One low-tech way to do it, working with shapes of arbitrary complexity, is to draw the shape on a PGraphics, then test the pixel under the mouse: if it is the color of background, you are not over the shape. If that's the color of the shape, all is good. Not easy on the memory with lot of shapes, but quite efficient (not much computations).

The problem is that I am drawing a multi-colored background under the object and the object itself will also be multi-colored. I'm using a lot of images.

EDIT: I looked at ToxicLibs but I am not sure if this is what I should be using. I don't see very much documentation that is accessible to a user of my level.

The shapes in the off-screen canvas should all be drawn with solid colors that are different from each other, as to distinguish between shapes (in more complex situations), so the multicolored real-canvas shape doesn't matter. If they were all drawn in solid colors in the first place, then you wouldn't need the off-screen canvas.

Calsign, I am a little confused what you mean by off-screen and on-screen canvas. Could you give me an example?

I'm referring to a PGraphics object. I would normally give you more information, but I'm a little bit crunched for time. There are more links behind the one provided that should help as well.

That was exactly what i needed in order to do further research. Thank you.

Every pixel has an alpha property. 100% opaque is 255, 100% transparent is 0.
My idea is to make your pictures, be them PImage or  PGraphics, to have alpha = 254 for example.
255 alpha & 254 alpha are practically indistinguishable!
So, if mouse cursor is over a pixel = 254, it means it's above such object! Pretty idea, huh? 

That is a very nifty idea, GoToLoop. Thank you, that will help me a lot. I'm having to learn how to use PImage/PGraphics already between now and Thursday, so having to learn one less thing makes my life a lot easier.

Hello, when I was talking your suggestions, I'm having the issue that when I use float value = alpha(click) I get returned 0 no matter where I click. Is there a reason that this is happening?

Here's my nearly finished code. Ignore the silly comments.

1. 
   //state is the amount of chakras that are put in place.
           int state = 0;
           float theta = 0;
           float x = 0;         //these variables are for my cos/sin math.
           float y = 0;         //they may not have been explicitely needed,
           int click = 0;
     PImage img1;
     PImage img2;
     PImage img3;
     PImage img4;
     PImage img5;
     PImage img6;
     PImage img7;
     PImage img8;
     PImage img9;
     PImage img10;
     PImage img11;
    
   void setup() {
     size(1024,768);
     noStroke();
   img1= loadImage("1.png");
     img2= loadImage("2.png");
     img3= loadImage("3.png");
     img4= loadImage("4.png");
     img5= loadImage("5.png");
     img6= loadImage("6.png");
     img7= loadImage("7.png");
     img8= loadImage("background.png");
     img9= loadImage("sillhoute.png");
     img10= loadImage("glow.png");
   }
   void draw(){
   image(img8, 0, -5100);
   translate(width/2, height/2);
   image(img9, -width/4.5, -height/5);
   rotate(theta);
     draw7();
   }
   void mousePressed(){
     float value = alpha(click);
     println(click);
   }
   void ch1(){
     fill(0, 0, 0, 254);
     ellipse(0,0,50,50);
     image(img1, -50, -50);
   }
   void ch2(){
      fill(0, 0, 0, 253);
        ellipse(0,0,50,50);
     image(img2, -50, -50);
   }
   void ch3(){
      fill(0, 0, 0, 252);
        ellipse(0,0,50,50);
     image(img3, -50, -50);
   }
   void ch4(){
      fill(0, 0, 0, 251);
        ellipse(0,0,50,50);
     image(img4, -50, -50);
   }
   void ch5(){
      fill(0, 0, 0, 250);
        ellipse(0,0,50,50);
     image(img5, -50, -50);
   }
   void ch6(){
      fill(0, 0, 0, 249);
        ellipse(0,0,50,50);
     image(img6, -50, -50);
   }
   void ch7(){
        fill(0, 0, 0, 248);
        ellipse(0,0,50,50);
     image(img7, -50, -50);
   }
   /*okay, okay; you got me. I have a thing for rotating circles.
   I love the planetary movements. I love how yin and yang moved.
   As a kid, I'd make whirlpools in the tub for fun. It's, strangely,
   a part of who I am!*/
   void draw1(){
             theta += TWO_PI/2000;
            ellipseMode(RADIUS);
             pushMatrix();
             translate(x, y+300);
             ellipse(0, 0, 25, 25);
             ch7();
             popMatrix();        
   }
   void draw2(){
             theta += TWO_PI/2000;
            ellipseMode(RADIUS);
             pushMatrix();
             translate(x, y+300);
             ellipse(0, 0, 25, 25);
              ch7();
             popMatrix();        
            
             pushMatrix();
             translate(x, y-300);
             ellipse(0, 0, 25, 25);
              ch6();
              popMatrix();
   }
   void draw3(){
             theta += TWO_PI/2000;
            ellipseMode(RADIUS);
             pushMatrix();
             translate(x, y+300);
             ch7();
             popMatrix();        
            
             pushMatrix();
             translate(cos(radians(30))*-300, (sin(radians(30))*-300));
             ch5();
             popMatrix();
            
              pushMatrix();
             translate(cos(radians(30))*300, (sin(radians(30))*-300));
             ch6();
             popMatrix();
   }
   
   
   void draw4(){
             theta += TWO_PI/2000;
            ellipseMode(RADIUS);
             pushMatrix();
             translate(sin(radians(45))*-300, (cos(radians(45))*300)); //in order for this to rotate I use trigonometry to tell it where around the shape its supposed to rotate.
             ellipse(0, 0, 25, 25);
             ch4();
             popMatrix();        
            
             pushMatrix();
             translate(cos(radians(45))*-300, (sin(radians(45))*-300));
             ellipse(0, 0, 25, 25);
             ch6();
             popMatrix();
            
              pushMatrix();
             translate(sin(radians(45))*300, (cos(radians(45))*-300));
             ellipse(0, 0, 25, 25);
             ch7();
             popMatrix();
           
               pushMatrix();
             translate(cos(radians(45))*300, (sin(radians(45))*300));
             ellipse(0, 0, 25, 25);
             ch5();
             popMatrix();
   }
   void draw5(){
             theta += TWO_PI/2000;
            ellipseMode(RADIUS);
             pushMatrix(); //this matrix is separate from the main matrix.
             translate(x, y+300);//x axis
             ellipse(0, 0, 25, 25);           
             popMatrix(); //back to main matrix.
           
             pushMatrix();
             translate(sin(radians(72))*-300, (cos(radians(72))*300)); //in order for this to rotate I use trigonometry to tell it where around the shape its supposed to rotate.
             ellipse(0, 0, 25, 25);
             ch6();
             popMatrix();
            
             pushMatrix();
             translate(sin(radians(72))*-300, (cos(radians(72))*300)); //in order for this to rotate I use trigonometry to tell it where around the shape its supposed to rotate.
             ellipse(0, 0, 25, 25);
             ch3();
             popMatrix();        
            
             pushMatrix();
             translate(cos(radians(54))*-300, (sin(radians(54))*-300));
             ellipse(0, 0, 25, 25);
             ch5();
             popMatrix();
            
              pushMatrix();
             translate(sin(radians(36))*300, (cos(radians(36))*-300));
             ellipse(0, 0, 25, 25);
             ch7();
             popMatrix();
           
               pushMatrix();
             translate(cos(radians(18))*300, (sin(radians(18))*300));
             ellipse(0, 0, 25, 25);
             ch4();
             popMatrix();
                   }
   void draw6(){
             theta += TWO_PI/2000;
             ellipseMode(RADIUS);
             pushMatrix();
             translate(x, y+300);//x axis
             ellipse(0, 0, 25, 25);           
             ch4();
             popMatrix();
            
             pushMatrix();
             translate(cos(radians(30))*300, (sin(radians(30))*300));
             ellipse(0, 0, 25, 25);
             ch6();       
             popMatrix();        
            
             pushMatrix();
             translate(cos(radians(30))*300, (sin(radians(30))*-300));
             ellipse(0, 0, 25, 25);
             ch5();
             popMatrix();
            
             pushMatrix();
             translate(x, y-300);
             ellipse(0, 0, 25, 25);
             ch3();
             popMatrix();
           
             pushMatrix();
             translate(cos(radians(30))*-300, (sin(radians(30))*-300));
             ellipse(0, 0, 25, 25);
            ch7();
             popMatrix();
            
             pushMatrix();
             translate(cos(radians(30))*-300, (sin(radians(30))*300));
             ellipse(0, 0, 25, 25);
             ch2();
             popMatrix();
                   }
                  
   void draw7(){
             theta += TWO_PI/2000;
             ellipseMode(RADIUS);
             pushMatrix();
             translate(x, y+300);
             ch1();
             popMatrix();
            
             pushMatrix();
             translate(sin(radians(51.428))*300, (cos(radians(51.428))*300));
             ch2();
             popMatrix();        
            
             pushMatrix();
             translate(cos(radians(12.806))*300, (sin(radians(12.806))*-300));
             ch3();
             popMatrix();
            
             pushMatrix();
             translate(sin(radians(25.714))*300, (cos(radians(25.712))*-300));
             ch4();
             popMatrix();
           
             pushMatrix();
             translate(sin(radians(25.714))*-300, (cos(radians(25.714))*-300));
             ch5();
             popMatrix();
            
             pushMatrix();
             translate(cos(radians(12.806))*-300, (sin(radians(12.806))*-300));
             ch6();
             popMatrix();
            
             pushMatrix();
             translate(sin(radians(51.428))*-300, (cos(radians(51.428))*300));
             ch7();
             popMatrix();
                   }
   
   

I'm sorry, it's a late night. I've figured it out. I just need to rest soon, this is due tomorrow.....

So do you need more help or not?

No, I am sorry, I do not. I'm just beginning to panic a little because it's late at night and this is due tomorrow.

Dead week, you know?

Most of Processing's functions ignore the alpha value!  
So, to deal w/ them, you need to directly access an array representation o  PImage/ PGraphics -> pixels[]
If you had asked earlier, we coulda tried to help ya out wit 'it before your dead-end!

But anyways, I don't get where your variable click gets any information from a pixel on screen!  

click does not get any information. I was half asleep and did not get anything done. So I went ahead and went to bed. At least I have until 2PM this afternoon to finish it. I'll use the pixel[] function, I read about it last night.

Thanks for your concern.

Just a detail -> pixel[] is not a function, but an int[], an Array of integers! 
And it's a field of class PImage!
Its content represents a full 32-bit of ARGB color pixel -> AARRGGBB.

how do i detect what is at mouseX, mouseY using pixels[] so that i can then use println and see what value is there? I can't seem to find any similar documentation.

An example on how to make all pixels of a PImage to change from Alpha 255 (0xff) into Alpha 254 (0xfe).
Or any other value, just change the code! 

PImage img = get();  // use canvas as PImage for this example

img.loadPixels();    // dumps the contents of img into pixels[]

println( hex(img.pixels[0]) ); // show that alpha = 255 (0xff)

for (int i = img.pixels.length; i != 0;) {
  color pix = img.pixels[--i];  // decreases iterator & gets pixel color
  pix &= 0xffffff;      // preserves RGB but removes Alpha
  pix |= 254 << 030;    // adds Alpha 254 (0xfe000000) to pixel
  img.pixels[i] = pix;  // store modified pixel back into pixels[]
}

img.updatePixels();  // reloads pixels[] back into PImage

println( hex(img.pixels[0]) ); // proof that alpha = 254 (0xfe) now

exit();

You're a lifesaver, GoToLoop. Thank you.

Now I just have to detect what "alpha" value is below my mouse. I assume this is by using the "alpha" function.

So far no luck getting alpha to detect what alpha is underneath my cursor.

I can't seem to be able to tell it to find the alpha of an x, y position and the documentation uses a variable for a color. It's very confusing to me.

EDIT: Using the code

1. void mouseMoved()
       {
           println("Alpha "+alpha(get().pixels[mouseX + mouseY * width]));
       }

I'm so sorry, but I've found out now that it's technically (or apparently) impossible
to recover an alpha attribute from a pixel after it was drawn to a PGraphics surface.
No matter whether it's from main canvas or a separate off-screen buffer!

I'm still learning Processing/Java, and haven't realized how Processing manipulates colors w/ alpha attribute!
Even though you've missed your (school?) schedule, I'll explain the technical reason why:

Imagine you draw a red ellipse w/ fill(#FF0000). If you try to get a pixel within its area,
you'd expect to find a pixel color = #FF0000, right? Well, most of the time you'll get exactly that!

But now, draw another shape somewhere else, but this time w/ fill(#FF0000, 200),
that is, a red color w/ alpha = 200.
However, if you try to get a pixel color from there now, you won't get a #FF0000 or a 0xC8FF0000.
Instead, another pixel color, which corresponds visually to 0xC8FF0000, but has its alpha attribute reset to 255!

Interestingly, the bottom surface layer retains all of its color code, including its alpha attribute!
Only the other pixels drawn above it have their alpha reset to 0xFF!
And even their RGB attributes are altered if they weren't 100% opaque before!

As you can conclude as well, any alteration of the alpha attribute is lost, since it gets back to 0xFF once drawn!
Adieu any hope to use a slightly altered alpha to serve as a pixel detection mark for your shapes!

Nevertheless, I've still got another plan to use slightly altered RGB attributes as a masking mark.
Gonna make one as soon as I have more time!

Here's a post in which I've made a technique to crop an image w/ transparency outta main canvas:
http://forum.processing.org/topic/wanna-change-direction-with-keypressed

That's where I've drawn hope of this whole mess alpha mark idea! 

See my debug program below to test this Processing's alpha color behavior for yourself:

final static short myAlpha = 251;
final static color bg = 0100;
PGraphics pg;

void setup() {
  size(300, 200);
  noLoop();

  pg = createGraphics(width, height, P2D);

  pg.beginDraw();
  pg.smooth();
  pg.rectMode(CENTER);
  pg.endDraw();
}

void draw() {
  pg.background(bg, myAlpha); // clears PGraphics w/ transparency color

  pg.fill(#00FF00);           // no alpha, intact color code
  pg.rect(width >> 1, height >> 1, width >> 2, height >> 2);

  pg.fill(#FFFF00, myAlpha);  // transparency, color will be modified
  pg.ellipse(width >> 1, height >> 2, width >> 2, height >> 1);

  pg.fill(#00FFFF, myAlpha);  // transparency, color will be modified
  pg.ellipse(width >> 2, height >> 1, width >> 1, height >> 2);

  background(pg);             // clears canvas using PGraphics image
}

void mouseMoved() {
  print( "mx: " + mouseX + "\tmy: " + mouseY );

  //println( "\t" + checkAlphaMarkOnMouseBGPixel(get(), myAlpha) );
  println( "\t" + checkAlphaMarkOnMouseBGPixel(g, myAlpha) );
  //println( "\t" + checkAlphaMarkOnMouseBGPixel(pg, myAlpha) );
}

boolean checkAlphaMarkOnMouseBGPixel(PImage img, int alphaValue) {
  loadPixels();  // dumps contents of PImage into pixels[]
  color pix = img.pixels[ width*mouseY + mouseX ];  // gets pixel's color
  print( "\n" + (width*mouseY + mouseX) + "\t");

  // true if mouse is over a pixel w/ matching alpha:
  print( hex(pix) );
  return pix >>> 030 == alphaValue; // returns true if alpha code is found
}