Deep receptive field networks
The invention provides a method for recognition of information in digital image data, said method comprising a learning phase on a data set of example digital images having known information, and characteristics of categories are computed automatically from each example digital image and compared to its known category, said method comprises training a convolutional neural network comprising network parameters using said data set, in which via deep learning each layer of said convolutional neural network is represented by a linear decomposition of all filters as learned in each layer into basis functions.
1. A method performed by a computing system for recognition of information in digital image data, the method comprising:
a learning phase on a data set of example digital images having known information, wherein the learning phase comprises:
computing characteristics of categories automatically from each example digital image;
comparing computed characteristics to their known category;
training a convolutional neural network comprising network parameters using the data set of example digital images having known information,
wherein via deep learning each layer of the convolutional neural network is represented by a linear decomposition into basis functions of all filters as learned in each layer; and
using a receptive field network (RFnet) including a convolution kernel F(x; y) of the form F(x; y)=G s (x,y)f(x,y),
where G s is a Gaussian function that serves as an aperture defining a local neighborhood of pixels with coordinates (x,y) in the sample digital image, and f(x,y) is a function that can be expressed as a linear combination of basis functions;
wherein a series of basis functions B m (x,y) and to-be-learned parameters α m (where m is an index) include the following terms:
B 0 =G s ; B 1 =G s x; B 2 =G s y; α 0 =f (0); α 1 =f x (0); α 2 =f y (0)
where x and y are pixel coordinates in the sample digital image, where f(0) represents function f(x,y) at local coordinates (0,0), and where f x (0) and f y (0) represent derivatives of function f(x,y) at local coordinates (0,0) with subscript indicating differentiation with respect to x or y, respectively, measured by the Gaussian linear filter of the same derivative order.
2. The method of claim 1 , wherein the network parameters of the convolutional layers are parameters expressing weights of each member in a set of basis functions selected from a Taylor expansion and a Hermite expansion, for providing approximators for a local image structure by adapting said network parameters during training.
3. The method of claim 1 , further comprising preprogramming the basis functions in the network as Gaussian-shaped filters to decompose the filters.
4. The method of claim 1 , wherein the basis functions are selected from a set of monomial basis functions:
1
,
x
,
y
,
1
2
!
x
2
,
xy
,
1
2
!
y
2
,
1
3
!
x
3
,
1
2
!
x
2
y
,
1
2
!
xy
2
,
1
3
!
y
3
,
…
for learning function values, where x and y are pixel coordinates in the sample digital image.
5. A method for recognition of categorical information from digital image data, the method comprising:
providing a trained neural network, trained in a computing system using a learning phase on a data set of example digital images having known information, wherein the learning phase comprises:
computing characteristics of categories automatically from each example digital image;
comparing computed characteristics to their known category;
training a convolutional neural network comprising network parameters using the data set of example digital images having known information,
wherein via deep learning each layer of the convolutional neural network is represented by a linear decomposition into basis functions of all filters as learned in each layer; and
using a receptive field network (RFnet) including a convolution kernel F(x; y) of the form F(x; y)=G s (x,y)f(x,y),
where G s is a Gaussian function that serves as an aperture defining a local neighborhood of pixels with coordinates (x,y) in the sample digital image, and f(x,y) is a function that can be expressed as a linear combination of basis functions;
wherein a series of basis functions B m (x,y) and to-be-learned parameters α m (where m is an index) include the following terms:
B 0 =G s ; B 1 =G s x; B 2 =G s y; α 0 =f (0); α 1 =f x (0); α 2 =f y (0)
where x and y are pixel coordinates in the sample digital image, where f(0) represents function f(x,y) at local coordinates (0,0), and where f x (0) and f y (0) represent derivatives of function f(x,y) at local coordinates (0,0) with subscript indicating differentiation with respect to x or y, respectively, measured by the Gaussian linear filter of the same derivative order.