proper amount of low order matrix and the same order function, original image can be approximately restored as image compression function is anyway obtained. 本发明提出一系列图像描述特征：雅可比-傅立叶矩系列。首先在极坐标系中构造雅可比-傅立叶函数系，此函数系由径向变形的雅可比多项式J#-[n](p，q，r)和角向的复指数函数exp(jmθ)构成。雅可比-傅立叶函数系是正交、完整的函数系，用此种函数系对图像进行正交分解，得到所谓雅可比-傅立叶图像矩。用雅可比-傅立叶图像矩与同阶的雅可比-傅立叶函数相乘，然后叠加求和，则可以完整、无冗余地恢复重建原图像。用适当数量的低阶雅可比-傅立叶矩与同阶雅可比-傅立叶函数相乘，然后叠加求和，则可以近似地恢复重建原图像。因此可以用适当数量的雅可比-傅立叶图像矩来近似表示原图像。雅可比-傅立叶图像矩数量，比原图像的总像素数要少的多，因此具有图像压缩作用。通过适当步骤的规范化处理，雅可比-傅立叶图像矩具有位移、旋转、比例、密度多畸变不变性。可以将规范化处理的雅可比-傅立叶图像矩用作多畸变不变图像识别的特征量。雅可比多项式中的两个参数的变化，可以形成一系列的雅可比-傅立叶图像矩。在雅可比-傅立叶图矩系列中，参数p＝2，q＝2的图像矩，就是正交傅立叶-梅林矩；而参数p＝4，q＝3的图像矩在r＝0和r＝1处，均取有限值0，因而克服了某些图像矩(如切比雪夫-傅立叶矩、圆谐-傅立叶矩等)在零点处发散的困难。