Classification of Rotated and Scaled Textured Images

大多数纹理分类方法都假设测试图像与训练图像具有相同的方向和尺度。因此，即使测试图像的尺度方向与训练图像的尺度方向略有不同，它们的性能也很差。本项目研究了一种新的基于光谱矩的旋转和尺度（RS）不变量的纹理分类技术。由矩导出的旋转不变量已被许多研究者研究。然而，使用它们的模式识别的成功结果仅限于有限大小的对象的二进制图像。由于灰度图像在边界上具有非零值，使得不变矩难以应用于灰度图像，本文利用图像谱密度函数（SDF）的矩来获得旋转不变量，而不是灰度图像的矩。当图像被旋转和缩放时，其SDF旋转相同的角度，并被逆缩放;此外，大多数纹理图像的光谱功率集中在原点周围，并迅速向高频衰减。此外，我们计划获得稳定的旋转力矩，我们定义为一个圆的积分区域的力矩计算和调整其半径的规模变化，通过设置一个恒定的速度的图像总功率在圆。由于谱矩具有相对于尺度的简单性质，我们可以通过旋转不变量的比率来定义RS不变量。我们使用Brodatz专辑中的16种纹理进行实验，以非常高的分类率证实了所提出方法的有效性。我们将该技术应用于（1）纹理图像的旋转角度和比例因子检测，（2）乳房X线片的缺陷检测和（3）微小钙化点检测，取得了较好的效果。

Most of texture classification approaches pose classification problems under the assumption that a test image possesses the same orientation and scale as training images. According1y, they perform poorly even though the orientation of the scale of the test image differs a little from those of the training ones.This project studies a new technique for texture classification based on rotation and scale (RS) invariants obtained from spectral moments. Rotation invariants derived from moments have been studied by many researchers. However, successful results for pattern recognition using them are limited only to binary images with a finite-sized object. Application of the invariant moments to gray-scale images is difficult because the images have non-zero values on the image boundaries.Instead of the gray-scale moments of the image, we use the moments of its spectral density function (SDF) to obtain rotation invariants because the SDF has advantageous properties. When an image is rotated and scaled, its SDF rotates by the same ang1e and is inversely scaled ; moreover, the spectral powers of most textured images are concentrated around the origin and decay rapidly toward high frequencies. In addition, we scheme to obtain stable rotation moments ; we define as a circle the integral region for moment calculation and adjust its radius to sca1e change by setting a constant rate of the image total power in the circle. Since spectral moments have a simple property with respect to scale, we can define RS invariants by a ratio of rotation invariants.We confirmed the validity of the proposed method in experiments using 16 textures from Brodatz album with very high classification rates. We applied this technique to detection of (1) the rotation ang1e and the scaling factor of textured images, (2) the defect of c1othes and (3) the micro calcifications in mammograms and obtained prosperous results.